Sunday, June 4, 2023

Logic and Dialectic, by Mário Ferreira dos Santos

Modern philosophy has repositioned the logical problem, influenced by Kant’s criticism and Hegel’s dialectical contributions. Despite being overlooked and subject to derogatory criticism, Dialectics has made significant contributions to logical categories and science. This book explores Formal Logic, General Dialectics, and Decadialectics, adhering to certain norms. Formal Logic is briefly covered as its achievements are considered definitive, while new possibilities within the field, including phenomenological analysis, will be explored in “Philosophical Themes and Problems.” Dialectics, a growing discipline, requires answers to emerging questions. General Dialectics encompasses various important themes and necessitates investigations in other fields, acknowledging the influence of sensory, somatic, and affective aspects. Hegelian thought and dialectical perspective are relevant to philosophy, leading to the construction of a comprehensive worldview. This volume focuses on general aspects and introduces Decadialectics, aiming to coordinate existing dialectical structures. Other works will delve into specific dialectical topics. The methodology presented in this book enables comprehensive analyses while recognizing the partial role of formal logic. Dialectics is a logic of existence and becoming, encompassing oppositions without excluding formal logic.

Preface

One of the characteristics of modern philosophy is, undoubtedly, the new placement of the logical problem, especially after Kant’s criticism and the dialectical contributions of Hegel.

Despite continuing to be absent from official curricula, relegated to a secondary level, and suffering from the derogatory criticism of those who are unaware of it or who have a caricatured view of it, it is not possible, in the face of the impact of the themes on the value of logical categories, to continue ignoring the immense contribution of Dialectics, especially since it has penetrated the field of science.

In this book, where we study Formal Logic, General Dialectics, and our Decadialectics, we adhere to certain norms that we wish to draw attention to from the outset.

First and foremost, we do not extensively delve into Formal Logic because, in this field, what has already been accomplished is definitive. There is little to add here. That is the reason why we only address the most important aspects in a general manner.

It is true that logic now offers a new problem and theme, in which the studies of logistics and the contributions of many philosophical currents, such as phenomenological analysis, with Husserl at the forefront, offer new possibilities to invest in unexplored veins and make some unexpected revelations, even within the formal field. We will address these topics in the volumes entitled “Philosophical Themes and Problems” from the decadialectical perspective.

As for dialectics, we approach the general aspect based on the most well-known contributions. It is true that the dialectical theme and problem grow each day because, as a new and developing discipline, it faces numerous aspects that require answers to the constantly arising questions.

Throughout this book, the reader will notice that General Dialectics, which broadly encompasses such an important theme, requires the contribution of new investigations in other fields. These investigations stem from the dialectics of intellectuality in its operative polarizations of the rational and those of purely intellectual intuition. Since our process of reasoning cannot disregard the influence of schemes of sensibility, sensory-motor schemes, and also the somatic aspect that greatly influence our perspectives, and which modern psychology is highlighting, we must also acknowledge the functional inseparability of the affective part of our spirit. Its roots also extend into this somatic aspect, which, in turn, reveals the functioning of all sympathetic and antipathetic schematic constructions, the genesis of symbolism, which cannot be disregarded.

Furthermore, all those who have a keen interest in dialectical study sense the relevance of Hegelian thought, from which philosophy, in its general lines, can no longer distance itself. The dialectical perspective, being encompassing and inclusive, containing opposites, differences, and distinctions within itself, invades the field of philosophy and necessitates the construction of a general view of the world, a true world-view, which implies the need for a revision of all philosophical achievements. Thus, dialectics becomes philosophy, and philosophy, through its influence, becomes dialectics.

Now, such themes demand special works that coordinate what has already been constructed, albeit dispersedly, within a dialectical structure. In this volume, we focus on the general aspects, including a methodology that makes it practical, under the name of Decadialectics, a construction we have carried out with the intention of utilizing everything useful in this field for a more skillful handling by scholars of the subject.

However, topics related to noetic dialectics, as well as pathic dialectics, symbolic dialectics, and global and synthetic tensional dialectics, will be the subject of other works. Nevertheless, as the reader will see, the methodology presented in this volume is already sufficient for the undertaking of comprehensive analyses without disregarding the contribution of logic, which is always employed but with recognition of its role that, although important, is partial and consequently deficient in the appreciation of facts. Dialectics aims to be what it truly is: a logic of existence, a logic of becoming, and thus a logic that deals with dialectically considered oppositions without excluding formal logic.

MÁRIO FERREIRA DOS SANTOS

Part 1 – “FORMAL LOGIC”

Theme I

Article 1 – Logic

When man reached the rational phase, his thoughts began to process with a certain order, allowing him to draw conclusions, to direct them, transforming them into a powerful tool. From these observations, in a more advanced phase, he finally concluded that the regularity in his thoughts showed him that there was an order governing them. This realization enabled him to construct a science of thoughts by discovering relationships, rules, and constants.

This set of rules is called logic, which is the science of thoughts as thoughts, independent of other aspects and elements related to them, which form the objects of other sciences.

The study of logic is of indispensable necessity because it allows for the better application of thought, avoiding common errors. The reader is reading and contemplating these words and could mentally utter the phrase: “I am reading this book.” If we analyze the elements that compose or condition this sentence, we will observe, firstly, the reader who is thinking about this book; secondly, the act of thinking about the uttered phrase, which occurs in the reader’s mind; and thirdly, the thought itself, the simple assertion that “I am reading this book.”

The reader’s perception also involves the verbal statement of the phrase and, finally, the object to which the thought refers, as every thought is a thought of something. Let us call the reader the subject and the referred object the object, and we find ourselves facing the duality that is essential in the field of logic.

Thus: subject — perception or thought — object

Objects are classified in various ways by logicians:

We have sensible or real objects, which are those provided by sensory experience, whether through external perception or internal perception. Those of external perception are called physical objects, and those of internal perception are called psychic objects.

Physical objects are corporeal facts that occur in time and space.

Psychic objects are facts of consciousness. Desires, representations exist only in time, not in space, because they do not occupy a place, although they are related to a conscious being that possesses a body, such as man, as such, who occupies a place in space, as revealed by the concept of body.

Ideal objects are those that do not have a place in space or time, such as numbers, relations, concepts, as the concept of a book does not have a dimension or age. Thus, it cannot be said that the concept of a book has a meter or less than a meter, or a year or two years of age. This way of understanding ideal objects is the most common in philosophy.

We can conceptualize the idea of a book, but this concept is always conditioned by the books we know or imagine. There are reminiscences of our experiences in this concept that still offer certain limitations because if we cannot have the idea of a horse or the idea of a book determined in time and space, these ideas cannot surpass certain real conditions that we know through the exemplars that represent these objects individually. Thus, the concept of a horse cannot include something that would be a contradiction, like a horse that is not quadrupedal, etc.

Logicians also classify other species of objects, such as metaphysical objects and values. The former are known through reasoning or intellectual or pathic intuition, as will be seen in “Ontology and Cosmology.” As for values, they are “qualities” of a special order, the study of which belongs to Axiology (the Science of values), and we study them in “Concrete Philosophy of Values.”

Article 2 – Thinking and Thought

The subject of thinking is the one who thinks, a real and temporal subject. It is the human mind that carries out the act of thinking (thinking, measuring, calculating). The act of thinking is always new as an act. So I think about the book in front of me, and every time I engage in this thinking, I perform a new act. I think about the book today, and I will think about it tomorrow as well. The act of thinking is different, but the thought book remains the same. This happens because what we conceptualize, we extract, abstract from things.

This concept remains virtualized in our mind because the concept of a book is not a real object but rather what we generalize from the book, an abstract schema. We call any object that, in actuality, that is, as an object, happens here and now, corresponding to that ideal book that we virtualize, a book. The concept remains in my mind as something virtual, which is not yet existentially in act.

The virtual being (which philosophers usually call being-in-potential, that is, a being that is not yet but can potentially become actual) is not being in time or space, as it does not occupy a place or change with time.

The book, as an act (this book, that book), “occupies a place in time and space.” Therefore, when we think about the concept of a book three times, we perform three mental operations of thinking, in other words, we think three times, but the concept of a book remains the same in all of them because we separate the concept from time and space, while in thinking, we are time and space, and thought is something we repeat because it is not time or space.

Thus, when we think about the triangle three times, we perform the act of thinking three times; however, we do not have three triangles but only one because the concept of a triangle is something we separate from time and space. The triangle that is here can be larger or smaller in actuality, even though, as a concept, it does not have dimensions or specific angle measurements other than the sum of two right angles, which is mathematically necessary for the conception of a triangle.

However, we all feel it when we say, “I had the same thought as you,” that is, when someone else’s thought coincides with ours. Thus, we see that we perceive the reality of one of the most important points in logic, which is the distinction between thinking and thought. The former is the object of psychology, and the latter, of logic.

Every thought corresponds to an object or objective situation to which it tends, directs itself, which is why thought is said to be intentional.

Intentional, because it has intention (from intendere). This expression comes from scholasticism but is currently used again in the sense of the application of the mind to an object of knowledge, the act that tends toward the object and also as the content, the object itself, to which the mind applies itself. Every thought is an application to an object; therefore, it is intentional because every thought is a thought of something.

Logic studies thoughts as thoughts, and when it empties them of their contents and studies them as generalities, observing them as forms, it is called formal logic.

Observation shows us that every science has its own logic. General or formal logic seeks to synthesize them into a universal, general basis. Let’s consider enlightening examples. If we consider the concept of Man, we will find that in anthropology, physiology, and anatomy, it has a content, particularities different from Man when used in philosophy or sociology. Each science gives concepts characteristics that are peculiar to it. Formal logic studies thoughts, concepts, etc., as forms (as “forms,” we could say, that is, emptied of their contents) and studies them independently of their peculiarities. That’s why it is called formal logic.

Logic is the science of thoughts, and formal logic is the science of thoughts as forms, in other words, just as thoughts, emptied of their factual content.

Both logicians and philosophers discuss whether logic is a theoretical science or a normative science or just an art or technique. Naturally, we won’t reproduce those lengthy discussions here, but we could say that each side has a valid point because logic can be regarded, employed, and studied from any of these aspects.

It is a theoretical science when it speculates about the elements that form its framework; it is normative when it offers rules by which we can assess whether a thought is right or wrong. Thus, it addresses all these aspects, which does not prevent those who are eager to delve into theoretical logic alone from doing so, while others study only its normative application. The great surge currently taking place in logistics, mathematical logic, and various dialectical formulations demonstrates the great possibilities of making it eminently practical and useful without denying the efforts of those who aim to study it solely as a theoretical science.

Article 3 – Logic and Psychology

It is very common to find, among logicians, including philosophers of the past and present centuries, the concern to reduce logic to psychology, that is, to consider thoughts as mere psychic data. This tendency is called psychologism, just as the tendency to reduce psychic phenomena to biology is called biologism, and the tendency to reduce the biological entirely to matter is called materialism. Logical psychologism defends the opinion that logic is based on psychology or is dependent on it.

Logicians who do not accept this opinion argue as follows: logical objects are not empirical objects but ideal ones, as we have already seen.

Secondly, the laws of logic are universal laws constructed a priori, and not inductive generalizations, that is, constructed from the observation of particular facts to reach the general. Thus, inductive laws are generalizations that have a high degree of probability but can never be asserted as absolutely certain, while the laws of logic offer evidence that nothing can destroy. Inductive laws are formulated a posteriori, that is, after the observation of particular facts to reach a generalization. They are therefore based on temporality since they are laws of an occurrence in time, while the laws of logic, like those of mathematics, do not depend on time.

As seen, the reasons are considerable, but on the other hand, we must also consider those offered by those who defend the reduction of logic to psychology. For example, they claim that logical data are perfectly explainable by psychology, and if they seem to occur outside of time, it is only the result of an abstraction that leads to placing thoughts outside of time. Currently, this is a pronounced tendency among modern logicians.

History of Logic – It was the Greeks who made logic an autonomous science, and among them, Aristotle, who studied it in his Organon and presented important investigations. However, Aristotle never considered logic merely formal, as a study of thoughts as thoughts, but rather as a kind of methodological introduction to philosophy.

In the Middle Ages, Aristotle’s work was continued, although sporadic voices arose against such an orientation, advocating for a more practical and experimental approach. Only in the so-called Modern Age, with Galileo (1564-1642) and Bacon (1561-1626), did logic employ consistent methods in combining experience and mathematics, as Leonardo da Vinci had already proposed. Bacon considered logic as a doctrine of knowledge through experience and facts to reach natural laws, strengthening the inductive method, which he studied extensively. John Stuart Mill (1806-1873) continued Bacon’s work and added some new rules to those presented by him. These two aspects of logic, the theoretical and the practical, have been debated since then until the present day.

Article 4 – Thought and Thinking – Logical Principles

Regarding thought, we still wish to make some considerations that we deem of utmost importance for the future understanding of logic and the disputes between psychologism and logical formalism. Philosophically, thought is considered in two senses: in an extensive sense and in a restricted sense.

In the first sense (extensive), thought encompasses all phenomena of the mind. Thus, thought is everything that possesses a character of rationality and intelligibility, even without actual consciousness. Some assert that nature, and even being as a whole, is a thought. Let us provide an example: in every fact, in universal occurrences, in objects, in psychic acts, in anything, all possible thoughts are already present. In the face of any event, we can grasp different or similar thoughts, as we have seen before. Thought, in this way, is not a product of our mind. Our mind merely apprehends, captures thought. Therefore, everything is thought, everything is, in essence, logic. Hence the tendency called panlogism (from the Greek word “pan,” meaning everything). This is one of the arguments that underlie theoretical logic against psychologism. Thus, our mind only plays the role of a receptor, apprehender, capturer, not producing or elaborating thought, but merely catching it. Thought, in this manner, permeates all of reality.

In the restricted sense, for some, thoughts are all cognitive phenomena (in opposition to feelings and volitions, which we will study in “Psychology”). Thus, thought is synonymous with intelligence, in the sense of the set of all functions that have knowledge as their object, in the sense of sensation, association, memory, imagination, understanding, reason, consciousness.

More narrowly, thought is understood only as synonymous with intelligence, but only concerning understanding and reason, as they allow for the comprehension of what constitutes the subject matter of knowledge, without being confused with perception, memory, and imagination.

Thus, thought, in the extensive sense, is distinct from the psychic act (act of thinking), as the latter occurs anew in each person, while the former can be grasped by different people without ceasing to be the same thought.

However, we could add that without psychological functions, the operation of capturing thought would be impossible. This argument will be important, especially when we study its virtual aspect, that is, thought not as an act, but as the virtualization of experience, after all factual aspects have been removed, when it becomes pure abstraction.

This operation of abstraction is possible and repeatable in everyone, although the product is the same.1

In every act of thinking, there is the apprehension of a thought; thinking thinks a thought.

In the act of thinking, there is a unity between thinking and thought, without reduction, without one being confused with the other, as logicians emphasize.

Thinking is a temporal, empirical, and psychic act, while thought is timeless.

The laws of thinking are studied in Psychology, while those of thought are studied in Logic. It is important to highlight this distinction between thinking and thought because, in dialectics, we will have the opportunity to analyze this aspect of our understanding. Thus, the functioning of the act of thinking falls under the study and analysis of Psychology.

As for thought, Logic, which is its science, studies and establishes its laws. However, Psychology is inseparable from Logic because, in the face of thinking thoughts, it studies the order and legality (the character of being governed by laws) that govern them and establishes their connections.

In Philosophy, there is a discipline, the science of “being as being,” which is Ontology. In this traditional sense, Ontology is the science that deals with being as being, that is, the being that constitutes everything that exists, the being that determines all beings. There are other ways to conceive them that it is not appropriate to discuss at this time. In this discipline, the “ontological principles” are studied, which apply to all objects, to which all others are subject, including logical objects. They are as follows:

  1. Every object is identical to itself — This is the statement of the so-called ontological principle of identity.

This fundamental principle of classical Ontology is also true for Formal Logic. For now, we only need to present it as a true axiomatic foundation of Ontology and consequently of Formal Logic. Thus, it can be exemplified as follows: this book is this book; this table is this table.

For traditional Ontology and Formal Logic, this book, formally, can only be itself; it is identical to itself. From this fundamental principle, other consequences follow, which are generally given as ontological and therefore also logical principles:

  1. No object can be both itself and not itself.

Ontological principle of non-contradiction. It is stated by saying that A cannot be both A and not-A under the same aspect.

  1. Every object must be A or not A.

That is: This object is a book or it is not a book.

Ontological principle of the excluded middle, as it excludes an intermediary between being and non-being.

The ontological principle of identity becomes in logic the “logical principle of identity”. It is true when we affirm that this book is identical to this book, that is, A is A.

The applications of this principle in Logic require a more detailed explanation and are studied in the part that deals with judgment, with practical applications and their systematization.

The “logical principle of non-contradiction”:

This principle follows from the first one. If we affirm, “what is, is; what is not, is not”, or in other words, “this book is a book”, and at the same time “this book is not a book”, one contradicts the other because in the first statement, we affirm that the book was a book and then the opposite, thereby denying the truth of the first principle.

And since we accept that the opposite of the true is necessarily false, we cannot simultaneously assert that something “is and is not”. The statement “the opposite of the true is false” is the enunciation of this second principle, also presented by the formula: “No object can be both itself and not itself”.

The “principle of the excluded middle”.

Now, if by the principle of non-contradiction, according to formal logic, we conclude that two contradictory statements cannot both be true, by the principle of the excluded middle, we conclude that if one is true, the other is necessarily false, although this principle does not decide which one is true and which one is false.

Thus, if we say, “Every man is mortal” and “Some man is not mortal”, one is true and the other false; a third position is excluded, that is, it is not possible to admit that a man is mortal and not mortal when he is mortal.

Therefore, it is called the principle of the excluded middle because it excludes a third positivity among those.

This same principle leads us to understand that when two statements contradict each other, they cannot both be false.

If we recognize the falsehood of one, we can affirm that the other is true, and vice versa. If one of the judgments is true, the other is necessarily false; a third position is excluded.

Principle of sufficient reason.

This principle is also considered one of the logical principles. It could be stated as follows: a statement is true or false; if it claims to be true, it needs a reason that supports it. This reason is called “sufficient” when it is enough to provide complete support.

It is a sufficient reason when nothing else is needed for the statement to be true.

Another principle also considered among the logical principles is the “Principle of the syllogism”, which can be stated as follows:

“If a implies b and if b implies c, a implies c”.

Implication (entailment), in the formal logical sense, is a relationship that asserts that one statement necessarily results from another.

Thus, the “idea of a mammal implies the idea of a vertebrate”, “the law of gravitation implies the law of the fall of bodies”.

Theme II

Article 1 – The Concept

For Formal Logic, the concept is an ideal, timeless object of thought: in short, it is the object of Logic. The concept, as a psychological operation, both in its genesis and in its action, belongs to the study of Psychology.

It is worth noting that while the concept in Formal Logic presents itself as a universal structure, isolated from time and space, detached and liberated from individual contingencies, the psychological operation varies from one individual to another, and within the individual, according to the variations they experience throughout life.

This distinction is important and becomes clear when we closely examine the difference between acts and contents in the concept. Acts are functions of consciousness, real, effective, temporal psychic processes. They are distinguished from the contents, which are independent of consciousness, ideal, timeless, and autonomous.

Logic studies these contents, while Psychology focuses on the study of acts. However, since both are correlated, since both condition each other, Psychology cannot do without the contents for greater assurance in its study.

This antinomic dualistic aspect of the concept, which arises in relation to Psychology and Logic, explains why when we pronounce the verbal statement of a concept, for example, book, there is something that occurs in the minds of those who hear it that is the same for everyone: the meaning, the concept. However, many other distinct elements, a series of psychic processes, accompany the effort of understanding that each individual performs. Within the same individual, from the suspicion of the concept’s content to its full comprehension, a process takes place.

The concept is the element on which logic relies. And the fundamental logical structure is judgment, which we will now study.

Judgment, in the broadest sense, is the act of positing the existence of a specific relation between two or more terms. As the scholastics used to say, it is the intellectual act by which we deny or affirm one thing of another, or in which we attribute a predicate to a subject, for example: “The book is green.” I attribute the quality of green to the book. Book is the subject of the judgment, green is the predicate. As for the element “is,” which is the relating element, we call it the “copula.” A judgment can have a multiple subject and a multiple predicate. For example: “This book and those ones are green and big.”

The concept follows a path of constant abstraction to the point where, in the logical-formal sense, it already sheds those characteristic notes of the object whose repetition allowed the mind to construct the common denomination of the concept.

If we take the example of the concept house, we will verify that it no longer reproduces the essential notes of the corresponding object.

For formal logic, the concept house is distinct from the object house. It is not difficult to understand the reason. If we ask a child what a house is, they will immediately have various images of the houses they know or have known. And if they try to define it, they will say, “Well, it’s where people live.” Finally, after showing that people also live in other places that are not houses, the child will say that they are covered places where we have the possibility of inhabiting.

In the end, they will give a delimited content to the concept of a house. But this concept, although referring to an object, because every concept refers to objects, in the cultured development of humanity, it takes on more and more its own formal significance. The concept stands out from the object itself in constant abstraction, to the point that when we speak of a thing, or think of a house, its jactic content is being replaced by an increasingly vague, separate, and abstracted eiaetic content, detached from the images associated with the material content of the concept, to form a logical entity. The need for simplification that the cultured man has in his relations with his fellow human beings, the continued, almost sick and addictive reading, the constant word he hears, the meditation and various thoughts that suggest a life in constant motion, all this would not allow the material content to be linked to each concept. We read pages and pages of books, experiencing the words without having to associate more or less precise images with each one when they represent concepts. Otherwise, we could not keep up with the rapid pace of our existence. This is why the concept becomes a logical entity, increasingly stripped of its material content, and when modern logicians believe they have discovered the true character of the concept, they are only verifying what is characteristic of our degree of culture and civilization, in contrast, however, to other pre-cultured eras, because even for logic, there is a historical conditioning.1

This also leads us to make the distinction between the concept and the image. It is said, for example, that the concept is a attenuated, more indecisive image. Now, the image is always individual and concrete, composed of sensible data. The image I have of a book is of this or that book, retaining the appearance and size of a book.

But the concept is general, and the concept of a book, with which I think about a book of any kind or size, has nothing singular about it. However, since I do not want to memorize just the image of a specific book, in every image that presents itself to my memory, which I “visualize,” I find that other images penetrate it, that it merges with others of similar objects, or is replaced by the image of another object.

So when I want to visualize the concept of a book, I can have the image of this book in mind, but other images penetrate it, or one is replaced by the image of another book.

It is natural that the armchair logician, accustomed to constant work with isolated concepts devoid of any material content, wants to give maximum value to what he calls pure intellection or eidetic intuition.

The same happens with these individual, singular concepts as well. Let’s take, for example, “Napoleon Bonaparte.” Napoleon Bonaparte was unique and will not be repeated as a singularity in history. However, we use him as a concept. But who could deny that we have a certain number of notes about Napoleon Bonaparte that individualize him, that form a kind of blurry image of what we know about him through what we have read, seen? We can use the concept Napoleon Bonaparte as a purely logical entity, stripped of its material content, when we read or when we speak or think. But that only indicates the capacity of our mind for increasing abstraction, abstraction that comes from simple perception, through the memorized image, to the concept with the material content, and from there to the concept of pure intellection and eidetic intuition, which modern logicians talk about so much.

The objective content of a concept is the set of these mental references, these notes of the object. However, the concept does not adhere to all the known notes of an object. There is a selection of notes; we find this selection in every vital phenomenon, which led Bergson to say these words: “… every living being, perhaps even every organ, every tissue of a living body… knows how to gather from the environment in which it exists, from substances or from the most diverse objects, the parts or elements that could satisfy one or another of its needs; it neglects the rest. Therefore, it isolates the character that interests it, goes directly to a common property. In other words, it classifies, and therefore, it abstracts…” (La Pensée et le Mouvant, p. 66).

This selection occurs by neglecting certain notes and by embracing others. The concept, therefore, cuts out from the object what interests it and sticks to that. This portion is what is called the formal object.

We see that the object is always connected to the concept. Some argue against this, citing certain concepts of fiction, such as myths (the centaur) or fictional characters like “Madame Bovary.” However, there is objectivity in these concepts because either they exist and move within the pages of literature or they are creations of the mind, which have objective contours, always extracted from human experience. The individual concept also leads us to form an opinion that we believe deserves examination. The individual concept is not the same as conceptualization, as we explained in Philosophy and Worldview. The long exercise of conceptualization allowed us to conceptualize, subsequently, even the individual. As we have had the opportunity to say, we will call concepts the common denomination we give to a series of similar facts that appear identical to us.

Initially, every concept is a denomination of something general. However, when we speak of concepts like Napoleon Bonaparte, America, the Sun, and others, it is necessary to observe that this work of conceptualization, of abstraction of individual notes, to become a logical entity, only takes shape later in humans, after the abstracting work of concepts has had extensive practice. Regardless of the limited number of logicians, there are a great many human beings who do not easily conceptualize the individual, which proves that a certain mastery in one function is not enough to justify such great leaps. In other words, the logician cannot conclude that there is a concept of the individual. The concept is general. The conceptualization of the individual is based on universal experience or on various notes, some similar and others different, formed from a particular singularity.

Let’s exemplify: America. Despite referring to a continent, which is unique in our world, an individual, therefore, it contains immense possibilities within that simple word: America is also the new continent, the land of great hopes, its history, its indigenous inhabitants, its functions in the historical events of humanity, habitat, and a place where diverse populations from many parts of the world live. America is thus a set of notes that allows for conceptualization. Let’s see another example: “Napoleon Bonaparte”: he is not just the man, the politician; he is the military, the revolutionary, the consul, the emperor, the Napoleon of Arcola, the Napoleon of the Russian campaign, the Napoleon of Saint Helena, etc. In short, a collection of notes that offer different perspectives to those who think about him. As for the concept Napoleon Bonaparte, it is the common denomination for this series of facts connected to an individuality that gives it a common name. This is how the concept Socrates is, and Plato, etc.

In the classification of concepts, we will provide here only the most general ones: specific concept refers to what corresponds to a species; generic concept refers to what corresponds to a genus; general concept (also universal) indicates specific or generic concepts, such as “color,” “animal,” etc.

Concrete and abstract concepts. The former refers to objects that are intuitively representable, such as “house,” “book”; the latter refers to those that are not, such as “passion,” etc.

Collective concepts express a homogeneous and unitary set of objects, such as “crowd,” “mass,” etc.

Content, extension, and comprehension of concepts — Every concept has content, which is given by the fact that it refers to an object, and it consists of the references it exposes. The content of a concept is its comprehension; it is the selected notes of the object.

Extension is the generality, the number of objects encompassed by the concept. The greater the generality, the larger the extension of the concept, and the smaller its comprehension, which is the number of qualities it encompasses. For example, the concept “animal” has a larger extension than “man” because it has greater generality, including all animal beings classified by zoology, including humans. However, the notes we select for this concept are fewer than those for the concept man, which, nevertheless, has a smaller extension but greater comprehension, because when we consider “animal” as a zoological generality, we have already excluded the rational note that belongs to humans. When forming the concept of “animal,” the number of notes is smaller; that is, the number of notes we can assign is smaller.

Thus, by increasing content, extension decreases. For example, “white man” is a concept with smaller extension than “man,” but it has greater comprehension, greater content.

Content can increase or decrease. We could add previously ignored notes or disregard others that were previously accepted, which are virtualized as non-existent.

Extension can be considered in an empirical sense, depending on all the objects falling under the concept, or in a logical sense, leaving aside concrete individuality, empirical individuals that arise or disappear, and focusing only on logical objects.

Singular concepts have no extension, such as Napoleon Bonaparte. It is the content that determines the extension. The more general the concept, the smaller the content and the greater the extension, as we have seen.

Concepts relate to each other. Therefore, there is a subordination of some to others. In this case, the subordinate concept has all the constitutive references of the dominant concept, plus some of its own. The actual content of the dominant concept is smaller than that of the subordinate concept. Polygon is the dominant concept of triangle, but the latter, in addition to the notes of a polygon, has the note of having three sides.

Coordination relation exists between two or several concepts that are in the same order, in the same classification; these are, in particular, in a classification by generality, two species of the same genus.

Dependent concepts are those whose objects have dependence among themselves. Example: father and son; cause and effect. They are also called correlatives.

Disjunctive concepts fall under the same superior concept but do not have any sector of their own extension in common. Coordinated concepts are also disjunctive; for example, species of a genus.

Contradictory concepts: those that negate each other’s content. For example: white and non-white.

Antagonistic concepts: those whose opposition is polar, for example: good and evil.

These are the most common classifications found in Formal Logic.

When a concept lacks meaning, it is said to be meaningless. For example: hat but satisfied.

Absurdity occurs when we think of contradictory notes in a concept. Absurdity can be logical or ontological.

Logical: for example, a round square. The contradiction is evident within the concept itself.

Ontological: when the incompatibility is verified by the object itself. For example, “a centimeter of love.” Although it does not contradict the laws of logic, it contradicts the laws of the object, as love, being an affection, does not have extension.

Functional concepts are those whose performance consists of relating concepts. For example: The book and the table are in the room. And, are, and not are functional concepts because they relate the concepts table and book.

Article 2 – Judgment

The study of judgment, from a psychological point of view, belongs to Psychology, where the operation of judging is examined, as well as the factors that influence it, in addition to its modalities. Here we are only interested in its logical aspect, that is, as an ideal object.

We can take advantage of a classical definition that says: Judgment is the intellectual act by which we deny or affirm one thing of another. When we affirm, the judgment is affirmative; when we deny, negative. For example, “The Earth is round,” that’s the first case; “the Earth does not have its own light,” that’s the second.

Judgment is expressed through words and is also called proposition.

Thus, the internal act by which I affirm that the Earth is round is a judgment; the words I use for that affirmation form the proposition. We can now distinguish the concept of judgment: the concept is of a presentative nature, while judgment is enunciative.

Reasoning is an ordering of judgments, a discursive operation by which it is shown that one or several propositions (called premises) imply another proposition (conclusion), or at least make it plausible. Judgment is not only a connection of concepts, as it is an act of thinking that can be considered true or false. In it, the taking of a position, the assertion (positive or negative), is essential. When I say, “neither this nor that table,” I make connections of concepts, but I do not elaborate a judgment because I do not assert anything.

In every judgment, there is a relation between one thing and another: what is affirmed or denied, and that of which it is affirmed or denied. It is the subject-concept, the object upon which the enunciation, the affirmative or negative assertion, falls. It is called predicate-concept or attribute, which is affirmed or denied, negatively or affirmatively, with regard to that subject-concept. Without this assertion, there is no judgment, because, as we have already seen, judgment is not only a connection of concepts.

A third element enters into the judgment, which is the expression of the relation between the predicate-concept and the subject-concept, which is the copula, which has the function of attributing the predicate to the subject, that is, of making the assertion. The verb to be is commonly used as a copula, for example: Love is a feeling. Love is the subject; feeling is the predicate or attribute; is is the copula.

In propositions where the verb to be is not expressed, it is understood.

According to the objects, judgments can be classified as:

Real or empirical judgments (also called judgments of existence) are those that deal with empirical facts, whose starting point is always a sensory experience. Example: This book is green.

Judgments of ideality or ideals are those whose object and predication are ideals. Examples: “The part is smaller than the whole,” etc. “7 plus 3 equals 10,” “two things equal to a third are equal to each other.”

Metaphysical judgments: those that deal with metaphysical objects.

For example: “the being of man is rationality.”

Pure value judgments: those that state something about values or their relationships: “Moral value is worth more than utilitarian value.”

Determinative judgments are those that state the essence of the subject-concept and answer the question what is this? For example: The lion is an animal.

Attributive judgments answer the question how is that?

For example: This book is red.

Judgments of being are those in which the predicate states the objective category to which the subject-concept belongs, for example: This book is a paper artifact.

Predication can be:

a) Comparative, when the subject-concept is compared with another, for example: France is larger than Belgium;

b) Possessive, when a relationship of ownership is affirmed or denied between the subject-concept and others, for example: This book is mine;

c) Dependence, when it is affirmed that the subject-concept depends in any way on another, for example: “Heavy rains cause rivers to overflow”;

d) Intentional, when the subject-concept receives an intention from another object. For example: The establishment of justice is the purpose of righteous people."

When studying the categories in Philosophy and Worldview, we saw that Kant divided them into four classes: quantity, quality, relation, and modality.

Every judgment can be considered from four points of view, which is important in the study of Logic.

Let’s see: According to quality, judgments are affirmative or negative, as we have already shown.

Regarding quantity, they are universal when the subject-concept contains the main concept in its entirety in plurality. For example: All Brazilians are Americans; particular when the main concept is taken in partial plurality, for example: Some men are Bahian.

The quality and quantity of judgment vary independently and allow for four classes of judgment that are important for the theory of reasoning. They are indicated by these four vowels: A, E, I, O.

  1. Universal affirmative judgments (A): all S are P. Example: All Brazilians are Americans.

  2. Universal negative judgments (E): no S is P. Example: No Brazilian is European.

  3. Particular affirmative judgments (I): some S are P. For example: Some Brazilians are Bahian.

  4. Particular negative judgments (O): some S are not P. For example: Some men are not Brazilian.

Regarding relation, judgments are divided into categorical, hypothetical, and disjunctive.

Categorical when the enunciation is not conditioned; it is independent. For example: “Today is Sunday.”

  1. The categorical judgment is subdivided into problematic, assertoric, and apodictic.

a) Problematic: when the proposition can be true, but the one who employs it does not expressly affirm it. Example:

“The world is the result of chance or an external and necessary cause.”

b) Assertoric: they are true in fact but not necessary. Example: “The moon is a planet.”

c) Apodictic: when the judgment is necessarily true, such as mathematical truths. “The whole is quantitatively greater than its part.”

  1. Hypothetical Judgment. Judgments are hypothetical or conditional when an affirmation or negation is subordinate to some condition or hypothesis. For example: “If the weather is good, I will go to the cinema.”

  2. Disjunctive Judgment. Judgments or propositions are disjunctive when they consist of two relationships, each of which is affirmed only when the other is denied. It is equivalent, in reality, to two hypothetical judgments. For example: “If John is not wise, he is ignorant.” “If John is not ignorant, he is wise.”

These two propositions must be proven separately. Together, they form an alternative.

If A is not C, it is B. If A is not B, it is C.

Regarding modality, judgments are assertoric (it is certain that…), problematic (it is possible that…), or apodictic (it is necessary that…).

Also called impersonal judgments are those that apparently lack a subject-concept. For example: It’s raining.

Relations between judgments. Contradictory judgments are those that, referring to the same situation, one affirms and the other denies. Contradictory judgments are the affirmative universal (A) and the negative particular (O); and the negative universal (E) and the affirmative particular (I), whose contradictory relationship is reciprocal. “Every S is P” is contradictory to “Some S are not P,” and vice versa.

For example: “every Bahian is Brazilian” (A) – “some Bahians are not Brazilian” (O); “no metal is a metalloid” (E) – “some metals are metalloids” (I).

Contrary judgments are those that, both being universal, one affirms what the other denies. Contraries are the affirmative universal (A) and the negative universal (E). Contrariety is reciprocal. Examples: “every Bahian is Brazilian” (A) – “no Bahian is Brazilian” (E).

Subcontrary judgments are those that, both being particular, one affirms what the other denies, and the relationship is also reciprocal. “Some S are P” is subcontrary to “Some S are not P.” Examples: “Some Americans are Brazilian” (I) – “some Americans are not Brazilian” (O).

Subaltern judgments are those that have the same subject and the same attribute but differ in quantity, not quality. The universal is the subalternating to the particular, which in turn is subordinated to the universal. “Every S is P” subordinates to “Some S are P,” and “No S is P” subordinates to “Some S are not P.” Examples: “Every Brazilian is American” (A) – “Some Brazilians are American” (I); “No Brazilian is European” (E) – “Some Brazilians are not European” (O).

Here is the traditional scheme:

Theme III

Article 1 – Definition

We can emphasize that the definition answers the question “what is this?” but offers a response with a sense of determination, of maximum determination. The definition aims to answer that question, not with just any clarifying response, but with the response that determines, that completes, that is an equality, the precise delimitation of the defining, that is, what is to be defined, a sufficient response for us to know what that is about which the question was formulated.

Now that we have studied what a judgment is, we can say that a definition is a judgment, as it states an affirmation about the being of the object, delimits it, says what it is, and at the same time separates it from what it is not.

Philosophers usually classify definitions as nominal, real, formal, and material. These are not the only classifications, as there are others. Let’s analyze them:

The nominal definition is also called verbal, and it consists of explaining the meaning of a word using another or other words with a known meaning. Nominal or verbal definitions are the ones most commonly used in dictionaries. Many consider these verbal definitions as tautologies, that is, repetitions. Although they are often considered tautologies, which they seem to be from a purely formal point of view, there is, however, an experiential layer in the definition that clarifies what is to be defined. Since this aspect already enters the field of Psychology, we will study it there. The definition refers to one, several, or all the notes of the object referred to by the concept, whose content is revealed to us. The real definition is the definition of the thing, a determinative formula that expresses what the thing the word signifies is.

Kant called the former synthetic definitions (nominal and conceptual definitions), and the latter analytic definitions.

Many philosophers distinguish real definitions from conceptual definitions, giving conceptual definitions a preference for the formal object, which is part of the total object. Many consider nominal definitions to be identical to formal ones and real definitions to be identical to material ones. However, the formal definition is properly a conceptual definition.

These divisions are arbitrary, and for that reason, some philosophers offer other ones. Thus, they propose the genetic definition, which defines the object by exposing its formation, its genus. For example, we want to define a circle and we say “a circle is the figure described by a line segment rotating around one of its endpoints.” Although such definitions are widely used in mathematics, like the one that says “a line is the result of a point moving in space,” many philosophers consider them unacceptable. However, as Hamilton, Krug, and Blondel point out, these definitions consider the defining in its progress or becoming, for, as Blondel says, it is the fieri (becoming) that clarifies the esse (being)."

To be rigorous, a definition is constructed with the help of the nearest genus and the specific difference. The former indicates the nearest genus to which the object to be defined belongs (for example, “a pentagon is a polygon”). The latter sets the pentagon apart from all other polygons (for example, “it is a figure with five sides”). The final statement will be: The pentagon is a polygon with five sides. Thus, for example, man is a rational animal. Animal is the nearest genus; rational is the specific difference that distinguishes man from other living beings.

Explanation should not be confused with definition. Explanation states something beyond the definition in order to clarify, showing properties, characteristics.

When we say that man is bipedal, lives in society, makes choices, appreciates values, cares, has an understanding of his possibilities, knows death, creates various ways of living, all of that would be explanatory, clarifying, not a definition.

There are some definitions that are called negative. They are characterized by negating some determination to the defining. For example, when we say, “immortal is that which does not perish.” In reality, the negativity of these definitions is only apparent, as it assumes the positive determination of the corresponding positive concept.

An essential definition is one that is stated by indicating the characteristics without which the defining would cease to be what it is.

An accidental definition sticks to an accidental determination, for example, when we say, “Peter is the person sitting next to the door.”

If we affirm that a definition, to be rigorous, must follow the classical rule, being constructed with the help of the nearest genus and the specific difference, we conclude that the ultimate genus is indefinable because it cannot be referred to another. This happens when we go from genus to genus until we reach the ultimate genus. For example, I can refer this book to being, but being is indefinable since I cannot refer it to the superior genus because it is the superior genus. On the other hand, both what is given to us as individual singularity and what represents the ultimate data of sensibility, such as colors, sounds… are indefinable, as well as space and time, since we do not have a genus that includes time and space.

The ultimate foundation of every definition is the indefinable, as if we define man as a rational animal, we would define animal as a living being, living being as being, and we would ultimately reach an indefinable (being). Thus, it is also evident that demonstrations are based on some axioms, which are indemonstrable.2

Genus is the group in which all individuals, in an indefinite and undetermined number, and endowed with certain common characteristics, are ideally gathered. The supreme genus is the one that contains all others.

Species is the term used when two general terms are contained in each other in extension, and the smaller one is called the species, such as in the case of the genus polygon. Man is a species of the animal genus.

We use some terms here that deserve attention. They are: genus, species, specific difference, accident.

Specific difference is the characteristic by which a species distinguishes itself from other species belonging to the same genus. Thus, rational is a specific difference of the species man, which distinguishes it from other animal species.

Accident is what happens, what is neither constant nor essential to the subject of the definition. For example, when we say that “Peter is the person sitting next to the door,” sitting next to the door is just an accident that happens to that person, but it is not essential or constant to them.

Logicians usually provide some practical rules for the proper enunciation of a definition.

  1. The definition must include the nearest genus and the specific difference.

  2. The definition should not be too broad or too restricted. It should be concise and use clear words. While brevity should never make it unintelligible, it should also avoid redundancy of terms or include elements that are foreign to it, that is, expressing more than necessary.

  3. The defining term should not appear in the definition. If the defining term were included in the definition, it would not add anything since it would employ the same term that needs explanation. If someone were to say that “obligation is what obliges us to do or not do something,” they would include in the definition what they seek to define.

  4. Another defect of a definition is being tautological, that is, repeating what should be defined. For example, “matter is extended substance.” And if we were to ask: But what is extended substance? And if the answer were: “it is matter.” Then we would have a vicious circle.3

  5. The definition should not be negative if it can be positive.

  6. We should avoid metaphorical or figurative words in a definition, which instead of clarifying and explaining, can further obscure the notion of what is being defined, as a basic element of the definition should clarify and not complicate or obscure:

These are the main rules of a good definition. With them, one can construct a definition that fulfills its purpose, which is to answer the question: what is this?

Article 2 – Significations

We do not want to conclude this point without giving some information about the theory of meanings that has sparked so much interest among modern logicians.

The theory of meanings emerged from the analysis of thoughts. Thoughts are no longer considered simple, elementary entities, and therefore, they are analyzable, decomposable into their parts. The search for what would be elemental in thoughts, a kind of thought atom, led to meanings. Just as propositions are composed of words, thoughts are composed of meanings.

Certain logicians believe that meanings are simple elements, that is, they are not composed of others. Are they elemental entities? This question is answered as follows: meanings are not elemental entities because, being elements of thought and thought not being an entity, how could they be entities?

Thus, they attribute merely axiological (from axios, value) character to thought.

Values are objects of a different consistency, they say. Values are not entities, but they have value, as the prevailing opinion holds, which we will have the opportunity to analyze and criticize in other works. Thoughts are not entities, that is, ontic things, a term used in modern philosophy that refers to the entity in terms of its form or structure. So, when I say “this house is green,” I can replace this proposition with this: “this house has the value of being green.” In this case, the being green is a meaning of this thought. We have stated that thoughts form a unity. So, how can we admit that meaning is an element? Wouldn’t it be admitting that thought is composed of parts? Yes, say the logicians, thought is a unity, but meanings are not independent units; they form an interdependence with each other.4 Words are not meanings, but merely arbitrary signs, although psychic laws interfere in their formation.

The reader may ask: what is the purpose of this theory of meanings? It was developed to solve the problem of categories. Categories are general meanings that deal with a particular realm, for example, being, unity, reality, ideality, etc. Categories are not determinations of objects but meanings that contribute to the constitution of a thought.

Article 3 – Reasoning

There is a significant difference between thinking and thought; the former is a psychological act that falls under the domain of Psychology, while the latter, apprehended by the former, is properly the object of Logic. The act of thinking, as we have seen, occurs in time, it is variable as a process, whereas thought is timeless and invariant.

Reasoning can be studied from two aspects:

a) the psychological aspect; and

b) the logical aspect, which we will now discuss.

There is a classical definition of reasoning given by Aristotle. Here it is: “Discursive operation by which it is shown that one or several propositions (premises) imply another proposition (conclusion) or, at least, make it plausible.”

In other words, when thinking consists of grasping an ordered series of interconnected thoughts, in such a way that the last thought necessarily follows from the first, we have what is called reasoning. Reasoning only occurs when we infer one thought from another. We can start from a singular fact to reach a general conclusion, or from a general conclusion to conclude that the singular is contained within it. Reasoning can take various forms, but in all of them, there is always the derivation of one thought from another, where the latter contains the former.

We have previously mentioned that knowledge can be acquired through acts of immediate apprehension or through more complex processes, mediate ones (by means of…). In the first case, we have intuitive knowledge, and in the second case, discursive knowledge.

The former is obtained through direct experience, for example, when I verify that this table is larger than the book. Discursive knowledge, or rational knowledge, results from previous knowledge, and we can give the example: “every man is mortal.”

We only arrive at this knowledge after verifying a series of facts and reaching a subsequent conclusion.

Discursive processes can be simple or complex:

a) simple when one knowledge is directly inferred from another; it is also called immediate inference;

b) complex when the transition from one knowledge to another is made through at least one intermediate member, such as deductive reasoning, mathematical reasoning, inductive reasoning, and reasoning by analogy.

In complex discursive processes (mediate reasoning, as we have seen), the transition from one knowledge to another is made through at least one intermediate member.

Traditionally, there are two known types: induction and deduction. Induction is generally defined as the transition from the particular to the general, while deduction is the transition from the general to the particular.

In reasoning, there are apprehensions of thoughts and their meanings, and these form a whole, a unity. This occurs in intuitive reasoning.

In discursive reasoning, one thought is inferred from another. Thus, discursive reasoning reduces to intuitive reasoning, as it is merely a complex form of the latter.

Deduction is based on logical principles (principles of identity, non-contradiction, excluded middle, and sufficient reason, which we have already discussed), which are true axioms for Formal Logic, governing all logical entities and ideal objects.

Induction is not based on logical principles but on the assumption of regularity in the course of nature, on a certain homogeneity in the succession of facts, a hypothetical regularity for many, but which is fundamental for induction, upon which it is based. The so-called scientific laws, the inductions of science, are based on the repetition of singular facts and the regularity of their repetition. Thus, for example, the regularity of planetary movements is not grasped by reason but by the repetition of facts. If the facts of physical reality are examined, it is easy to see that they have something to do with reason. However, the observation of singular and particular facts has allowed us, based on the postulate of the regularity of cosmic facts, the foundation of science, to establish the hypothesis that they will continue to occur in the future, which leads to the formulation of induced universals.

There is no sensible intuition of the universal. Sensible intuition is only of the singular, the individual, as we have seen many times before. The universal is founded on singular facts. Therefore, deduction is based on prior induction. However, the formulation of a universal implies accepting the possibility of formulating the universal. Hence, we have to admit that, to formulate a universal from an induction, the acceptance of the possibility of the universal is a prerequisite. How is this possibility given to us? It arises from the repetition of facts, whose occurrence, in the past and present, leads us to believe in their reproduction in the future. As the future confirms the actualization of this possibility, under the influence of the rational part of our mind, which desires homogeneity (based on similarity), we postulate that there is regularity in cosmic facts. Based on this regularity, we can make the leap from induction to the universal, which is the starting point for subsequent deduction. Therefore, the attainment of the universal is not merely a consequence of induction, as it is corroborated by accepting the principle, whether hypothetical or not (which is not currently up for discussion), of a universal regularity, a certain universal legality, that the cosmos is indeed ordered by constants that do not vary (invariants) and allow for the formulation of universal principles.

Theme IV

Article 1 – Syllogism

Of the discursive processes we have discussed, we highlight deductive reasoning among them, which has been identified with the syllogism.

The syllogism is a formal deduction; it is a form of reasoning that goes from the general to the particular or singular. It consists of establishing the necessity of a judgment (conclusion), showing that it is the forced consequence of a judgment recognized as true (major) through a third judgment (minor), which establishes a necessary connection between the first two.

Thus, we have two premises – the name given to the first two judgments – from which a third, called the conclusion, is inferred.

Let’s give a classic example of a syllogism:

All men are mortal (Major Premise) Now, Socrates is a man (Minor Premise) Socrates is mortal (Conclusion).

Being a deductive reasoning, the starting point is always a universal judgment, whether it occupies the first position, the place of the major premise, or not.

The syllogism has three terms: the major term, the middle term, and the minor term. These terms are the ones that appear in the judgments (or propositions) that constitute the syllogism.

The predicate of the conclusion is called the major term.

Let’s examine the aforementioned syllogism: Mortal is the major term.

The subject of the conclusion is called the minor term. The subject of the conclusion is Socrates. The middle term is the one present in both premises but absent from the conclusion, which is man in this example.

If instead of considering the three judgments that constitute the syllogism, we consider the three terms that appear in these judgments, the syllogism consists of establishing that one of these terms, the major term, is the necessary attribute of the other, the minor term (that mortal is the attribute of Socrates), because it is the necessary attribute of a third term, the middle term (man in our case, man is mortal), which in turn is the necessary attribute of the minor term (Socrates, as man is an attribute of Socrates). In summary, mortal is the necessary attribute of Socrates because it is the necessary attribute of man, and every man has the attribute of being mortal.

Thus, the syllogism consists of showing that an object or a class of objects belongs to another class because it or he belongs to a class of objects that, in turn, belongs to that other class.

This syllogism can be reduced to a simple formula: let’s call the major term C, the middle term B, and the minor term A, which in our example would be:

B is contained in C, and A is contained in B, therefore A is contained in C.

Syllogism rules: There are eight rules that the scholastics formulated through Latin verses:

  1. Terminus esto triplex, medius, majorque minorque (The syllogism has three terms: the major, the middle, and the minor). This is necessary to make the comparison of the two with a third.

  2. Nequaquem medium capiat fas est (The conclusion must never contain the middle term).

  3. Aut semel aut medius generaliter esto (The middle term must be taken at least once in its entirety). Yes, because the middle term serves to compare the extremes, and in the conclusion, the result, that is, the relationship between the extremes, must appear.

  4. Latius hunc (terminum) quam premissas concluso non vult (No term can be more extensive in the conclusions than in the premises). This rule is a consequence of the first rule, as if they were more extensive, the terms would be altered.

  5. Utraque si praemissa negat nil inde sequitur (If both premises are negative, nothing can be concluded). It is clear that nothing can be concluded from two negative judgments. If two terms do not identify with each other, how can they both identify with a third term? And if two terms do not identify with a third term, it does not mean they are identical to each other. If house is not animal and if hat is not animal, house is not necessarily hat. Two terms equal to a third term are equal to each other. Two terms not equal to a third term are not necessarily equal to each other.

  6. Ambae affirmantes nequeunt generare negantem (Two affirmative premises cannot produce a negative conclusion). Yes, because if two terms identify with a third term, they are necessarily identical to each other and cannot be distinct from each other.

  7. Pejorem sequitur semper conclusio partem (The conclusion always follows the weaker part). The particular or negative premise is called the weaker one. This rule is derived from rule number 4. The terms cannot have greater extension in the conclusion than in the premises, as we said. Now, if one of the premises is particular or negative, the conclusion must be particular or negative. It is clear that if one extreme is equal to a third term, and the other is not, we can never conclude that one is the other. Therefore, the conclusion cannot be affirmative if one premise is negative.

Some A are B

Some B are C.

We cannot know if the some B in the second premise precisely refers to the B in the first premise, which would result in four terms instead of three, violating the first rule. Moreover, the middle term is not taken in its entirety in any of the premises, which violates rule number 3. If both premises are negative, there is no conclusion according to rule number 5.

Modes and Figures of Syllogisms – In Logic, the figures of the syllogism are called the forms it adopts based on the position of the middle term in the major or minor premises. The four possible forms are called the four figures, which are characterized as follows:

  1. By having the subject term in the major premise and the predicate term in the minor premise. Ex.: All men are mortal; Socrates is a man; therefore, Socrates is mortal;

  2. By having the middle term as the predicate in both premises: "All men are rational; no plant is rational; therefore, no plant is a man;

  3. By having the middle term as the subject in both premises: “Some men are philosophers; all men are bodies; therefore, some bodies are philosophers”;

  4. By having the middle term as the predicate in the major premise and the subject in the minor premise: “All men are mortal; all mortals are animals; therefore, some animals are men”.

The mode of the syllogism results from the quantity and quality of the premises that compose it. These judgments fall into four classes, as we have already studied:

Universal affirmative (A), Universal negative (E), Particular affirmative (I), Particular negative (O).

They can be combined in 64 forms, but not all of them are conclusive. If we apply the studied rules, we have 19 valid modes, which are distributed as follows:

4 for the first figure; 4 for the second; 6 for the third, and 5 for the fourth.

Since each judgment is symbolized according to its quantity and quality by a vowel, each valid mode is traditionally symbolized in logic by a Latin word that contains the sign-letters of the judgments that compose the syllogism.

These are the valid modes for each figure:

First figure

A A A (Barbara)

E A E (Celarent)

A I I (Darii)

Second figure

E I O (Ferio) E A E (Cesare)

A E E (Camestres) E I O (Festino) A O O (Baroco)

Third figure

A A I (Darapti) E

A O (Felapton) I A

I (Disamis) A I I (Datisi)

O A O (Bocarão)

E I O (Ferison)

Fourth figure

A A I (Bamalip) A

E E (Camenes)

I A I (Dimatis)

E A O (Fesapo)

E I O (Fresison)

Examples: from the first figure: The middle term is the subject in the major premise and the predicate in the minor premise.

Barbara:

A. All metal is a body;

A. all lead is metal;

A. therefore, all lead is a body.

Celarent:

E. No metal is a plant; A. all lead is metal;

E. therefore, no lead is a plant.

Darii:

A. All metal is a body; I. some mineral is metal;

I. therefore, some mineral is a body.

Ferio:

E. No metal is a living being; I. some body is metal; O. therefore, some body is not a living being.

Examples from the second figure: The middle term is the predicate in both premises.

Cesare:

E. No living being is metal; A. all lead is metal;

E. therefore, no lead is a living being.

Camestres:

A. All lead is metal; E. no plant is metal;

O. therefore, no lead is a plant.

Festino:

E. No plant is metal; I. some body is metal; O. therefore, some body is not a plant.

Baroco:

A. All lead is metal;

O. Some body is not metal;

O. therefore, some body is not lead.

Examples from the third figure: The middle term is the subject in both premises.

Darapti:

A. All metal is mineral; A.

all metal is a body; I. therefore,

some body is mineral.

Felapton:

E. No metal is a plant; A. all metal is a body;

O. therefore, some body is not a plant.

Disamis:

I. Some metal is lead; A. all metal is a body; I. therefore, some body is lead.

Datisi:

A. All metal is a body; I. Some metal is lead;

I. therefore, some body is lead.

Bocardo:

O. Some metal is not lead; A. all metal is mineral;

O. therefore, some mineral is not lead.

Ferison:

E. No metal is a plant; I. some metal is lead; O. therefore, some lead is not a plant.

Examples from the fourth figure: The middle term is the predicate in the major premise and the subject in the minor premise.

Bamalip:

A. All metal is a body;

A. all bodies occupy space;

I. therefore, some bodies that occupy space are metal.

Camenes:

A. All Brazilians are Americans;

E. no American is European;

E. therefore, no European is Brazilian.

Dimatis:

I. Some Americans are from São Paulo;

A. all Paulistas are Brazilians;

I. therefore, some Americans are Brazilians.

Fesapo:

E. No Paulista is French;

A. All French people are Europeans;

O. therefore, some Europeans are not Paulistas.

Fresison:

E. No Brazilian is European;

I. some Europeans live in Brazil;

O. therefore, some men who live in Brazil are not Brazilians.

All these modes and figures that we present here are done exclusively to comply with the old norms of formal logic. However, all these rules and norms can be reduced to just one law of syllogism, based on an ontological principle: Two things equal to a third thing are equal to each other. If these two things are not equal to a third thing, but only in part, they may not be equal to each other, not even in part.

If A is partially equal to B, and C is equal to B, it does not mean that A is equal to C, not even in part.

Everything that can be affirmed or denied about the entirety of a genus can also be affirmed or denied about all the individuals that compose that genus. This is a principle of syllogism that follows from the principle of identity.

“All men are mortal, therefore a man (Socrates) is mortal.” All figures of syllogism (2nd, 3rd, and 4th) can be reduced to the first figure, which Aristotle called a perfect syllogism and which is the concrete application of the rule we mentioned above. Thus, it can be seen that the syllogism is just a form of deductive reasoning, as we have already explained.

In everyday language and even in more precise demonstrations, one of the articulations of the syllogism is implied when it is evident. The syllogism is then called an enthymeme. In an enthymeme, one of the premises is omitted. For example: all metal is heavy because all matter is heavy. The premise “all metal is matter” is omitted.

Syllogisms can be combined with each other and form what is called a polysyllogism. For example: “Freedom allows for the development of culture; all development of culture is an elevation of man; the elevation of man is a duty of everyone, and if freedom allows for this development, it is our duty to facilitate it; therefore, striving for freedom is the duty of all of us.”

A prosyllogism is one in which the conclusion serves as the starting point for the next one. For example: “All felines are mammals; cats are felines; therefore, cats are mammals; now, the Angora cat is a cat, so the Angora cat is a mammal.”

Epicheirema is the syllogism in which one or two premises are proven by an incompletely expressed prosyllogism.

Sorites is a sequence of syllogisms chained one after another.

Hypothetical syllogism is a syllogism in which the major premise is a hypothetical proposition.

Disjunctive syllogism is the syllogism in which the major premise has two attributes that exclude each other. A is B or C, etc.

Dilemma falls into this category of arguments. It consists of a disjunctive judgment and two conditionals, both leading to the same conclusion. For example: “Man, who obeys his passions, either achieves what he desires or not; if he achieves it, he becomes bored and therefore unhappy; if he doesn’t achieve it, he is anxious and for the same reason unhappy.”

Faulty reasoning is called paralogism, sophism, or fallacy.

When there is good faith, it is called paralogism; in the opposite case, sophism or fallacy. This is the commonly accepted meaning. Any syllogism that violates the rules of logic is fallacious. Examples of fallacies: “White cannot be pink, therefore paper cannot be dyed pink.”

Ignorance of the issue (ignoratio elenchi) is the name given to paralogism when one responds to something different from what is at issue or proves something that was not meant to be proven. For example: “If someone is wise, they are hardworking; they are hardworking, therefore they are wise.”

Begging the question occurs when the same thing that needs to be proven is assumed. For example: “Smoke rises because it is lighter than air, and it is lighter than air because it is part of light objects.”

Article 2 – Practical Rules for the Proper Use of Logic

It is unnecessary to explain the value that Formal Logic represents for humans as a powerful instrument for consolidating knowledge. Even if its principles based on the facts of life, on what is flowing, dynamic, changing, and varying, do not encompass the entire extent of the process of existence, it does not diminish the value of Formal Logic. The only thing that has been undone by the criticisms made by so many philosophers is the aprioristic application that was attributed to it (as rationalists did), without ceasing to be a useful tool for humans.

When seeking truths, as they belong to such different classes, it is also not advisable to employ similar or identical methods. Each discipline requires its own logic. Scientific research must adhere to scientific methods to become useful and fruitful. The investigation of a historical, psychological, or sociological fact requires different methods. However, in all cases, there is always a formal aspect that homogenizes them.

We easily intuit certain facts and have a vision of them, but when we attempt to express them in words, we encounter such difficulties that we consider them to be the result of a weakness in our intellect. In reality, the weakness lies in our vocabulary, which is overly static and overly generalizing. This is why poetic language, by escaping the narrowness of rationalism, often manages to express to others what the mechanics of words and the rigor of terms would not be capable of doing, through images, daring comparisons, and audacious analogies.

However, this fact does not justify our disregard for the schematic contents of verbal terms, which, as the vehicles of our thoughts, must adhere to an imperative of clarity essential for proper understanding.

But knowledge is something impersonal when studied in a universalizing manner. Feelings, affections, tendencies, and sympathies exert an influence whose extent we are still far from understanding.

Let us consider an example: someone is in a life-threatening situation, seriously ill, on the brink of death. Several people are around them, a friend, an acquaintance, a doctor, a spouse, a mother. It is not difficult to understand how different the knowledge of this fact is for each of these people. There are details that are perceived or overlooked by some and not by others. How much do our passions, affections, tendencies, and psychological type influence our knowledge? We can never exclude our personal situation, class, or environment, which influence our thoughts. We grasp thoughts that correlate, that are possible in accordance with our conditions. A cold thought, completely detached from all affectivity, is impossible, but that does not prevent us from seeking to reduce the conditionality of our reasoning, to make it increasingly free. This is what Logic aims to do and achieve.

Now, when we reason, we do so with thoughts that present themselves as a whole. Through judgments, we express them more or less. Generally, they are loose words that serve as signals to draw attention to them. Let the reader conduct a quick experiment with themselves. Observe how thoughts arise, how affections and pleasant or unpleasant emotions emerge among them. You accept one, reject another. Suddenly, a glaring term emerges, but is immediately overshadowed by a dominating thought. Contradictory forces oppose each other. You are undecided, make a choice, but quickly realize that the choice is not appropriate. You reject one thing, emphasize another. Ultimately, when we think, thoughts arise without any order, they come with all their conditions, as they reflect what is existential and deepest in humans.

But order must be established. Well, that order is provided by Logic. By examining thoughts, classifying the elements that compose them, Logic has allowed us to have an order capable of avoiding the observable confusions, for example, in daydreaming.

Our reasoning does not arise solely from within us. The facts of the external world are the great stimulators and lead us to prefer one thought over another.

Our thoughts arise from our knowledge of the facts of the external world.

We have our senses as important means of knowledge, which provide us with the data that our mind then coordinates. They assist us, but they can also deceive us.

Let us see what rules we should follow to make good use of them so that our reasoning is more secure.

We all know how many illusions our senses can present to us. Thus, perception provided by only one of them can be deceiving. However, when corroborated by others and not contradicting the regular course of events, it should be accepted as true unless it contradicts the perception of other people, as advised by Balmes.

Imagination contributes significantly to the formation of judgments and reasoning, as well as to the acquisition of knowledge. The natural course of events greatly helps us examine the presence of imagination in our psychological processes.

Another important consideration for the proper organization of reasoning is the careful use of words, which must be employed with accuracy and precise meaning in order to avoid the confusions that often arise from reasoning based on words with unclear meanings.

Therefore, one of the exercises that must be constantly practiced is analyzing terms and seeking to understand their scope, significance, and various meanings. Let’s say that in one of those moments, the word “conta” (account) comes to mind. We start analyzing it. Immediately, the sense of calculation, computation, arithmetic operations comes to mind. Memories of childhood in school are immediately associated. However, we direct our thoughts, inhibit the memories, and focus our attention on the word “conta.” The expression “dar por conta” (to settle a debt) comes to mind, amortizing a debt, “andar com as contas em dia” (to keep one’s affairs in order), that is, having one’s obligations fulfilled. But “gastar sem conta” (to spend recklessly) conveys the idea of spending without care, making unnecessary and superfluous expenses. “Ele não dá conta do serviço” (He cannot handle the workload) implies being overwhelmed with work to the point of not being able to handle it properly, causing delays. “Tomar contas” (to demand explanations) means asking for clarification. “Ter em conta” (to take into account) means giving importance. “Tomar conta” (to take care) means to look after. “Ter alguém em boa ou má conta” (to hold someone in good or bad esteem) means considering someone in a positive or negative light. “Dar conta a alguém de alguma coisa” (to give an account to someone) means giving explanations, providing information, keeping someone informed about what is happening or has happened. With the exception of the term “conta” in the sense of a spherical object, such as those used for rosaries, ornaments, etc., we see that the term always has a sense of calculation, comparison, and measurement. Such an analysis, as exemplified, of words, especially the terms used in philosophy, allows us to gain complete mastery over words. Now, philosophers work more with abstractions than with concrete things. The danger often lies there because words can mean many things; they are signs with multiple connotations. These continuous exercises allow us to take care of our vocabulary and prevent words from being used with one meaning in one judgment and a different meaning in another.

If someone were to say, “This climate is sweet,” now, what is sweet is pleasant to the taste; therefore, the climate is pleasant to the taste. What do we have here? We have an equivocation. And this equivocation arises from the different connotations of the word “doce” (sweet). This example is very rudimentary, but it serves to show how many dangers arise from the equivocal use of a term (“equi” means equal, “voco” comes from “vox,” voice), that is, when it is used in one sense and taken in another sense as well.

Let’s take a more complex example: let us focus on the distinction between “pensar” (to think) and “pensamento” (thought). However, not all psychologists and logicians grasp this distinction. The confusion between thought and the act of thinking is common.

If someone were to say, “thinking is a psychological act. Thought is a product of the act of thinking, therefore, thought is a psychological act.” Such a syllogism would be correct for someone who considers thought as the product of the act of thinking. But for those who, like us, see it differently, although they subject the apprehension of thought to psychological conditions (hence the variety of thoughts that can be gleaned from facts), such a syllogism is a fallacy.

All theories are based on a principle accepted as axiomatic. Thus, when examining reasoning, it is necessary to examine the terms that compose it in order to identify the errors that corrupt them.

For complete mastery of thought, let us propose another method with extraordinary effects when employed repeatedly, as it is an exercise of great value for reading itself.

The reader should select a passage from the work of a philosopher. Without rushing, start reading the first sentence calmly. Then arrange the judgments and analyze the terms that compose them. Next, observe the connection of the judgments and, finally, the connection of the sentences within a passage. Understand the meaning of each term as employed by the author. Undoubtedly, with the help of a philosophical vocabulary, the reader can greatly benefit by finding the various connotations that a term usually has in the works of philosophers.

This continuous exercise intensifies attention and concentration of intelligence, and it trains us to achieve a faster understanding of meanings. Once this phase is achieved, the reader is capable of reading whatever they wish and not being carried away by the equivocations and amphibologies that generate so many fallacies and errors.

One aspect that the reader should always seek when performing these exercises is the psychological aspect. Try to discover within the words the influence of affections and emotions and never forget the era, the situation, and the historical influences that greatly condition the work of philosophers.

We are very accustomed to the hurried reading of newspapers, fiction books. This haste is one of the greatest evils of the present time. Most books are books made of books. There are only a few hundred truly great works in world literature. It is useless to read everything or want to read everything because we do not read, especially because we read quickly. Let us remember that reading is rereading. A book that does not deserve to be reread is not valuable. And only a few are the great works we read, and we can always reread them. Those should be the chosen books.5

Let us now delve into the practical study of syllogism.

Many philosophers criticize it.

  1. Aristotle defined the syllogism as “a statement in which, having proposed some things, another thing necessarily follows from them, solely by virtue of being given.” Thus, the syllogism does not say more than what has already been said; it does not conclude more than what is already contained in one of the premises. Now, the syllogism is a reasoning that goes from the general to the particular, so what is contained in the conclusion is already in the premise. It offers no inventive value but only an expository one. It is not equivalent to analysis based on the mathematical process, as Descartes argued when criticizing it.

  2. Others argue that the syllogism is not a natural form of our thinking but an artificial one because, in reality, we do not think syllogistically.

However, despite the arguments and reasons presented by its critics, we should not disregard a form that, within the formal canons, offers great advantages. If Formal Logic is the logic of identity, the syllogism can only conclude an identification of something with something else.

Indeed, we can reduce all syllogisms to very simple rules.

We have seen the classical rules, which are eight and encompass everything necessary for a rigorous syllogism.

The fundamental principle of syllogisms can be reduced to the axiom that “two things identical to a third thing are identical to each other.” Indeed, the syllogism is a deductive reasoning in which two extremes are compared to a third.

Formal Logic is extensive, it operates with extension. Relations are always extensive, quantitative. Terms in the syllogism are taken in their quantitative aspect, as we have seen in the analysis we have made of the various proposed rules when discussing the syllogism, which we recommend rereading.

As simple as the classical practical rules of the syllogism are, which are also given in Latin verses, logicians have always sought to reduce them to a single rule.

Let us give some of the most famous ones. Balmes presents this: “The fundamental principle of simple syllogisms is as follows: things identical to a third thing are identical to each other.” It is based on the principle of non-contradiction: “it is impossible for a thing to be and not to be at the same time.”

The conclusion is always contained in the premises and is, therefore, implicitly affirmed in one of them.

Port-Royal Logic gives this rule that immediately indicates the truth or falsehood of a syllogism: “One of the two propositions must contain the conclusion, and the other must show that it contains it.”

Pay attention to the quantitative sense of this rule, which is accurate because every conclusion is deduced, is drawn. Every syllogism serves to draw a conclusion from a premise.

Consider this rule by Euler: “Everything that exists in the container exists in the content. Everything outside the container is outside the content.”

Observe the purely quantitative sense of this rule, which is also accurate.

Now consider this other one: “What can be affirmed or denied of an entire genus can also be affirmed or denied of all individuals composing that genus.”

The genus has the general characteristics, the characteristics that are found in all individuals. The characteristic denied to the genus is denied to the individual.

This rule works very well for Aristotle’s perfect syllogism, which we have already studied.

Quantitatively, what we affirm of a whole, we affirm of its part. We cannot deduce from a whole what is not contained in this whole (Euler’s Rule). In this way, what is concluded is deduced from one of the propositions (Port-Royal’s rule).

Euler, in his “Letters to a German Princess,” presented a very interesting method, representing the three terms of the syllogism with circles. With these circles, which form 36 figures, he examined all kinds of syllogisms.

We will not reproduce these 36 figures, but we can reduce them to only 3 figures, which are sufficient to address the 19 legitimate combinations that can be formed from syllogisms. We thus simplify graphically what has been one of the biggest problems for students.

  1. Either one whole (with its parts) is included in another;
  2. or it is not (and in this case, its parts are also not included);
  3. or only part of the first participates in the other.

These are the three quantitatively possible situations in which, simplistically, any syllogism is included. What I affirm of the whole, I affirm of the part. What I affirm of the first whole, I negate in the second, both in part and in whole, if I assume that this whole is separate from the first. If part of a whole is contained in another, what I affirm of the first whole may not be contained in the other because I assumed that only a part is.

These are the three diagrams that graphically show us all the possible legitimate combinations.

Let us now examine the 19 combinations that can be compared with the diagrams:

First figure of the syllogism

  1. Every B is C

now, every A is B

thus, every A is C

(1st diagram; Barbara)

  1. No B is C

now, every A is B

thus, no A is C

(2nd diagram; Celarent)

  1. Every A is B

some C is A

thus, some C is B

(3rd diagram; Darii)

  1. No B is C

now, some A is B

thus, some A is not C

(2nd diagram; Ferio)

Second figure of the syllogism

  1. No C is B

now, every A is B

thus, no B is C

(2nd diagram; Cesare)

  1. Every A is B

now, no C is B

thus, no C is A

(2nd diagram; Camestres)

  1. No C is B

now, some A is B

thus, some A is not C

(2nd diagram; Festino)

  1. Every A is B

now, some C is not B

thus, some C is not A

(2nd diagram; Baroco)

Third figure of the syllogism

  1. Every A is B

now, every A is C

thus, some C is B

(1st diagram; Darapti)

  1. No A is C

now, every A is B

thus, some B is not C

(2nd diagram; Felapton)

  1. Some A is C

now, every A is B

thus, some B is C

(3rd diagram; Disamis)

  1. Every A is B

now, some A is C

thus, some C is B

(3rd diagram; Datisi)

  1. Some A is not C

now, every A is B

thus, some B is not C

(3rd diagram; Bocardo)

  1. No A is C

now, some A is B

thus, some B is not C

(2nd diagram; Ferison)

Fourth figure of the syllogism

  1. Every A is B

now, every B is C

thus, some C is A

(1st diagram; Bamalip)

  1. Every A is B

now, no B is C

thus, no C is A

(2nd diagram; Camenes)

  1. Some C is A

every A is B

thus, some B is C

(3rd diagram; Dimatis)

  1. No C is A

now, every A is B

thus, some B is not C

(2nd diagram; Fesapo)

  1. No C is A

now, some A is B

thus, some B is not C

(2nd diagram; Ferison)

In summary: Either one whole is contained in another; or one whole is outside the other, or part of one whole is contained in another.

Within these three quantitative situations, all rigorous syllogisms are found. From this, we can still conclude: if one thing is contained in another, what is affirmed of the second is affirmed of the first. If one thing is not contained in another, what is affirmed of the first is not affirmed of the second. If both participate in each other, the affirmation only applies to both in terms of the participating part. What is affirmed of the remaining part, which is not the participating part, is not affirmed of the other.

Every syllogism is a deductive reasoning. One cannot deduce from something what the thing does not possess. Thus, two things can be entirely equal to each other, entirely different, or resemble each other in part. The same applies to two ideas: they are either equal, entirely different, or resemble each other in some way.

Every regular syllogism adheres to these rules, which we have repeated in various ways to better engrave them in the reader’s memory.

Theme V

Article 1 – Knowledge and Knowing – Truth

Logic limits its interest, regarding knowledge, only to formal aspects. It studies thoughts and their relationships, and it does not concern itself with the relationships between the knowing subject and the known object, which belongs to the Theory of Knowledge or Epistemology.

However, the topic of truth is of great interest to Logic. In general terms, truth is the correspondence of knowledge with the objective situation it corresponds to. But logic distinguishes truth from logical validity. Logical validity is based on the obedience to logical laws. For example, a syllogism like this, formally presented: all B is A; all C is A; therefore, all C is B, is logically true.

However, we can fill these forms with objective contents that can be false. Let’s say someone says: “All Brazilians are Europeans,” from then on, the entire syllogism is false in its assertion because it is based on a completely false premise, although it is logically rigorous in form.

For logic, truth is always the correspondence between knowledge and the objective situation, and from the moment there is conformity between the judgment and the situation to which the judgment refers, we have truth in logic. Also, for logic, truth does not admit degrees; it is always absolute. Yes, a thought is either false or true because the relationship between the judgment and the objective situation indicates their correspondence or lack thereof.

For logic, there are no practical truths because every truth is theoretical. The so-called practical truth is merely a false statement because when we say that Brazil has practically 9 million square kilometers, we are making a false statement because it does not have that much. The true statement would be to say that it has 8 million and 525 thousand square kilometers if the geographers are not mistaken.

There is a very common confusion between truth and accuracy, which is worth clarifying. Knowledge can be vague or precise, accurate.

A statement can be true, albeit vague, and it can be both true and accurate. Accuracy admits degrees, but truth does not. If I say that Brazil is a South American country, I provide a true but vague statement. If I say that Brazil is located in the eastern part of South America and I specify its geographic, political, economic characteristics, etc., as I state them, I increase the accuracy of knowledge about Brazil.

The concept of false is easy to construct because any knowledge that does not correspond to the objective situation to which it refers is false or erroneous knowledge. We usually affirm that the criterion of truth is evidence because we consider it as the immediate apprehension of the correspondence between the judgment and the objective situation, a correspondence so clear that it does not allow any doubt.

Doubt occurs when we hesitate, when we oscillate between an affirmative and a negative.

Ignorance is the absence of knowledge and admits degrees like accuracy.

Error consists of taking the false for the true. It is a subjective act, which distinguishes it from falsity, which is objective. We can make a mistake when we take the false for the true, but there is falsehood when the judgment is false. Thus, falsehood occurs in the judgment, and error occurs within us.

An opinion, for logic, consists of a state of consciousness in which one thinks that an assertion is true, but of which we hold some reservation because it may be false.

There is probability when there is a greater or lesser possibility of knowing a truth or of a statement being true.

There is certainty when we recognize the truth of knowledge as evidence. Certainty is a mental state and does not admit degrees, unlike doubt. If we admit probability in certainty, we are in doubt and not in certainty.

Article 2 – Scientific Knowledge and Method

In previous articles, we distinguished between common knowledge and scientific knowledge. Modern man, when educated, incorporates much of scientific knowledge into his common knowledge, and the same applies to the common man, albeit to a lesser extent. This is why a clear distinction is impossible. We studied the formation of theoretical knowledge in Philosophy and Worldview and that of scientific knowledge as a subsequent stage. Scientific knowledge leads to the formation of science as a set of certain and probable knowledge, which is methodically founded and systematically arranged according to their respective objects. Although this statement is not a definition, as it could be confused with the meaning of philosophy, we could add that in science, knowledge is related to experience and the experiencable, without ever transcending it, whereas in philosophy, transcendence occurs.

We speak of probable knowledge because we all know that science is based on hypotheses and works with probabilities, especially when employing the inductive method, which encompasses a high degree of probability. Science distances itself from dogmatism because a true scientist presents their conclusions and expects their peers to examine and analyze them. Science deals with the general; there is no science of the singular.

Among the forms of scientific knowledge, we can highlight mathematical knowledge, which works with mathematical objects, ideal objects that we have already discussed. Logic also has an ideal object. All other sciences that have real, temporal objects are called natural sciences (physics, chemistry, biology, etc.). These sciences are empirical; they are real sciences.

The term method refers to the rational way of conducting thought to reach a specific result and, above all, to discover the truth. Thus, in the method, there is a means that tends towards an end.

The method is the “good path (meth’odós in Greek) that leads to achieving this end.” All scientific knowledge, like philosophical knowledge, requires a method, and it must be grounded, analyzed, and studied, avoiding the disorderly use of various means. However, the method is conditioned by the nature of the object to which it is applied and the purpose it serves. These conditions are essential to any method.

Some objects exist in space and time, such as objects in the natural sciences; others exist only in time, such as psychological phenomena, and others are neither temporal nor spatial, such as mathematical objects and those of logic. These differences require different methods. Therefore, the application of deductive method in physics, as Descartes did, could not yield the expected results, as the texture of physical phenomena is not purely mathematical. Similarly, the application of experimental method in psychology only grasped a part of psychological phenomena because life is resistant to systematization. The predominance of one of the energetic orders, either intensity or extensity, requires the application of different methods.

Analysis and synthesis are the most general methods.

Analysis is the operation that consists of separately considering the parts of a whole. This can be done in reality or mentally, that is, real analysis or intellectual analysis.

Synthesis is the inverse; it is the composition of a whole with the help of the elements that constitute it.

Article 3 – Logic of Mathematics and Natural Sciences

Despite its genuinely rational framework, mathematics today presents significant and profound problems that are of great interest to researchers who undertake exhaustive studies everywhere to solve them.

Reason has a particular attraction to mathematics and feels at ease when applying its rules. Now, mathematics works with ideal objects, abstractions of abstractions. Reason, as an abstracting organ, follows a constant process of purifying its mode of operation, which is genuinely spatial and homogeneous, always identical to itself. The abstraction of homogeneity of space, of quantitative homogeneity, abstracted in turn from all spatialization, is the field of mathematics, which, being a science of the quantitative, abstracts quantities to move among them in a homogeneous field of possibility. Thus, the number, when it ceases to be a concrete number like “5 books” and becomes merely 5, a quantitative possibility, transitions to a higher abstraction, a possible quantity, abstract, represented by n, for example, undetermined as a specific quantity.

This is why mathematics achieves such homogeneity in its general lines, an immutability that lends it the security it reveals. This is why it pleases reason so much, as mathematics is the ultimate realization of reason in its abstracting process.

And its concrete applications, when referring to homogeneous quantities, generally receive the stamp of experience. As mentioned above, despite all the rigidity of its foundations and the fixed structure of its object, mathematics encounters problems that are of great interest to those who undertake the analysis of its foundations.

One of the major problems concerns the nature or essence of its object. Although it is a problem that goes beyond the field of logic, logic cannot abstain from studying it, at least within its scope. Another problem is that of the method of mathematics. As a powerful tool for studying nature, which is both quantitative and qualitative, it finds an extraordinary field of application by considering the dynamism of extensity. Therefore, science has in mathematics not only its great working tool but also, to some extent, its foundation.

Closely related to philosophy, mathematics has held a prominent place in it, and the problems it raises are of great interest to the field of philosophical research. Thus, in studying the nature or essence of mathematics, various answers have been given by philosophy, and we will summarize the most important ones presented by modern philosophers.

According to Kant, space and time are pure forms of sensibility, which are given a priori in any experience, or rather, no experience occurs without the prior acceptance of space and time, which shape and mold every single experience. These forms are given aprioristically to experience, which does not imply that, for Kant, the notion of space and time is innate, as many believe. Kant only wanted to emphasize that they precede all sensory experience, meaning that once they are structured, they become prior to any new experience and allow it to be shaped by them, as two pure forms of sensibility. They are present in all perceptions; they are present in all phenomena captured by the senses.

Space governs only the external phenomena perceived by us, while time governs both the external and internal phenomena, the intuition we have of ourselves, of our inner states. Let us quote Kant: "Time is the a priori formal condition of all phenomena in general.

“Space, as the form of all external intuitions, only serves as an a priori condition for external phenomena. On the contrary, since all representations, whether or not they have external things as their object, nevertheless belong by themselves, as determinations of the mind, to an internal state, and since this state, under the formal condition of internal intuition, belongs to time, time is an a priori condition of all phenomena in general; it is the immediate condition of our internal phenomena (of our soul) and the mediate condition of external phenomena. It can be said a priori that all external phenomena are in space and are a priori determined according to spatial relations. In a broad sense, based on the internal sense: all phenomena in general, that is, all objects of the senses, are in time and are necessarily subject to temporal relations.”

Geometry is the science that synthetically determines a priori the relations of space. Let us recall the analytic judgments and synthetic judgments, as explained by Kant. Let us remember that an analytic judgment elaborates an analysis of the subject; it is explanatory.

“All bodies are extended” is an analytic judgment. It does not add new knowledge because being extended is being a body. Synthetic judgments are those in which the predicate is not obtained through the analysis of the subject and add something new to the subject, thus providing new knowledge, that is, a new synthesis. For example: “The sun is a star.”

Up to this point, what Kant affirms was already known before him. But Kant (and this is his new contribution) discovers that not all synthetic judgments are based on experiences (syn and thesis, Greek words meaning construction, composition), but there are also synthetic judgments a priori, which add knowledge without relying on confirmations from experience (the a priori). Examples of such judgments are mathematical judgments and those of exact natural science. They become possible because of the elements that the subject puts into knowledge.

Let us quote Kant: "At first glance, one could believe that the proposition 7 + 5 = 12 is purely analytic, that it proceeds, according to the principle of contradiction, from the concept of the sum of seven and five. But if we consider it more closely, we will verify that the concept of the sum of seven and five contains nothing more than the union of the numbers into one, which does not lead us to think about what that unique number is that comprises the other two. The concept of twelve is not at all conceived by merely thinking about the union of five and seven. Therefore, the arithmetic proposition is always synthetic."6

Thus, for Kant, mathematics has its ideal origin and its foundation in certain pure or a priori forms that regulate our capacity for sensory knowledge. Mathematics penetrates all sciences of reality and underlies them because, like exact sciences, the perceived objects have the determinations of time and space.

On the other hand, the empiricist conception we have studied asserts that sensory experience is the only source of knowledge and that general truths are derived from singular facts through abstraction or induction.

According to John Stuart Mill, all knowledge comes from experience. However, while some sciences remain tied to experiences, others become rational and deductive, such as mathematics.

“The points, lines, circles, and squares in our mind are mere copies of points, lines, circles, and squares that we know through experience.” These copies are generalizations, and axioms are a kind of induction from experience, simpler and easier generalizations of positive facts. Stuart Mill continues: “In human nature, nothing is more generally admitted than the extreme difficulty it feels in conceiving, as possible, something that contradicts an ancient and familiar experience, and even deeply rooted habits of thought; this difficulty is a necessary result of the fundamental laws of the human mind.” This is what arithmetic shows us.

Logicism views the problem differently. For them, mathematics is purely of a logical nature, and there is no process or principle specific, peculiar, or exclusive to the formation of mathematical notions, and the methods of mathematical foundation, both proof and demonstration, are purely those of logic. Thus, logic is the foundation of mathematics, and both Logic and Mathematics become part of general Logistics.

The most important representative of this trend is Bertrand Russell, whose words we reproduce below:

“Mathematics and logic have historically been marked as two completely separate fields of study. Mathematics was associated with the natural sciences, and logic with philosophical sciences. However, something else happens as both develop in modern times. Logic becomes mathematics; mathematics becomes logic. Therefore, it is now completely impossible to make a radical separation between them; in fact, they are the same thing. They differentiate themselves like the young and the adult. Logic is the adolescent of mathematics, and mathematics is the mature man of logic. Logicians defend this conception, having spent their time studying classical texts and becoming incapable of understanding work that involves symbolic proofs. It is also opposed by those mathematicians who have only learned a technique without ever bothering to investigate its legitimation and meaning. Fortunately, these types, both of one kind and the other, are becoming increasingly rare. A part of modern mathematics is clearly approaching the boundaries of logic, and on the other hand, modern logic is mostly symbolic and formal. The close affinity between mathematics and logic is evident to any educated and cultured person.”

Intuitionism asserts that mathematics is a product of human spirit’s creation, with no existence until it is created. In this way, mathematics is purely and simply a construction, which, like language, is an “active” realization of man.

Having examined the various opinions on the nature of mathematics, we can study how mathematical reasoning works. The primary elements of this reasoning are the axioms. They are propositions that express obvious truths and cannot be demonstrated because they are absolutely evident starting points.

These undeniable truths do not require proof, such as “the whole is greater than its part.” In addition to axioms, geometry also uses postulates that are self-evident and cannot be demonstrated but whose truth is accepted because consistent consequences are derived from them. Mathematics employs demonstration, which consists of deducing other judgments recognized as certain and necessary from one judgment, and these, in turn, from axioms and definitions. Since every definition is based on indefinables, every demonstration starts from something indemonstrable. Mathematical demonstration differs from syllogism in having more than three judgments and also in using equalization, as it establishes the equivalence of two terms, allowing one to be substituted for the other. The judgment one aims to demonstrate is called a theorem.

According to Poincaré, the great French mathematician, the proper method of mathematics is what he called reasoning by recurrence. “First, establish a theorem for the number 1; then prove that if it is true for the number 1, it is true for n, and from here, conclude that it is true for all integers.” The evidence of reasoning by recurrence is explained by Poincaré as follows: “It is nothing more than the statement of the mind, which feels capable of conceiving the indefinite repetition of the same act since that act is possible once. The mind has a direct intuition of this power, and experience can only provide an opportunity to exercise it and thus become aware of it.”

“It cannot be denied that there is a remarkable analogy here with the usual processes of induction. But there is an essential difference. Induction applied to physical sciences is always uncertain because it rests on the belief in a general order of the universe, an order that exists outside of us. Inductive mathematics, that is, demonstration by recurrence, imposes itself necessarily because it is nothing more than the affirmation of a property of the mind itself.”

The foundation of induction, which is practiced in natural science, is the belief in the regularity of the course of phenomena, while the foundation of mathematical induction (or reasoning by recurrence) is the regularity of the mind itself.

The explanation of the value of the method studied by Poincaré is firmly grounded in the regularity of the human mind. The field of mathematics is a homogeneous field, absolutely homogeneous, which is the field of extensity as pure quantity. As we have mentioned before, mathematics only includes intensities when reducing them to extensity.

This field is absolutely identical to itself because, as we have seen, quantity, when considered abstractly, is identical and homogeneous; it is the “same-absolute.” The human mind, through reason, comes to conceive it this way. Therefore, what occurs in one part must occur in any other part because it is the same absolute, identical. Through a long series of chains of syllogisms, reasoning by recurrence becomes established as something immediate to reason. This is also what Husserl thinks when he says that essences are intuited through a single exemplar, such as perceiving a single manifestation of a color to intuit the essence of that color. For example, when faced with a new and unknown species of tree, we immediately intuit the essence of that species. To exemplify, if someone encounters a color they are unfamiliar with, such as purple, upon seeing an object that is purple, they immediately intuit the color purple, just as a zoologist intuits a new species upon encountering a new animal, inferring that the characteristics of that animal must be the general characteristics of the species. This is what Husserl calls eidetic intuition.

We are faced here with the same previous fact. The development of reason, its abstracting process, its conceptual work, creates in the mind this emergence of intuiting the essence from just a single exemplar. It does not need to first conceptualize through the abstract work of the characteristics of one or many other identical exemplars to form the concept. It induces the essence from a single empirical exemplar. When someone shows an object to another person and says, “This is an airplane,” that person, who has never seen one before, grasps the essence of an airplane and understands its nature. However, the content of this concept can be expanded. A pilot has a richer concept of an airplane than an ordinary person.

Mathematics, in its abstract phase (such as contemporary mathematics), which works with quantitatively considered possibilities, that is, considered only as extensions, could only arise in a developed phase of reason.

However, we ask: is this the only possible mathematics? Are there no other possibilities for mathematics, such as a mathematics of intensities as intensities, without reducing them to the extensive?

A traditional definition tells us that scientific knowledge is knowledge based on causes and that science is founded on the law of cause and effect. This statement, which seems definitive in science, has been vehemently criticized by philosophy, especially by Hume and Nietzsche. It was with Hume and Mach (Ernst, 1838-1916) that the term “function” was proposed to better express what science had previously called cause. The topic of “cause and effect” is addressed and analyzed in our book Philosophy and Worldview because the law of causality is one of the fundamental principles of reason. In logic, it is not possible to give this theme the prominence it deserves. Rationalism identifies the principle of causality with that of sufficient reason. However, what deeply impressed philosophers was the fact that the principle of causality, difficult to avoid thinking at first, eventually became difficult to think. Whether we truly grasp cause and effect relationships among phenomena or merely relationships of antecedents and consequents, as Hume and Mach argue, all of this becomes clear when studying this fundamental necessity of our reason, which always seeks identification.

Observation, which provides us with the means to empirically investigate sensory objects, is one of the most effective uses of real sciences, which are therefore also called empirical or experiential sciences, observational sciences. Experimentation provokes the phenomenon and produces it under favorable circumstances for observation to yield its fruits. Thus, experimentation is provoked observation. However, experimentation is not mere observation since it includes certain directions; it is guided by hypotheses and embodies a suspicion that desires verification.

It was with Galileo that induction began in science to establish the natural laws, the regularity of nature. It was Bacon, after Leonardo da Vinci, who theorized it, and John Stuart Mill established a theory of the inductive process. The justification of induction (which starts from the particular to arrive at the general) is an extremely important topic for both science and philosophy. Science uses it to arrive at the general and deduce the particular from it. Science employs the inductive-deductive method.

However, we have established some principles outlined in philosophy, such as the views of empiricists, mainly represented by John Stuart Mill, which are based on the axiom that the course of nature is uniform. According to Stuart Mill, this axiom is a result of experience and thus grounds induction.

A theory is an intellectual construction that encompasses several laws and seeks to explain a sector of reality, whether restricted or expanded. The theory is based on inductions and develops through reasoning.

Modern science, with its great discoveries, has challenged many accepted theories. This fact gives many the impression that science has failed. However, let us never forget that science is not an elucidation of the world but primarily a domination of nature, and its greatest confirmation and strength lie not in the theories constructed to explain it but in the significant value that technology has given it, allowing it to achieve its main purpose: to dominate nature.

If one theory is replaced by another, there are true progress and simplifications in these substitutions that better clarify the facts. What proves a theory is experimentation. With empirical evidence at hand, science has means, superior to philosophy in many ways, to achieve the accuracy of its statements.

Determinism, indeterminism, and indetermination are extremely important topics in modern science. Founded mainly on determinism, which seems to govern macrophysical phenomena, science today tends to consider indeterminism as fundamental in microphysical phenomena because it is impossible to determine them precisely.

The principle of determinism was elevated to science under the influence of reason dominant in scientific analysis. As one of reason’s dearest concepts, we had the opportunity to study it in Philosophy and Worldview.

However, what is not relevant to establish here is that determinism, in its rigid form, is no longer accepted by science, which recently ventured into unexpected territories. Indetermination consists of the impossibility or incapacity to precisely determine a phenomenon.

Statistics and probability are mainly used in social sciences due to the great complexity they present since these sciences involve a modification of the dynamic order, as found in all living things, with the predominance of intensity over extensity. In science itself, the use of statistics and probability is done alongside indetermination, partly explained by the impossibility of reducing the totality of natural phenomena to homogeneity.

These are the logical processes used by science. Based on mathematics, its most efficient working tool, science aims to construct an exact view of the universe.

Article 4 – Culture and Civilization

Spirit is always employed in a broad sense and refers to human psyche, already differentiated from animal psyche, encompassing instinctive activities, affectivity, and technical intelligence. Considered in this way, we can now understand that the so-called sciences of the spirit are those that study the realm of the spirit itself, humanity as the creator of the world of culture, and culture itself. These sciences, such as Psychology, Science of Culture, Sociology, History, Ethics, Language, Technology, etc., are as real as the natural sciences since they occur in time and allow for sensory experience. They are also sciences of experience, but they differ from the natural sciences in terms of their objects, which, as we mentioned, are psychic-spiritual.

While nature is foreign to us, spirit is our own property.

Individual in this context is the psychic unit, while person is the organizer of the spirit. Both coexist within humans and are possibilities and actualities that are constructed dialectically.

There is a constant conflict between the individual and the person. Often, the individual yields to the person when we prioritize what we should do over what we desire by accepting values that we place in a higher hierarchy. It is a conflict between immediate interest and value, and this conflict shapes and strengthens personality.

Culture is the specific world created by humans, and it is their own environment. Culture is the creative work of humans, such as philosophy, science, technology, etc. There is culture when there is a certain unity in creation during a specific period of time; hence, we talk about Greek culture, Egyptian culture, magical culture, etc.

A distinction is made here between culture and civilization. There is confusion between these two terms, and therefore, we will try to explain them.

Culture in general has a dynamic, intensive, heterogeneous, and creative sense.

Civilization is the work that has already been accomplished, extensive and quantitative.

Spengler considered production as culture and the produced as civilization, the works already accomplished. Culture is creative; civilization is the sum of what is created by culture. However, this distinction is not accepted by everyone, and it would be lengthy to enumerate the various meanings and nuances that these two terms assume throughout the history of philosophy, where they are sometimes confused, sometimes distinctly separated, or where this separation is only apparent.

Hegel distinguishes, by accepting that culture is the spiritual objectification, between objective spirit and subjective spirit. The former refers to the ensemble of cultural organisms such as art, science, language, etc., while the latter refers to the creative spirit of culture that modifies and shapes it, etc.

This matter is not settled in philosophy since there are several ongoing debates and conflicting interpretations. We can make some distinctions between the sciences of culture and the natural sciences. The natural sciences demand exactitude, and their logic is monovalent. Yes, it is. And not: “what is, is; what is not, is not.”

In formal bivalent logic, we can affirm that either something is or it is not. In the natural sciences, it simply is. The natural sciences know and assert. At least, that is their intention. It is easy to see that they do not always achieve the desired ends, but that is the direction they aim for: exactitude. In the sciences of the spirit, exactitude becomes more difficult because they work more with the temporal and the historical, not encountering repetitions as secure as those in the realm of science. Here, there is no exactitude that offers a macrophysical phenomenon in comparison to its law. Here, there is only rigor. The sciences of the spirit are sciences whose objects are intensive, different, heterogeneous, qualitative, and varied, while the natural sciences deal with quantities, extents, homogeneities, similarities, sameness, and equality. Therefore, the methods of the natural sciences must differ from those of the sciences of the spirit because the latter works with the individual and seeks in it a constant.

Thus, the rigid concept of law, which loses much of its strength in the natural sciences, is replaced in the sciences of the spirit by the idea of a constant, an invariable, greater or lesser. In short, it finds its true ground in heterogeneities. This is why Logic, in its formalist sense, which holds great value for the facts of the natural sciences, encounters limitations when applied to the realm of culture, where dialectics are more beneficial.

As this distinction has become clear in modern times, remarkable progress can be observed in this field that has not yet exhausted all its possibilities. Much remains to be done, especially since the sciences of the spirit work with the organic, which naturally leads them to follow their own dynamism, whose dynamic order is the inverse of the inorganic order, as we have had the opportunity to examine in our previous works. The methods to be better applied by the sciences of the spirit must vary from one to another. Furthermore, the sense of totality, the sense of the object’s “field” of action, prevents the reduction of psychic facts to one another.

Attempts to reduce psychic phenomena to physical ones, that is, to explain the intensity of those phenomena through the extensity of the latter, have failed. Just as Psychology is not merely a chapter of Biology, nor is Biology a chapter of Physics, because the phenomenon of life does not fit solely within the physical realm. Consequently, Sociology cannot be explained solely as a psychological phenomenon. This irreducibility of the different to the similar, of the heterogeneous to the homogeneous, shows us that there are “fields” of action that, although they operate alongside and among other fields (the same is true in microphysics, and it is what led us to this idea), are not reducible to one another. That is, one is not simply the other but something entirely different. This qualitative aspect, or at least this different field aspect, does not allow us to explain the phenomena of the spirit as mere manifestations of matter, where extensity prevails over intensity, because in the realm of the spirit, an inverse and irreducible finalism occurs.

Philosophy is a broad, systematic or nonsystematic, constructive or nonconstructive knowledge that encompasses the entirety of knowledge to transcend it in a general vision. This statement is not a definition because, given so many definitions, and so disparate, it is better not to define philosophy, which is active, which is dynamic since defining it would confine it within the narrowness of a perpetually limited framework.

As it is now a collection of multiple disciplines, whose objects are increasingly distinct, philosophy forms a general body that may have a transcendent or non-transcendent aspect for some or for others. However, it at least transcends the specific objects of the various disciplines to have, as its object, what we consider the totality and be able to comprehend it in an overview.

All particular sciences are immanent to their object; they never transcend it. When they do, they engage in philosophy.

Whether they affirm the unknowability of being or not, whether they affirm the convenience of seeking it or not, they always philosophize.

Philosophy is thus a desire to know, which is active and dynamic, an unattainable ultimate knowledge because it establishes an ideal: truth, the goal it seeks to achieve. It does not matter that this ideal, like all ideals, is unattainable. Philosophers may despair and construct philosophies of despair, but that will not prevent philosophy from continuing its march, confident in the unexpected, in the unforeseen, which can change the entire nature of the facts. In this unwavering struggle lies the dignity of the philosopher.

Part 2 – “DIALECTIC”

Theme I

Article 1 – Concept of Dialectic

Frequently, the origin of the word dialectic is considered to be the Greek word dialektikê, formed by the prefix diá and logos, from which dialogê (discussion) and the verb dialegeyn (to exchange words or reasons, to converse, to discuss) derive. It also includes the adjective dialektikôs, which means concerning discussion through dialogue.

Consequently, dialectic would be the art of discussion.

However, we prefer to seek an origin based on these two etymologies that is clearer and more consistent with the true purpose of dialectic, which has always been considered, in its eminent sense, as the art of clarification.

The prefix diá indicates reciprocity, exchange, and also implies “through,” which is the most commonly used sense, as seen in words like diaphanous, diameter, diagonal, diastasis, etc. It is also used to denote passage through…

Plato spoke of “a journey through ideas” and used such terms. It is in Plato’s dialogues that we find dialectic employed in its eminent sense most of the time, as a philosophical science that surpasses all others, although on some occasions it also appears as the art of discussing and even the art of deceiving.

In this way, we can distinguish various meanings of the term dialectic:

Pejorative Meanings Eminent Meanings
Art of deceiving; Art of clarification;
Art of merely arguing with Art of discovering the truth
words; through ideas;
Art of merely persuading. Art of discussion.

The way dialectic is judged by its adversaries depends on whether it is employed well or poorly. This is why we see dialectic experiencing its ups and downs in the history of philosophy, in accordance with the old law of alternation. Sometimes it is elevated, as in Plato, sometimes later degraded by Aristotle due to the excesses of the sophists. Sometimes it is elevated in scholasticism and then later lowered during the Renaissance, seen as an art of deceiving or merely verbal discussion. Sometimes it rises again only to fall under Kant’s critique, and then reaches its pinnacle with Hegel. It remains in a state of flux, the highest point in history, despite the exaggerations and misuse that have turned it into an “art of justifying errors.”

In the future, we will see that these exaggerations require us to classify dialectics in order to avoid the confusion employed by many to subvert its true meaning, serving the interests of this or that ideological current. Such activity is far from dialectical.

To avoid further confusion, we wish to clarify this vague term from the outset. In truth, it was Plato who constructed dialectic in its eminent sense. In a pejorative sense, we can accept the attribution made by Aristotle to Zeno of Elea, although it deserves justification since Zeno, with his famous arguments, only sought to demonstrate the fragility of those who attacked the doctrine of Parmenides, nothing more.

Thus, dialectic is the art of clarification through ideas. And clarification, because alétheia, the truth in Greek, which should not be confused with our Faustian concept of truth or with Aristotle’s concept of adequacy, meant illumination, enlightenment, shedding light on what is in darkness.7 Revealing the truth meant seeing it, penetrating through the shadows, and fully perceiving, with the eyes of the mind, the true beauty of things. This was the truth for the Greeks. And since the spirit (nous) possesses reason (logos), it is through reason (dia) that light can emerge, dissipating darkness and revealing the alétheia that all things contain within them.

Dialectic, therefore, works between darkness and light, between good and bad opinions, weighing values and opinions. Its most concrete realization is found in discussion, in reasoning, in moving from one point to another, from one idea to another—hence, in dialogue. In dialogue, opposing sides, positioned differently and facing each other, confront diverse opinions in order to clarify through them (dia). We still retain this meaning when we say that “light emerges from discussion,” meaning that by discussing, by presenting and weighing opposing, contradictory ideas, the final clarification will ultimately arise.

And from opposition, from standing in front of the other (and position in Greek is thesis, and opposition is antithesis), it is not difficult for a composed clarification of both opposing positions to often emerge (and synthesis is composition).

Therefore, it is common for dialecticians, whenever they confront a statement with its contrary or divergent and opposing opinions, to say that such a procedure is dialectical.

By understanding this, it will not be difficult for us to delve into its major themes as long as we accept:

a) Dialectic is the art of clarification through ideas;

b) Every dialectical method involves posing and opposing opinions to observe the results of the clash between opposing, contrary, contradictory, or distinct ideas;

c) Dialectic can be applied not only in the realm of ideas but also in the realm of nature, and it can constitute a worldview, which involves considering the finite being as becoming (a constant coming-to-be), revealing an internal reason for the opposition of orders, etc., while still understanding being as immutable in its essence but mutable in its manifestations.

Theme II

Article 1 – History of Dialectic up to Plato

If we do not find the outline of dialectic as an art of clarification among the pre-Socratics in philosophy, we do find a dialectical thought in the works of Hesiod to Plato.

In Hesiod’s “Theogony,” the study of structures needs to be unveiled amidst its little-understood symbolism. In Hesiod’s genesis, successive differentiations arise from Chaos, revealing a surpassing (an Aufhebung in the Hegelian sense), the becoming (devir) of them into a cosmic, ordered, self-generated form that continues to surpass itself (Chaos, Earth, Heaven…).

This Chaos, the primeval immediacy, like Hegel’s immediate Being, contains everything in the form of a principle and experiences two cosmic revolutions (Chronos and Zeus) in which the being of time externalizes itself, generates Earth, extension, and, by expanding, engenders the third dimension (Tartarus). Hesiod’s creation is an evolution of all forms, with their distinctions, oppositions, and contradictions (Night and Day, Darkness and Light).

In Empedocles, we also find a dialectical thought in the dichotomy (diastema) of the one that creates the multiple, from whose center all directions emerge, like from the center of a sphere, from whose surface we can always move toward the center, the one.

Until Parmenides, metaphysics is naturalized; it is within nature. With him, we move towards a de-naturalization, towards something beyond the physical. Alétheia is obtained by lifting the veil of appearance, where the unique being is hidden in all its splendor. Parmenides cannot be understood without Heraclitus. Let us examine Heraclitus, whose role in dialectic is so important, especially in our day.8

Heraclitus

Heraclitus (ca. 535-475 BC) lived during the Persian Wars and witnessed the struggle of opposites in all sectors of social and economic life in his homeland (Greece), whose internal situation worsened as a result of the clash with the Persians and the conflict between various social classes.

Existence revealed to him the perpetual flow of things, but he accepted that diversity did not prevent them from being one, as he admitted a principle of unity and uniqueness of being. All things originate from the one, and the one from the all.

“This world, the same for all, no one, neither god nor man, made it; but it always was and will be an ever-living fire, kindling and extinguishing itself rhythmically” (frag. 27). “All things are exchanged for fire, and fire for all things, just as goods for gold” (frag. 49). Fire here is a symbol of a fluidic principle, constantly and incessantly creative, rhythmic, ascending and descending constantly (alternating without ceasing).

“The hidden harmony is greater than the manifest, because in it, by virtue of a divine mixture, differences and diversities are involved in obscurity” (frag. 40).

Actual multiplicity reveals a virtual unity.

In the original fire, in the active and creative force of the first substance, opposites are resolved in harmony. Things are born and preserved through conflict (polemos), the “father of all things,” through the opposition of contraries, which alongside the opposite forms harmony.

The unity of opposites is the unity of all things in harmony and justice. Everything flows and is constantly transmuting. There is no rigid, unchanging being, but perpetual flux, eternal becoming, constant movement. Thus, Heraclitus’s dialectic is the dialectic of opposites (“we are and we are not”); every being is opposed to itself because every being is in constant becoming, every being is while becoming.

“Everything opposes itself, and everything agrees with itself when it separates” (frag. 51).

This constant mutation of being is fire because fire is the symbol of being, of being in perpetual flow.

Therefore, “everything flows.” “You cannot step twice into the same river, for fresh waters are ever flowing upon you” (frag. 91).

Parmenides

A great philosopher vigorously contradicted Heraclitus’s assertions and set a direction that prevailed in Western philosophy for twenty-five centuries: Parmenides of Elea. In the controversy with Heraclitus, he deemed his theory absurd because it concluded that a thing is and is not at the same time, as for Heraclitus, being consisted of constantly becoming, of flowing. Parmenides observed in Heraclitus’s idea of flowing, which we can replace with the Portuguese word devir (which means becoming), that being ceases to be what it is to begin to be something else. He argued that all things were in constant becoming, that is, they ceased to be what they were to become something else. If something ceases to be what it is to become something else, at the same time that it becomes something else, it ceases to be something else.

Parmenides identified a logical contradiction in Heraclitus: being is not, and what is, is not. For Heraclitus, what is now is no longer in this moment, as it becomes something else.

Therefore, Parmenides realized that there was a logical contradiction in Heraclitus’s philosophy: being is not, and what is, is not; for what is at this moment is no longer in this moment, as it becomes something else.

Thus, Parmenides concluded that there was a logical contradiction in Heraclitus’s philosophy: being is not, and what is, is not; for what is at this moment is no longer in this moment, as it becomes something else.

So, what characterizes being is non-being. Parmenides considered this idea absurd because how can someone understand that what is, is not, and what is not, is? This idea is unintelligible. Therefore, Parmenides established this principle: being is; non-being is not.

Apart from this, everything else is an error. Furthermore, what changes, what flows, is something that flows, that changes. And if being is only a transition to non-being, it would be incomprehensible, unintelligible. Thus, things have a being, and this being is. And if they have no being, they do not exist because non-being is not.

It is thanks to Parmenides that the fundamental principle of logical thinking was established, which philosophers later called the “ontological principle of identity.” Parmenides’s contribution allowed a series of attributes to be formulated for being, logically derived from the concept of identity. Let’s see: being must be unique. Suppose there are two beings; in this case, what distinguishes the first from the other “is” in the first but “is not” in the second. We would understand, then, that the being of one is not the being of the other, and in this case, we would arrive at the contradictory absurdity of non-being. Indeed, if we admit two beings, we would have to admit a non-being between them, but saying that there is non-being is the same as saying that non-being is, and this is absurd.

In this way, we reach the conclusion that being is unique, one.

We can also affirm that it is eternal because if it were not, it would have a beginning and an end. In this case, we would have to admit that before the beginning of being, there would be non-being. Since we cannot admit non-being because to admit it would be to affirm that non-being precedes being, therefore, being had no beginning, and for the same reason, it has no end because we would admit non-being at the end. This being is also unchanging because any change in being would imply the admission of the being of non-being, since every change is ceasing to be what it was to be what it was not, and in both ceasing to be and becoming, the affirmation of the being of non-being is implicit, which is absurd.

This being is limitless, infinite. It cannot have limits or be in any place because being in one place would give it the character of extension and, therefore, limits, and it cannot have limits because if we admitted them, we would have to admit, beyond the limit, non-being. And if being cannot have limits, it is not, therefore, in any place; it is limitless. Furthermore, being is immobile; it cannot move because that would mean moving from one place to another. Now, since being is limitless and unchanging, it cannot be in any place; therefore, it is immobile.

Plato

Plato (427-327 BC), in response to the relativism of Protagoras, who reduced knowledge to human measures, sought to free scientific method from this subjection.

Founded on reminiscence, Plato wanted to build knowledge upon it. He understood that we can only know what we already have schemata for, which allow us to assimilate it. Plato expressed this viewpoint, which is a familiar expression of knowledge, by admitting that the human soul, before its birth, contemplated the supreme eidetic forms (eide), and therefore knew things because they reminded it of those forms.

Amidst Platonic thought, it is difficult to clearly see what he intended to convey. It is not our task in this book to strip Plato of customary interpretations and reclaim his thought based on his works, which we do in other works.9

However, it is important to understand that Platonic thought has foundations that must be presented within our Western frameworks to allow for easy assimilation.

If we start from a relational standpoint, a corporeal fact such as an apple, for example, has an internal form and an external form. The first is eidetic (eidos), while the second is spatial-temporal and geometric. Morphologically, one apple distinguishes itself from another in its external part as well as the matter that composes it, and so on. But within the relationship of this apple and that apple, there is an internal form that is like the number in the true Pythagorean sense, which gives the essence of the apple, the reason that makes it an apple and not something else.

These forms (eide) of corporeal facts, however, conform to the realization of other internal forms of a more general order, higher forms. If the apple takes the form of an apple, it is cosmic, but the form (eidos) allows other apples to emerge. Following this line of thought, we would arrive at a set of forms (commonly called Platonic ideas), which would be the first, the original sources (archai) of all things—the Platonic archetypes.

All things seek their own good. Even when someone commits evil, they are actually seeking good. In Metaphysics, it can be observed that being is good because everything that attains the fullness of its being reaches goodness. Now, the good that all things seek reveals that all beings aspire to the supreme Good, from which all other concepts—such as truth, beauty, justice, etc.—can be deduced. Thus, this set of supreme archetypes forms the ideal of all things, the supreme aspiration of existence towards which all tend. And things, in their existence, approach these supreme archetypes to a greater or lesser extent, allowing for hierarchical evaluation based on the degree of approximation.

In every entity, there is an impulse towards the supreme good and consequently towards the values hierarchically placed closer to it. We have the order of these values intrinsic to us because it was humans who acquired awareness of the values of goodness, which manifest in other beings through irrational yearnings and blind impulses.

Platonic reminiscence is simply the possibility of actualizing, through consciousness, the yearning for the Supreme Good and the hierarchically placed values.

This reminiscence enables human beings to know, definitively answering the critique of Antisthenes, who claimed that the pursuit of knowledge was in vain because either you already knew what you sought, and therefore should not search, or you did not know what you sought, making it impossible to find because you wouldn’t even know how to do it.

Therefore, to know is to remember, and for Plato, dialectic is the art of remembering, thus a methodology but different from that of Heraclitus. For Heraclitus, motion and the struggle of opposites are the dialectical objects of dialectic, but for Plato, it is the supreme forms from which things are mere copies that more or less approximate the originals. Dialectic is, therefore, a path to be traversed through appearances to reach the reality of forms, thereby unveiling the hidden alétheia through the veils of appearance.

Plato places dialectic at the pinnacle of the classification of sciences because it organizes, classifies, distinguishes, and chooses among the oppositions that find their identity in being.

In “The Republic,” Plato presents his dialectical method, which he details in his “Seventh Letter.”

There are three modes that allow for the acquisition of knowledge for each being, which in itself is knowledge, and in fifth place, the object itself, cognizable and truly real:

The first mode is the name;

The second is the definition;

The third is the image;

The fourth is knowledge.

“Let’s take an example,” Plato continues, "to understand what I have just said and apply it to everything. Circle, here is something expressed, whose name is the very same one I just mentioned. Its second mode is the definition, composed of verb names: it is that which has its ends equidistant from the center, that is the definition of what receives the name round, circumference, circle. The third mode is the drawn circle, then erased, drawn again, then destroyed; but the circle itself, which all these objects correspond to, experiences nothing of the sort, for it is another.

In fourth place, we have knowledge, understanding, and true opinion, relative to these objects. They must be grouped together, as they do not reside in voice or bodily figures but in souls. Hence, it is clear that they are distinct from the nature of the circle itself and from the modes we have just mentioned. Among them, it is understanding that, through kinship and similarity, comes closest to the fifth, while the others are more distant."

And later he tells us, “Whoever cannot, in one way or another, possess these four modes will never achieve perfect knowledge of the fifth.” It is the exercise of all these modes, going up and down from one to the other, which, with great effort, manages to create knowledge.

Plato says, “Dialectical activity is the only science worthy of this name. The dialectical method cannot be reduced or compared to the methods of obscure sciences.”

Subsequently, Aristotle (384-322 BC), who is the coordinator of Formal Logic, was one of the greatest opponents of dialectic in light of the exaggerated verbalism of the sophists. He regarded dialectic in a pejorative sense, to the point where the word became an offensive term for its practitioners.

Nevertheless, Aristotle employed dialectic in the sense of the art of arguing and persuading, as an aid to rhetoric, and thus in a subordinate position to Formal Logic, which he constructed on its foundations.

The Triad in Plato

Among the most important points of Hegelian thought, essential to his dialectic, are the triad (thesis-antithesis-synthesis), as well as his idealistic conception, and the prevalent opinions about the Platonic foundation, or lack thereof, of ideas in Hegel, the origins of which are debatable. The Hegelian triad and the aforementioned themes will be complemented by a study of the Marxist critique of Hegelianism and an analysis of the many confusions made by Marx, Engels, Lenin, and their followers.10

To delve into such significant territory that requires thorough examination, it is necessary to have a constructivist view of Plato’s idealistic conception before we can judge the claims linking Hegel to Plato.

We will also examine the triad in Nicholas of Cusa to be able to visualize Hegelian thought and determine the aspects we promised to analyze above.

We will conclude with an evaluation of antinomian dialectic in light of frequently expressed opinions.

Let us begin, therefore, with a brief overview of Platonic philosophy. First and foremost, we should not separate Plato from the past of Hellenic philosophy and the influences he received from Pythagorean philosophy and, to a large extent, Egyptian influences.

We have already had the opportunity to make certain assertions in other works, and since we do not wish them to be considered the result of hasty judgment, we intend to justify them with some elements that we consider important for the clarification of certain aspects of that philosophy.

For example, we affirm:

a) The Pythagorean influence on Plato, especially regarding the theme of the One and the Multiple, which we examined in a work of our own that we previously mentioned.

b) Concerning the ideas (we prefer “forms”), these are derived from a single form (the Good).

c) The concept of the Demiurge, which is generally understood as an intermediary between the eternal world (the world of truth) and the finite world (the world of appearance), does not imply, in any way, a dualistic or triadic conception of the universe.

d) In Plato, there is a marked tendency (especially in the later phase) towards a unified explanation of the Whole.

Let us examine these four points as quickly as possible.

Plato lived during a multiple and confusing period in Greek life, and furthermore, he was an aesthete who lived philosophy aesthetically.

Being susceptible to all ideas, he experienced them with such intensity that he never remained indifferent to any opinion.

In short, Plato had a firsthand experience of all ideas and he represents quite well the multiplicity of issues in Hellenic philosophy. The enthusiasm of the Platonic characters clearly reveals their experiences. For us, Plato was a philosopher in the most potentialistic sense of the term because he was capable of living, with the utmost intensity, all the moments of philosophy known up to that point and all the themes and problems that stirred Greek thought.

Therefore, it is difficult to establish a rigorous system in his works. However, in our view, the oppositions are not irreconcilable.

Plato exemplifies what we later came to understand in Nietzsche: the ability to experience the multiple, to be multiple without ceasing to be Plato or Nietzsche, in other words, preserving authenticity when examining diverse theses.

The influences that Plato received from Heraclitus, Pythagoras, and Parmenides reflect the universe of Greek philosophy.

For that reason, it was a culminating moment in that philosophy. An analysis of all these influences would be unnecessary since it would not contribute to the study we wish to undertake.

What remains is for us to present, in broad terms, the basis of our assertions.

The Pythagorean influence is undeniable. According to Plato, the divine artist, the Demiurge, in order to create the world, consulted the eternal realm.

Are the forms created by God or do they exist in and of themselves?

We will dispense with the controversy based on Plato’s own works, where this contradiction is evident. But to claim, like Brochard, that there is no statement in Plato’s works affirming that the forms were created by God is incorrect, for in the “Republic,” we read a passage where Plato affirms that God is the creator of the forms.

However, subsequently, in the “Timaeus” and throughout his works, this affirmation is not reiterated. On the contrary, the forms are presented as existing in and of themselves.

We know that for Plato, the highest form is the Good, and all other forms emanate from it. In the “Timaeus,” the cause of creation is the Good that exists in the Demiurge. Because it is good, the Demiurge desired to bring order to chaos and enliven the world. The Demiurge shapes the world through itself because it is good. The opinions of Thomas Aquinas and Stallbaum and the attempted reconciliation by Lutoslawsky do not imply absurdity or naiveté.

But let us first see how Plato conceives the forms and their hierarchy. Let us reproduce a famous passage from the “Republic”: “Among the heavenly gods, who do you believe to be the cause and author of this, whose light enables our sight to see in the best possible way and the visible objects to be seen?...”

This being is the Sun. And Plato continues:

“… Now, can you say the same thing I believe about the offspring of the Good… that is, in the intelligible sphere, it becomes, for the intelligences and the intelligible objects, what this sun is to the visual sphere, for the eyes and the visible objects…”

And further:

“— The sun, you will say, I think, not only provides visible things with their growth and sustenance, although it is not their birth, etc… And it affirms that the cognoscible things not only owe their being known to the Good but that from it, they derive their being and essence, without the Good being the essence; on the contrary, it remains superior to the essence in dignity and power…”

And later he says:

“In the sphere of the cognizable, the idea of the Good is the furthest away, and one must strive to see it; but once perceived, it must be understood that it is the cause of all things just and beautiful, and in the visible realm, it engenders light and its author, and in the intelligible realm, it itself is the author and producer of truth and intelligence.”

For Plato, the forms are both one and multiple simultaneously. In the “Parmenides,” he says: “It would not seem strange to me… if someone were to demonstrate that all things are one because they participate in the One, and that these very things are multiple because, vice versa, they participate in the Multiple. But if he were to demonstrate that the One (the form) itself is multiple and that these very multiples are one, that would truly amaze me.”

"In what way… being each one always one and the same… firmly united in its unity, should it be considered simultaneously dispersed in engendered things, infinite and multiplying, and wholly intact in itself, separately: that, to me, seems the greatest impossibility. In other words, that the identical and the one are simultaneously engendered in one thing and, in many things, at the same time (“Philebus”). But the ancients, who had more value than us and were closer to the gods, transmitted to us the following oracle: that beings, of which it is said that they exist eternally (forms), stem from the One and the Multiple, and they bear, congenitally within themselves, limit and infinity (“Philebus”).

“Therefore, the One, being one, is in a certain way one and multiple and whole and parts, and finite and infinite in multiplicity (Parmenides).” “But it is necessary… not to apply the idea of the infinite to plurality before having recognized, for it, number as the means between it and infinitude” (“Philebus”).

The world of Platonic forms is not a motionless world, as Aristotle himself and Plato affirmed in the “Sophist” and the “Philebus.” The forms are alive. Through them, we also reach the Supreme, the Good. Measure preserves the mixture, Beauty is the proportion by which the mixture is perfect, and ultimately, Truth is the condition of ontological reality.

But these three forms show us the Good, the cause of the mixture and the goodness of the mixture. The hierarchy starts from there. The closer they approach, the more hierarchically lowered they are. The Platonic god is a mixture of forms. But mixture is synonymous with participation: the Platonic god participates in the forms, and in this case, we refer to the Demiurge, the mixture of forms, for it is the participation in the forms that constitutes it.

The form of the Good is above Essence and Being, as we have seen. There lies the supreme Platonic God, from which everything is born.

In general, in the critique of Plato’s work, it is customary to see the triad: Forms — Demiurge — Matter.

According to our constructive synthesis, the second is reduced to the world of forms by being a mixture of them, and these are the manifestations of a supreme form, that of the Good.

Now we come to the third element: Matter.

Platonic critique sees it as something separate from form. But is this general assessment correct?

In the “Timaeus,” there is a very expressive passage that we wish to reproduce:

“By saying that (matter) is an invisible and shapeless species that contains everything, it participates, in a certain way — which is very difficult to comprehend — in the intelligible; by saying this, we would not be mistaken.”

Brochard comments on this as follows: “Matter is, therefore, a genus that participates in the Intelligible. Doubt is decidedly not possible in our view: unquestionably, we find ourselves here not only in the presence of the Other, but of the very idea of the Other, that idea which, in the “Sophist,” is identified with Non-Being. And isn’t the expression aposôtata curiously evident if we recall the laborious efforts undertaken by the author of the “Sophist” to demonstrate the existence of Non-Being?”

Plato’s synonymy for matter is extensive, a synonymy common to philosophers of this category, combining both the aesthete and the philosopher.

Now, the Platonic doctrine asserts that outside of form, there is no other reality. Matter is not something separate from reality, but merely Non-Being. The difference lies in one being the model and the other being the copy. But the copy cannot be entirely different from the model; rather, it is, to some extent, identical to the model, for otherwise, it would not be a copy.

To summarize: in the world of forms, they exist separately as intensive manifestations of the supreme form, the Good. The Demiurge is constituted by this mixture of forms when necessity follows Intelligence. To avoid the confusion and chaos of mingling forms, the Demiurge, being good, imposes order that molds the chaos, the boundary of the real world. It is the possibility of forming all combinations that, when formed, constitute matter, perpetual change, eternal becoming, the Proteus of Hellenic mythology that assumes all forms, which diverges precisely from the Aristotelian conception, although this conception establishes a relationship between form and act, to which all apparent reality must owe itself.

We know that interpretations of Plato’s works vary greatly.

The one we propose is merely a possible constructivist sketch, and we do not, however, want to attribute it to Plato’s “total” intentions. And this is for a very simple reason: being an aesthete, he lived with great intensity the various philosophical visions, such as those of Pythagoras, Heraclitus, Parmenides, and Socrates.

Thus, he went through different phases, but that is not the subject of study here.

However, these assessments we are making now become necessary for future analyses, when we will often need to refer back to his opinions.

The evolution and complexity of Western philosophy, still dominated by the Parmenidean identity, prevent us from fully understanding Plato in all his specific and antinomic character.

But these antinomies, as in the case of Nietzsche, are largely reconcilable. And in both cases, we must never forget that they were aesthetes in philosophy, which predisposes one to synonymous and symbolic language. These aspects create many difficulties for philosophers and students of philosophy who are concerned with the determination of terms, as they become entangled in a network of fixed, formal concepts that are often inadequate for situating philosophies like those of Nietzsche and Plato.

Article 2 – From the Middle Ages to Nicholas of Cusa

It is not easy to delve into the study of dialectic among the Neo-Platonic Pythagoreans and Neo-Pythagoreans, as this is one of the most controversial fields of philosophy, filled with falsifications of thought, misunderstandings, and erroneous interpretations. We find ourselves in a tangle of mutual misunderstandings, especially in certain Western authors of the past two centuries who have written about philosophy. Due to their lack of clear understanding of both Platonic and Pythagorean thought, based on one disciple or another, they interpret these currents and ideas according to their own frameworks, thus contributing to further confusion.

In order to clearly present dialectic through these currents, whose role is more significant than commonly believed, we would have to write a special work where we could detail our affirmations that, in rare instances, coincide with the common explanations given by analyzers of these currents. These analysts perpetuate errors that are repeated by others. This is indeed an important point in philosophy: to highlight the errors that persist through textbooks—interpretation errors, cunning lies, caricatures, and distortions of a philosopher’s thought—that are later repeated solemnly in philosophy lectures.

The study of dialectic in scholasticism, from its origins in patristics to its development through Thomas Aquinas and Duns Scotus, and then through Suarez and the Coimbra school up to the present day, also deserves special attention.

As we have seen, dialectic partially merged with formal logic, as certain methodological aspects that had already been acquired were utilized. Scholasticism, the high point of Western philosophy, is also misunderstood and poorly presented by teachers and philosophers who were educated in the spirit of the 18th and 19th centuries.

These giants of philosophy, such as Saint Augustine, Albert the Great, Thomas Aquinas, Duns Scotus, Suarez, Fonseca, Saint Bonaventure, and others, include in their works moments of broad and profound dialectical insight.

An examination of Saint Thomas Aquinas' “Summa Theologica,” for example, or Abelard’s “Sic et Non,” reveals the meticulousness of dialectic in presenting opposing ideas to establish a final synthesis. These thinkers employ an analysis of oppositions with such firmness and mastery that we cannot help but benefit from the great methodological lessons they offer, which we will have the opportunity to examine in our subsequent work.

In Albert the Great’s exploration of opposites, such as God as the unity of two species of truth synthesized in him (the principle of double truth), we encounter a dialectic-analytical development of such proportions that those who study dialectic should not overlook or ignore.

Furthermore, within the mystical movement in the Church, from Dionysius the Pseudo-Areopagite to German and Spanish mysticism, we also find dialectical thought alongside a certain methodology that enriches this emerging discipline, which has not yet yielded all the fruits it is capable of producing.

Dialectic, which experienced periods of ebb and flow during the so-called Middle Ages and the Renaissance, reached an entirely new level with Nicholas of Cusa (1401-1464), one of the greatest figures in philosophy.

According to Nicholas of Cusa, knowledge has four levels:

  1. Sensation and imagination can only grasp indeterminate and meaningless images.
  2. Reason distinguishes these images from one another and gives them names.
  3. The intellect endeavors to unite the separated opposites resulting from reason’s distinctions into higher units, into general notions.

Considering these three levels, we see that knowledge of reality through concepts is imperfect. Truth is unattainable, but we can approach it through constant pursuit of knowledge. Hence, we conclude:

  1. The highest knowledge cannot be obtained through concepts. “Learned ignorance” (docta ignorantia) recognizes this limit of our knowledge. Only direct, intuitive knowledge would give us the truth, the vision of truth. However, since consciousness is not excluded, it cannot be considered a mystical vision in the common sense of the word. Instead, it is an aesthetic sense of what is symbolized, a technique of penetrating the hidden through symbols. The Greek root myō (hidden) gives us mystos (the initiate in the mystery), mistagōgos (the guide), and thus mystikē (the technique of penetrating these mysteries, of what is hidden).

Unconscious mysticism is different from conscious mysticism, and the vision of God, which is truth (visio Dei), is conscious—it is absolute knowledge. God is the coincidentia oppositorum, where opposites coincide, meaning that in the infinite realm, the opposites of the finite world disappear. God is unity, but not number, because God is not numerical (according to Pythagorean principles, number only exists where there is the multiple, and the one and only God is not number).

Thus, God is the beginning and end of all things. Multiplicity exists in God as possibility (complicatio), from which the external world is merely an outward manifestation (explicatio).

In this way, God is the act and power of everything, as God encompasses everything that can be. God is the Possest, qui in omnibus partibus relucet totum, shining as the whole in all parts. The unity of the universe appears in three modes of existence:

  1. As absolute possibility or necessity.
  2. As limited necessity or reality.
  3. As the union of possibility and reality.

For Nicholas of Cusa, opposites are present in all existence; they separate within existence but coincide in the whole, in the Possest, which is God. Nicholas of Cusa’s thought influenced Giordano Bruno and Spinoza, whose dialectics also present us with the same vision of implicatio, explicatio, complicatio.

The characteristic of the Thesis-Antithesis-Synthesis triad in Marx is the succession of these terms. According to Marxist dialectics, as we will see, the antithesis follows the thesis, which, in turn, is replaced by the synthesis.11

It is immediately apparent that Marxist dialectics only concern themselves with “otherness,” neglecting other important aspects that we will have the opportunity to examine in the future.

"For Nicholas of Cusa, God (Possest) is the Maximum and the Minimum.

If the Maximum is that which is such that nothing greater can exist, and the Minimum is that which cannot be smaller, then God, as the absolute Maximum, is everything because He is everything, He is One.

He contains everything because He is the Maximum; if He did not contain everything, He could be greater and would cease to be the Maximum. And since nothing opposes Him, the Minimum coincides with Him. Being absolute, He is, in actuality, all possible being.

"...The absolute Maximum, being all that can be, is entirely in act, and as He cannot be greater, He cannot be smaller either, for He is all that can be. Now, the Minimum is that which cannot be smaller. Since the Maximum also corresponds to this definition, it is clear that the Maximum and the Minimum coincide.

This becomes even clearer when we reduce the Maximum and the Minimum to their quantitative aspect. The maximum quantity is, in fact, the greatest magnitude, and the minimum quantity is the smallest magnitude.

Let us consider the superlative quality without any quantitative consideration, abstracting it, through understanding, from the large and the small. The coincidence of the Maximum and the Minimum then becomes intuitive truth. The Maximum is superlative, just like the Minimum. An absolute quantity is not predominantly maximum rather than minimum, for in it, the Maximum is identical to the Minimum in the sense in which they coincide" (Causa “Docta Ignorantia,” Chap. IV).

God (the Possest) contains, in actuality, everything that exists in potentiality in an absolute manner, to such an extent that even the minimum can coincide with Him. He also transcends all affirmation and all negation.

"All that we conceive Him to be is not more true when we affirm it than when we deny it; all that we conceive Him not to be is not more true to affirm that He is not than to affirm that He is.

He is not thus a certain thing but rather being all things, and yet He is not all things except when He is none of them. He is not the Maximum of this or that unless He is equally their Minimum." Furthermore, it is added: "Such truths transcend the power of our understanding. Our understanding cannot, through rational methods, attain the synthesis of the contradictories in their principle; we progress only through truths that are naturally evident to us.

Now, reason only participates in infinite power to a very limited extent, and the contradictories themselves are separated from each other by an infinite distance; reason is thus powerless to simultaneously grasp them in their synthesis.

However, the fundamental characteristic, and it would be lengthy to demonstrate this through the reproduction of texts, is that for Nicholas of Cusa, unity precedes otherness.

Indeed, otherness implies change. That which naturally precedes the potentiality of change is itself unchangeable and therefore eternal.

“Otherness presupposes the presence of the One and the other. Just like number, it follows unity; therefore, unity is naturally prior, and as it naturally precedes otherness, it is eternal.”

Therefore, unity is synthetic, and the realities united to one another are also synthetic. The dyad emerges as division, the first division. If unity synthesizes, the dyad divides.

As unity naturally precedes the dyad, synthesis therefore precedes division; division and otherness naturally go hand in hand. Thus, synthesis is no less eternal than unity since it precedes otherness. “Unity… is not the name of God in the strongest sense. For it is the movement of reason that imposes names on things to distinguish them, and reason is inferior to understanding. Since reason cannot surpass contradictories, there is no name to which another name does not oppose it, following the movement of reason. This movement opposes unity to polarity or multiplicity. Consequently, Unity does not apply to God, unless it is a unity that is not antithetical to otherness, polarity, or multiplicity.”

For Nicholas of Cusa, nature is the synthesis of absolute necessity, from which it arises, and contingency, without which it does not exist. “God is opposed to nothingness, and being is the middle term between them.”

However, nothing can be composed of being and non-being. It seems, therefore, that the creature is neither being because it represents a fall in relation to Being, nor non-being because it precedes nothingness, and yet it is not a compound of the two. It is not possible to provide an extensive analysis of the books of the famous cardinal in a few words, but the scheme we present here of his dialectics reveals the principal aspects that are sufficient for a clear understanding of his thought.

Every unity is a synthesis of opposites. God, as the Maximum and the Minimum, is the synthesis of opposites. It is the “coincidentia oppositorum,” transcending all affirmation and all negation. “Now, if Aristotle had interpreted the principle he calls privation in such a way as to designate the principle that constitutes the coincidence of opposites by calling it privation because it is deprived of any form of contrariety while preceding the duality necessary for the existence of opposites, then his doctrine would have been correct. But he feared conceding that the opposites could coexist inherently in the same reality and thus close the path to the true knowledge of the synthetic principle.”

In this last sentence lies one of the foundations of dialectics, which we will further explore in the following pages.

Article 3 – Kant, Fichte, and Schelling

With Kant, following the contributions of Bacon, Giordano Bruno, Hobbes, Leibniz, Rousseau, Wolf, in which they all sought to study and resolve in a synthesis the fundamental opposition of nature or that of the spirit, dialectics is considered as a “logic of appearance,” and this is the sense he employs when he constructs his “transcendental dialectic,” where he seeks to show that from the false application of categories, man constructs a transcendental appearance, the illusion of reason that he wishes to destroy. In the examination of the antinomies, which we have already studied in Philosophy and Worldview, Kant seeks to demonstrate the weakness of reason and its impossibility to resolve the most important problems of cosmology.

However, these antinomies of reason also reveal themselves in existence, in the antinomy between the self that seeks an ideal and the empirical, practical self.

In Fichte (1762-1814), we find important elements for the formation of Hegelian dialectics, which are of great interest to us due to their significant influence on current thought.

For Fichte, “the self postulates itself, through the force of simple postulation.” This would be the thesis and the antithesis, starting points of his dialectic, and the opposite of this self is the non-self. The self, affirmed, postulates the principle of identity; the non-self, affirmed, postulates the dialectical principle of contradiction. The synthesis is formed by accepting that the non-self is contained within the self. This opposition between the self and the non-self does not result in the destruction of the self by the non-self; the self continues to exist; they merely limit each other reciprocally. From this limitation arises divisibility and consequently, the concept of quantity, from which Kantian categories of reality, negation, and limitation derive.

With Schelling, “dialectical thought is characterized by accepting a dialectical unity of the world, a positive and a negative principle, and these two forces, in combat, united and present in the course of the struggle, lead to the idea of a principle that transforms the world into a system, the idea of the world soul.” Nature is visualized as both a producer and a product; it produces itself, infinite in its activity, finite in its products. Nature tends toward the absolute and represents the absolute in its continuity. Thus, species is not limited; it is the individual that is limited because the species can always actualize itself in individuals.

It is with Hegel, the climactic moment of dialectics, that it takes shape with the characteristics of modern dialectics. We will proceed to study him, and in the development of the analytical part, we will have the opportunity to refer to the contributions of his philosophical thought to the construction of the current state in which we find this important discipline, whose principal fruits have not yet fully matured.

Theme III

Article 1 – Hegel and Dialectic

With Hegel, dialectics returns to its favorable sense. He defines it as “the very and true nature of the determinations of understanding, of things, and, in general, of everything finite.” It consists essentially in recognizing the inseparability of contradictions and in discovering the principle of this union in a higher category.

Hegel accepted the existence of God, and for him, the ontological argument was sufficient.12 The essence of Being implies existence because claiming that Being does not exist would be a contradiction in terms. But it would also be contradictory to admit the existence of any form outside of Being. Thus, for Hegel, everything is Being. God is the Absolute Idea, an idea that is, in and of itself, independent of a spirit that conceives it because Being, by essence, exists in and of itself. But this Idea is pure indeterminacy.

It determines itself in nature when it externalizes itself because to determine oneself is to become something in the world. Thus, the Idea becomes other, reaches the state of alterity (being another). This world, which is the Idea, in its alterity, in its moment of highest tension, the limit of its being-other, evolves until the appearance of man and thought, through which the Absolute Idea becomes self-aware, initially in the form of subjective or individual spirit and then in the form of objective or collective spirit, through the forms of family, various societies, and the State, to finally return, after this great cycle, after going through the successive moments of its alterity, to the absolute, to the unity of Spirit, to the absolute idea that had dispersed in nature, to become self-aware.

Thus, Spirit (the absolute idea) goes through a dialectical cycle of being-in-itself, as subjective spirit, becomes outside-of-itself, or for-itself, as objective spirit, to become being-in-itself and for-itself, as absolute spirit.

Hegel expresses it as follows: “Spirit has the certainty of finding itself in the world, that the world must harmonize with it, and that, as Adam says of Eve, she is flesh of his flesh, the reason it must seek in the world is only its own reason.”

Now let us briefly examine Hegelian dialectics.

Hegel distinguished two kinds of reason: “abstract reason,” which operates on abstractions, separated from reality, such as that of mathematicians; and “concrete reason,” which operates on reality itself, such as that of physicists, etc.

The former is based on the principle of non-contradiction, which we have already studied in Logic. The same does not apply to concrete reason. We do not obey the laws of logic when we reason. Instead of moving from the same to the similar, we move from the same to the other, to the different. We need contradiction because the spectacle of the world shows us contradictions, differences, and diversity that excite us. If we compare one thing to another, it is because we acknowledge the different, for we would not conceive of the similar, the alike, the equal if we did not have an intuition of the different, as can be easily verified. In this way, the spirit accepts the similar and the different, and in grasping it, we have intuition and reason, and this, in its abstract phase, is abstract reason. Just as our mind proceeds, the same occurs in nature, which is the exteriorization of the idea, in the Hegelian sense. In nature, we observe a struggle of opposing forces.

Reality is both identical and contradictory. Let us listen to Hegel: “In the face of it, identity is the determination of the simple immediacy of being, while contradiction is the root of all movement; it is only because a thing has a contradiction in itself that it moves, that it has an impulse and an activity.”

The reconciliation of opposites, both in things and in the mind, constitutes dialectics for Hegel. The dialectical process consists of three moments: thesis, antithesis, and synthesis. Let us see how Hegel explains it: "Being is; this is the affirmation or thesis. But it is a completely indeterminate being, without being this or that, which is equivalent to nothingness. Thus, we have a negation or antithesis, ‘Being is not.’ But the indeterminate being, which is and is not, becomes determinate, becomes determinate being, and this becoming is the synthesis of the two because it negates the affirmation and negates the negation. In this way, the synthesis overcomes the contradiction but preserves the two opposing propositions. This is what Hegel calls ‘Aufhebung,’ an untranslatable word in our language, which means superseding and preserving at the same time. But the synthesis is not definitive because the being, which determines itself, by determining itself, negates the previous determination, and thus the series of theses, antitheses, and new syntheses continues. Thus, in dialectics, it is a pure and simple reproduction of the transformation of things. It describes, in this way, a dialectic of things, and when one idea elicits the opposite, it is because reality, represented by the idea, demands the contrary reality.

For Hegel, Logic is the “science of pure thought.” And logical considerations “are not really things in their materiality but the essence of things, their concepts, which acquire the quality of an object.”

Metaphysics, then, would be, for Hegel, the “a priori knowledge of reality in itself.”

The thinking subject is the Self. Hegel places it as follows: “As self-consciousness, the Self intuits itself, and its pure expression is: I + I, or I am I.”

“Self-consciousness is being-for-itself as complete and self-positing; the side of relation to another, to an external object, is removed. Self-consciousness is thus the nearest example of the presence of infinity…” Self-consciousness is an entry into oneself from consciousness itself. It does not consist of the identity I + I since it requires consciousness beforehand. There is the prerequisite of the external world and the transformation of oneself as an object, which implies an affirmation and an interior negation, one and the other. Self-consciousness is one and the other consciousness simultaneously, as Hegel explains.

Let us illustrate: Self-consciousness, of the Self, occurs when it isolates itself from others, when it removes the relationship with others. In this way, the Self, not receiving the limits of others that would render it finite, sets an example of the presence of infinitude. Self-consciousness starts from itself, not requiring beforehand the identity I + I. But for this to happen, the external world is indispensable beforehand because no one would become self-aware without being in an external world that precedes it. Therefore, self-consciousness affirms itself and negates the external world, which is not itself.

The limit, by its nature, is both itself and not itself, other than itself. When we think about ourselves, the Self actualizes itself by becoming other than itself.

Let us clarify:

The limit is the boundary, and the boundary separates two things; one and the other. Therefore, the limit, between one fact and another, is itself and is not itself because it is the limit of this fact and the limit of that fact; it is one and also the other. Thus, when we think about ourselves, we divide ourselves into the thinking self and the self that is being thought, unfolding into subject and object. The Self, which we actualize as an object or as a subject, already becomes other to the other.

The contradiction that is evident in the Self, as we have explained thus far, also reveals itself in the rest of existence.

Things present themselves as opposition, as contrariety, as contradiction. The opposition of contradiction arises in the thing, whose being presents itself to itself as content and repels itself from itself.

“It is, however, a fundamental prejudice of traditional logic and common thinking that contradiction would not be as essential and immanent a determination as identity. But in truth, if it were a matter of hierarchy, and if the two determinations were to be kept separate, it would be necessary to consider contradiction as the deepest and most essential. Faced with it, identity would only be the determination of simple immediacy, of dead being, while contradiction is the root of all movement and all life. It is only because a thing has a contradiction in itself that it moves, that it has an impulse and an activity” (Logic, p. 67).

“This thought, that contradiction is essentially and necessarily placed in reason by the determination of understanding, marks the most important and profound progress of modern theology. The more profound this viewpoint, the more superficial is the solution to the antinomies. There was a kind of tenderness for the world; it was thought that contradiction was a flaw in it and that it should be attributed to reason, to the essence of the spirit. One will easily recall that the spirit encounters contradictions in the phenomenal world, that is, in the world as it appears to subjective thought, to sensibility and understanding. But when the essence of the world is brought close to the essence of the spirit, one is astonished at this kind of ingenuity and humility with which it is affirmed that it is not the essence of the world but only the essence of thought that contains contradiction. It is believed that the difficulty can be avoided by saying that reason falls into contradiction only through the application of categories. But it should be noted that this application is necessary, that reason has no other determinations as its content except the categories, for knowledge: it is, in fact, having a determining and determined thought; an empty reason, an empty thought, thinking nothing. One wants to reduce reason to the thought of an empty identity; we will indeed free it from all contradiction, but at the same time, we will strip it of all reality and all content. The essential point (which must be noted here) is not only that there are four antinomies (Kant), but that they exist in all objects, of whatever nature they may be, as in every representation, every notion, and every idea. Establishing this point and recognizing this property in things is the essential object of philosophical investigation” (Hegel — Logic, pp. 54-55).

It is not the role of philosophy to solve the problem by accepting the principle of identity and rejecting the principle of contradiction in dialectics, which should not be confused with the “principle of non-contradiction” of formal logic, but rather to understand the coherence between the principle of identity and the principle of contradiction. Thus, as a conclusion, unity is inherent in multiplicity, as we will see further.

Hegel distinguished the “good” universal from the “bad” universal. The former is that of Formal Logic, emptied of all factual content, and the “good universal” is the one that is not emptied of its concrete content, the individual as the actual universal, in which the individual and the species do not exist separately from each other, now fused into unity.

The concrete universal, when apprehended, gives us synthetic knowledge because we not only know the individual, intuitionally through sensory activity but also eidetically and intuitionally, as in Bergsonian intuition.

Having established this point, we can understand the dialectical process.

“The dialectical process is, in the sphere of Being, the transition into another, and in the sphere of Essence, the appearance in another. The movement of the Concept, on the other hand, is development, through which only what is already present in itself is posited” (Hegel, VIII, p. 161).

Let us clarify:

The content of concepts is given to us by sensibility, by cosmic becoming, which shows us the infinity of time-space relations. Thus, the awareness of spirit is only realized when consciousness is placed in Nature.

Hegel did not claim that abstract thought gave rise to the reality of things. Nature is always given in Hegel, and thought implies Nature because it is in Nature that it actualizes itself.

In the sphere of being, the transition of the dialectical process occurs in the passage from indeterminate being to determinate being, which, by determining itself, becomes other than the first. Let us exemplify with a potentiality that becomes actualized: before, it is indeterminate; when actualized, it becomes determinate, it undergoes the transition because it becomes different from what it was. When actualized, it is no longer potentiality. It denies the previous situation but also affirms it because, by becoming actualized, it confirms the possibility. In the sphere of Essence, the transition of the dialectical process occurs in the appearance in another, which forms the essence of what appears.

Hegel is generally accused of constructing a closed system. However, in the “Greater Logic,” we find the following words: “How could I think that the method I follow in this system of Logic… is not capable of many improvements; but I also know that it is the only method capable of truth. And this is evident from the fact that it does not differ in anything from its object and its content, for it is the content itself, dialectics, that propels it forward” (p. 51).

Being and Thought in Hegel

The identification of being and thought in Hegel’s Logic could be explained as follows: The universal inherent in the known thing is immanent to it, just as the species is in the individual. In the individual, the universal becomes singularized. Our reason disregards this singularity to consider universality. Integrating this singularity back into thought is one of the characteristic aspects of Hegelian dialectics. Reason considers singularity irrational because, as singularity, it is non-rational (non-universality, and let us never forget the universalizing activity of reason). And since Hegel accepts that singularity can only be grasped through affectivity or sensory intuition, through sensibility, he appears as an irrationalist due to such affirmations.

For him, the true universal is the concrete universal, the synthesis of the universal and the individual, and this unity is revealed to us by the object itself.

According to Kant, knowledge results from the activity of the subject, which imposes a priori forms taken from sensibility on things. The categories themselves arise from this activity. But Hegel sees these categories as forms of thought activity, whose selection is purely rational. One category implies another; therefore, when one category is given, the others necessarily follow. Thought, to posit itself, requires the whole set of categories. It does not need the thing-in-itself to explain knowledge; the movement of thought is sufficient, and it is by positing the “otherness in itself” that thought limits itself. The act of thinking is a departure (it is intentional), a return from there to oneself. By relating the determination it placed outside of itself to itself, the act of thinking is activated.

Hegel’s absolute is the unity of the finite and the infinite, and thought, thinking about itself, accomplishes something analogous to God, and logic is thus a kind of “itinerarium mentis ad Deum” (journey of the mind towards God).

Reason and Knowledge

In his critique of Reason, Hegel shows us that reason can only universalize a precept by detaching it from the historical and concrete totality to which it belongs.

Hegel reproves modern science for considering material forces as purely quantitative, thereby removing from nature its “also irrational” character, which led it to stubbornly look at categories and laws separate from the inexhaustible activity of life, contrary to the Greek sense of creative Eros, the mysterious sympathy that unites the soul with the universe.

In the Encyclopedia, he says: “Under the action of thought, the richness of nature’s infinitely varied forms becomes impoverished, its springs wither, its toys of colors fade. The noise of nature’s life is silenced in the silence of thought; its warm fullness, which unfolds in a thousand graceful miracles, dries up into lifeless forms and amorphous generalities resembling a cold northern breeze” (pages 37-38). And further: "The content is pulverized, shattered, isolated, deprived of intrinsic connection, and therefore finite. Let us take, for example, a flower; reason points out its particular qualities, chemistry decomposes and analyzes them. We thus distinguish: color, leaf shape, citric acid, ethereal oil, carbon, hydrogen, etc… We say: the flower is composed of all these parts. Chemistry calls this ‘encherisis naturae.’

It mocks itself and knows how it has the parts in its hands; unfortunately, it lacks the spiritual bond," as Goethe says. The spirit cannot linger in this conceptual reflection" (p. 45).

The analysis of knowledge decomposes by assimilating abstract schemas, but the fact, as tension, is qualitatively different as a whole, although it is composed quantitatively of the parts that structure it, as shown in the “General Theory of Tensions” we presented.

When Chemistry says that it knows a body because it is composed of carbon, oxygen, etc., it offers analytical knowledge because it goes from the individual to the universal. Synthetic knowledge, on the other hand, starts from the universal to the individual, as observed in historical sciences, where the individual is intelligible only in its relation to a preceding totality. These two forms of knowledge pass into each other. Knowledge that breaks down the object, such as analytical knowledge, can only attain existence through a process of abstraction and reciprocal separation, and the part can be thought through differentiation from the other parts. However, the spirit must keep the ideal totality of the thing in mind to determine the respective aspects that allow for their separation from each other.

Now, the known thing is other than itself (universal) and at the same time itself, and there we have the transition from analytical knowledge to synthetic knowledge.

Hegel finds the transition from the thing into another in the definition, as it goes from its immediate existence to acquire universal value.

Through knowledge, the subject affirms a given content of consciousness, which, however, is other to it, but to which it now grants objective and universal value. But this other is posited as identical to the subject, an act by which transcendence of otherness occurs. Through knowledge, the subject goes beyond itself to an existing being that it recognizes as different from itself, but this movement of going beyond is also a movement of entering into oneself because knowledge is a transcendence, but a transcendence to the self due to the elevation of the thing to the universal.

Idealism for Hegel

Hegel always opposed subjective idealism, the “bad idealism,” claiming for himself a concrete idealism. Thus, Hegel is a real-idealist. Let us hear his words: “The proposition that the finite is ideal constitutes the basis of what is called idealism. Philosophical idealism consists solely in refusing to recognize true existence in the finite. Every philosophy is essentially idealism (or at least has it as a principle), and the question is simply to what extent it goes in the application, in the development of this principle. Philosophy has something in common with religion here since religion also refuses to recognize true being in finitude as something final, absolute, unplaced, uncreated, eternal. Consequently, the opposition of idealist philosophy and realistic philosophy is meaningless. A philosophy that ascribed true, final, absolute existence to finite existence as such would not deserve the name of philosophy.”

“However, it is also necessary to conceive being in itself in general as ideality, while existence is precisely designated by the name of reality (Realität). Generally, ideality and reality are considered as two determinations placed with equal independence face to face, and it is said, according to this way of conceiving it, that besides reality, there is also ideality. However, ideality is not something that exists outside and alongside reality; the notion of ideality consists expressly in this: that it is the truth of reality, which means that reality produces itself as ideality by positing that it is in itself. Therefore, one must not imagine that ideality has been deprived of what belongs to it when one simply agrees that there is, besides reality, also ideality. Such an ideality that would be alongside or constantly above reality would indeed be nothing more than an empty word. Ideality only has content when it is the content of something. And that something (Etwas) is not an indeterminate here or there, but determined existence as reality, existence that, considered in itself and finite in its limits, has no basis of truth.”

In the Encyclopedia, Hegel seeks to equate knowledge with the totality of the real and seeks to integrate nature into the totality of the real.

The unity of the subject + object, ideal + real, finite + infinite, soul + body is the idea that expresses the becoming of what has already become.

“The idea is the adequate concept, the true objective, or the true as such. If something has truth, it is only in the idea or something has truth only to the extent that it is idea” ...; “… all reality only exists to the extent that it has the idea within itself and expresses it.”

The idea is the unity of concept and reality. It is an activity that determines itself but remains within itself in its determination.

The idea is not abstract in Hegel, as many think: on the contrary, it is concrete. In response to the criticisms made against him, he said these words:

“A common prejudice is that philosophy deals only with abstractions, pure universals, and that intuition, our empirical consciousness, the feeling of ourselves, the feeling of life – these are the concrete. In truth, philosophy belongs to the domain of thought, it deals with generalities, its object is abstract, but only in form: in itself, the idea is essentially concrete, it is the unity of different determinations. This is what distinguishes rational knowledge from the simple knowledge proper to understanding. Philosophizing is necessary to show, against understanding, that the true, the idea, does not consist in emptying generalities but in a universal that is, in itself, the particular, the determined. Philosophy is entirely opposed to the abstract and leads to the concrete” (p. 400 of "Wer denkt abstract?", cited by Niels).

It is a grave mistake to take the German word “Idee” in the common sense of the word “idea,” which is more corresponding to the German “Vorstellung.” The word “idea” should not be judged as equivalent to the Platonic term, as it is generally interpreted, as the eternal law of things according to which the phenomenal world is constructed. In Kant, the transcendental idea is the product of subjective activity of reason. In Hegel as well, it is the product of subjective activity. But there is a difference that should be emphasized: to think something in its idea is to think it as a freedom that gives itself a determined content. What separates the Idea from the Concept (Begriff) is that the concept refers to something, but in turn is distinct from it, whereas in the Idea, this distinction is abolished because it is the unity of concept and reality, as we have seen. It is now easy to understand what absolute idea is: it is the totality of the real conceived as the product of spontaneity, not individual but immanent to all beings, now grasped in its unity. In this way, the finite has infinite value, and the finite is within the infinite, and it is there that we apprehend beings in their truth.

Article 2 – The Role of Logic in Hegel

In the act of thinking, according to Pfänder, we can distinguish five essential elements:

  1. The subject that thinks;

  2. The thinking thought (that thinks);

  3. The thought that is thought;

  4. The verbal expression of thought;

  5. The object to which thought refers.

The last two elements deserve the following comments: the 4th does not belong to the essence of knowledge, and the 5th is already contained in the third.

In light of this classification, the question naturally arises: which of these elements, and how many, properly constitute the object of logic? Should logic be conceived as a real or merely ideal science, or both?

If we consider, as Virasoro does, three modes of thought:

  1. The thinking thought in the “individual,” and if we emphasize this, we fall into the psychologism of Stuart Mill, Spencer, Lipp, etc.;

  2. If the thought is in the universal (“transcendental ego” of Fichte or Kant’s, which does not depend on the individual but refers to general consciousness, as in Kant’s transcendental perception), we fall into transcendental logic, Kant’s gnoseology, Fichte’s metaphysical-gnoseology (which Virasoro also considers as Hegel’s, with which we do not agree), or in the more modern manifestations of neo-Kantians like Cohen, Natorp, etc., and neo-Hegelians (and here we agree), like Gentile and even Croce.

  3. The thought that is thought in the universal, and if it is so, then we have the abstractionist logic of Aristotle, Leibniz, Lotze, Bolzano, Herbart, etc., including Logistics, Pfänder, and even Husserl’s pure logic.

Hegel’s logic is characterized by considering the concretion of the second two aspects. We will see in due course that it is necessary to concretize all three aspects if we want to have a clear and convenient view of logic, which, however, we will not be able to clarify in this book. Hegelianly, we could distinguish two essential modes of logicality:

  1. Objective logos, presupposed as existing in and for itself, opposed and independent of the thinking subject;

  2. Subjective logos, which is the act of knowing itself.

Thought cannot transcend beyond the scope of its own activity, and Hegel rejects a universal essence in itself. It is abstract logos that projects onto the transcendent what is unique to its own activity, immediately included in the reality of consciousness, as concrete logos.

Objective logos becomes present in consciousness through the act of intellection.

In rationalist metaphysics, it is assumed that the laws of thought are the same as the laws of being, identifying subjective spirit with the objective.

Hegelian dialectic is that of concrete logos, which includes both the positions of rationalist metaphysics and abstract logic. Thus, it includes abstract logos but surpasses it by including the objective process of abstract logos, which comprehends them in knowledge.

The Hegelian dialectic does not want and does not intend to study its opposite and affirms substantial unity, as it considers this the only way to achieve the integrity of logical content. This is the opposition of Hegel’s immanent idealism, opposed to the transcendent idealism of many of his disciples, such as Gentile and others.

Let’s examine the objections that arise from realists and subjectivists; in short, from all quarters of thought.

Hegel distinguishes himself from abstract positions by not accepting the subordination of the subject to the object, as realists do, nor the subordination of the object to the subject, as subjectivists do, but by coordinating both in the concrete act of knowing.

However, since we do not capture objective reality by incorporating it into ourselves, only the image, the internalization through images and thoughts, measurements, schemes, forms, etc., objective reality is transformed within us, where it is assimilated according to our accommodated schemes, although without denying its action in enriching and multiplying them.

But it must be considered that the activity of consciousness in knowledge does not have a role as distorting reality as is often believed. The plasticity offered by psychological adaptation, through the schemes we possess, a subject we studied in “General Noology,” allows for optimal accommodation to the forms of reality. Our intellect, which is abstract by excellence, in attention to vital usefulness, intentionally constructs autonomous schemes of facts, mentally separating them from reality and including them in orders, in delimited domains. While the intellect does not entirely falsify reality, it cannot be concluded that one can explore the entire philosophical field by merely manipulating concepts and intellections.

This is what materialism did, reducing all reality to matter and endowing it with metaphysical attributes (such as unity, absoluteness, etc.).

Transcendentalists criticize Hegel’s immanence, which repeats, albeit inversely, the excess of materialism by reducing knowledge to the absolute forms of knowing, originating in the intellect, which, however, acquire universal validity.

This is unfounded, and an analysis of Hegelian works would clearly reveal that this is not Hegel’s thought.

He did not consider the laws that govern thought to be separate from the laws that govern existence, and therefore, he admitted that the external world could be penetrated in its essence by thought (as an act of thinking).

He did not separate subject from object, as he included both in the concrete act of knowing. Furthermore, logic was not purely a formal science.

The human intellect captures thoughts and verifies them concretely. Science shows us that thoughts, captured through the act of thinking, may differ from reality, but reality is reestablished through experiences and errors. Thus, logic does not work with reality to control it technically, to use it economically, but to grasp the nexus of thoughts that exist both in things and in humans. The individual is inseparable from existence, and knowledge is concrete with existence. The role of Hegelian logic is to seek this reality where both elements of knowledge—the being that knows and the known—are present.

Hegel recognizes the universal subjective self-awareness in relation to individual self-consciousness (of this or that individual). Reason is the objective universal spirit. Universal subjective consciousness is not a psychological being, temporospatial, like a body, etc. We must not forget that, for Hegel, the individual is concretized universality. Each conscious being concretizes and actualizes human universality. If each consciousness were valid only for itself, how would science be possible? How could there be understanding among humans? Consequently, there exists a subjective universality among them, which is present in everyone and each person, allowing for the mutual assimilation of expressed thoughts. Moreover, one must never forget that the individuation of the human being as a person, which distinguishes them, is subsequent to the formation of the same being that preserves, maintains, and never denies their great universal human heritage, the human universality that is actualized within them through individualization. There is a human identification in this underlying consciousness, despite the diverse temporal and spatial manifestations of individuals. Otherwise, how would science and the socialization of thought and knowledge be possible?

Hegel divided the system of sciences into three disciplines:

  1. Logic, as the science of the idea in itself and for itself;

  2. Philosophy of Nature, the science of the idea in its exterior existence;

  3. Philosophy of Spirit, as the science of the idea that, after externalizing itself, retracts into itself.

This classification, which is definitive for Hegel after several other experiences, is characterized by the total elimination of metaphysics as a science separate from logic, which ultimately becomes identified with it.

For him, Spirit is absolute becoming, concrete and living reality that develops, engenders itself, unifies in oppositions, an identity that should not be understood as merely undifferentiated but realized through differences.

“It has already been noted that the different philosophical sciences are nothing more than various determinations of the idea” (Note that, for Hegel, the idea is always concrete, as the synthesis of concept and reality; the idea of the apple is in the apple, not in a world of ideas as many believe his thought to be)—“and that it is in them that the idea develops, developing in its various elements. In nature, as in spirit, what we find is the idea; but in nature, the idea assumes the form of an external existence, while in spirit, it is the idea that exists in and for itself. Each of these determinations in which the idea manifests itself is a moment of itself that it traverses without stopping: therefore, each particular science consists both in determining its own content and in immediately recognizing itself as a transitional moment to a higher sphere” (Encyclopedia, p. 42-45).

From this, Maggiori affirms that for Hegel, “there is no path that leads to logic because we are always within it, just as we are within the air we breathe.”

These aspects led many to classify Hegel as a panlogist, which he defended himself against in his later days.

Even disciples accuse him of having overlooked the positive meaning of intuition, which nourishes thinking, and considering it as engendered by thinking. Intuition is the source of general knowledge.

However, there is a group of poorly outlined notions that we cannot analyze in this book. Nevertheless, we can say that thought and thinking, as psychological acts, should not be confused. Furthermore, thinking is not purely intellectual but also sensorimotor. There is thinking throughout life, although it may not be logicized into purely intellectual schemes, as Gestalt theory and Piaget’s psychology of assimilation have already demonstrated. Naturally, if Hegel reduced all thinking to the intellectual, then we would have reason to accuse him of making intuition subsequent to thinking. However, since we understand that thinking is universal, it is the functioning of the idea, which becomes intellectual thinking when considered in itself and for itself, and as nature, in its external existence and self-engendering, it thinks, measures, combines, numbers (in a genuinely Pythagorean sense), it becomes evident that the Hegelian perspective differs from what we usually adopt when we place ourselves under purely intellectual perspectives. We will have the opportunity to show this further in the development of this exposition and, mainly, in future works of ours to be published.

Logic is, for Hegel, in itself and by itself, a solution, and a unique one, in action, to the problem of knowing. It does not properly analyze knowledge but actualizes it, and in this actualization, it reveals self-consciousness. In this statement, Hegel declares his departure from the positions of logicians who turn it into an independent organon of knowledge that projects itself onto its object, whereas for him, it is the object of itself, and it is structured by differentiations that only affirm the final identification with the unfolding of the idea.

Therefore, being Logic, for Hegel, the science of the Idea, it is not the thought considered only as formal but as the totality of determinations deduced dialectically. “But to penetrate the essence of thought, we must first try to characterize it in its opposition and difference, in the face of other cognitive modes of the spirit: sensory perception and representation. Regarding the former, or in other words, the objects apprehended through it, Hegel says that they are believed to be sufficiently explained by referring them to their external origins and the organ that perceives them: sensations. But the instrument that is sufficient by itself to explain the object of sensory perception is always the individual, and since the individual is necessarily connected to other individual objects, one of the fundamental characteristics of the sensory is reciprocal externality, that is, its temporal-spatial essentiality, given that its first abstract forms are juxtaposition and succession” (Virasoro).

“Reflection is the activity of thought applying itself to objects, and its product is the universal, and this universal is what constitutes the foundation (Grund), the intimate essence, and the reality of the object” (Encyclopedia, page 55).

“Through reflection, a change occurs in the way objects are; first in sensation, intuition, or representation, and how they appear to our spirit. And only through this change does their true nature reveal itself to consciousness” (ibid., page 56). “Logic, therefore, coincides with metaphysics, which is the science of things given in thought, which, for this very reason, expresses the essence of things” (ibid., page 59).

Objectivity is not only in external things but also in thoughts, and in their objectivity, they are objects of Logic. It is not a mere analysis of subjective thought, as transcendental idealism proceeds, for it considers thoughts not only as mere forms but as contents of reality in itself.

Thus, objectivity and universality are characterized in thought.

“Thought, which produces only finite determinations and moves within them, is called intelligence in the most genuine sense of the word. But if we delve a little deeper, we will see that the finitude of conceptual determinations occurs in two ways: one, while they are merely subjective and are in permanent opposition to their object; the other, while these determinations contradict each other due to their limited content, and even more so with the absolute” (ibid., page 60).

If we consider the concept only in itself, we have Aristotle’s logic; if we consider it in its relation to the absolute, as a part or moment in the becoming of the Idea, we have the Hegelian position.

The former constructs the principle of identity, which only reveals a law of abstract intellect, Hegel emphasizes.

“The form of the proposition (A = A, the principle of identity) immediately contradicts itself because every proposition promises a difference between subject and predicate, and this difference is not realized here as promised by its form. But it is worth noting, especially, that it is denied by the other laws of thought, which proceed differently. When it is stated that the principle of identity can only be proven by consciousness giving its assent to it and that experience, as supposed experience, must be countered with the universal experience that no consciousness thinks, has representations, etc., or even speaks according to this law, and that no existence, whatever it may be, exists according to it. Speaking according to this so-called ‘law of truth’ (a planet is a… planet; magnetism is… magnetism; spirit is… spirit) is rightly regarded as stupid speaking, and that, indeed, is universal experience. The school that valued only these laws, with its logic in which they were seriously presented, lost credit long ago, both in terms of common sense and reason” (Encyclopedia, pages 203-204).13

Contradiction is the inner driving force of all thought, just as it is of all nature, and it is what leads thought to overcome its limitations. Light asserts itself through darkness. Thought cannot remain within itself, as formal logic does, but must be considered as dialectical, not confined to the closed circle of its identity but transcending it, revealing its universality. This universality is not to be understood as an empty idea, as attributed to Platonic conception, but as a constitutive moment of a totalizing systematic organization; not as ideal, static, and unchanging archetypes, as is often said (especially by those who consider themselves disciples, both on the right and the left), to which the reality of becoming should conform, but as infinite becoming itself, which is the development of Spirit, of the entire universe, and which, based on this becoming, gives thoughts significance and the value of objective reality.

For Hegel, any position of the spirit that arbitrarily separates any element that participates in concretion from concretion itself, considering it only as a part, without returning it to the concretion it belongs to, is abstract. Thus, Hegelian dialectic is a logic of concretion, not abstraction.

“Truth is concrete,” he proclaims, “it is entirely dialectical; therefore, logical judgment is an improper form to express the concrete; it is one-sided, and therefore, false” (ibid., page 31).

Ontology, as a region of metaphysics, is the discipline of the abstract determinations of being. And the abstractness of reason leads to identity. But all things contradict themselves, Hegel exclaims; this is the supreme law of reason, just as it is the supreme law governing the universe. This contradiction does not pose an impossibility for human thought. On the contrary, it stimulates thought to overcome, to penetrate to the core of all existence in order to discover the laws that govern it.

Rationalistic empiricism is mistaken when it considers representations as the fundamental contents of knowledge. Generality would be achieved inductively. But for Hegel, universality is expressed in action, in the individual. Thought is not merely an abstracting and generalizing action but also a grasp of the reality of objective universality.

Our forms that shape reality are not mere a priori forms in the Kantian sense, as we have already explained in Philosophy and Worldview, but contents of reality itself.

After this long introductory discourse of Hegelian thought, we are ready to study his dialectic. To acknowledge that Hegelian thought is difficult would not be anything new. There are thoughts that are easy, expressed with ease, while others, like Hegel’s, require the utmost attention and easily elude those who do not commit to examining them with all their intellectual strength. We have sought to synthesize from Hegelian philosophy those points that are indispensable for a clear understanding of his dialectic, which has been so influential in subsequent developments. We can do without studying Hegel, but we will not have a clear view of the historical development of dialectic if we do not engage with his thought. This is why we could not fail to present this exposition. And above all, we are led to do so because of the general distortion of Hegelian thought, which is presented as an unrepentant idealism, as it is usually described by those who claim to be his disciples.

Article 3 – Problematics of Knowledge in Hegel

Every act of knowledge is also an act of refusal because it repels, virtualizes, as we have seen before. (The oppositional activity of knowledge sometimes becomes negative when it deprives the entity of the presence of the opposite).

Thought is always the negation of what we have before us, said Hegel. (Here thought is taken as what we think, measure: what is grasped from something through the psychic activity of the act of thinking).

Hegel considered thought as an act of thinking. He did not clearly distinguish it from thought as what we can grasp from the relations between tensions.

This distinction leads us to affirm that everything is thought because everything is measurable, quantifiable, ponderable, etc., whenever we consider such concepts in their quantitative and qualitative aspects, and not unilaterally, as is commonly done.

Thus, the act of thinking, as we repeat, is an activity, sometimes affirmative, sometimes oppositional, sometimes negative, but always affirmative, as negation is only the refusal of the presence of a predicate.

In the act of thinking, we accept certain thoughts and reject everything that opposes or denies them, depending on the cases. All knowledge is a simultaneous actualization and virtualization, which can only be concretized in a global understanding through dialectics.

Values, constructed as transcendental concepts, that is, arranged as such, are always polar, just like all the epithets that humans construct. The same goes for all concepts constructed based on activity, which always requires an opposing, polar activity to assert itself.

The polarity of concepts, which appears to us in philosophy through synonyms and antonyms, already reveals to us the alternating activity of the human spirit, which fits perfectly within the universal law of alternation (flows — refluxes; positive — oppositional, etc.).

When we know the content of this knowledge, it is a thought that we affirm in a positive act of affirmation and reject its opposite through another positive act of refusal.

When we affirm a value, for example, we virtualize its opposite, and our act of “negation” does not imply the annihilation of that value, which can be actualized in other circumstances for us or simultaneously actualized for others when we virtualize it.

The good for some may simultaneously be the evil for others.

In this case, the affirmation of a positive value does not prevent the affirmation of an oppositional value at the same time. And the one who affirms the positive cannot categorically reject the affirmation of the positivity of the polarly opposing value.

Thus, in knowledge, our affirmations, in one way or another, do not prevent contrary affirmations, even though we think differently and do not desire them most of the time.

Within a unity, we can only make exclusive affirmations, as we have seen, when we affirm the existence or non-existence of tension, that is, when we ontologically consider its being, as we have seen and demonstrated.

What we reject in knowledge and virtualize, we commonly consider nonexistent, as nothing, therefore negative and not oppositional, because what is oppositional already has positionality, even though it is antagonistic.

The negating act of thought, as an act of thinking, and of thought taken as thought, as formal logic does, is always impoverishing, the first in its abstracting activity, depriving the second of what is opposed to it through the activity of the first.

In this way, contradiction is already inherent in the negating, refusing activity of the spirit, as well as in the thought itself that affirms, negates, and refuses.

They engender the negative, that which belongs to another and not to them.

"Negation is thus the mediator of its own destruction; it affirms a ‘false infinite,’ only an ‘always beyond…,’ ‘another than the same.’ Such thoughts are Hegelian.

That negation acts as a means of destruction is not difficult to accept because it places the positivity of what contradicts the affirmed, and it will lead man, through the dialectical action of the spirit, to find the opposite and affirm it afterwards, finally destroying the first position, which was false because it was exclusive due to immanent unilaterality. (Flows and refluxes of ideas throughout time, which sometimes affirm one aspect and are then denied by the proponents of what was refused, who in turn are fought by the former, in an eternal clash of antagonists, who are such because they take unilateral positions).

The ‘false infinite’ is the quantitative infinite, the potential infinite of quantitative mathematics, which suffers, as we would say, from exaggerated actualization of extensity. It is the infinite in size, while for Hegel, the true infinite is the one that has no finitude, no quantitative or qualitative limits. But negation is a refusal of the 'beyond…’. But at the same time, it is an affirmation, not of the actuality of that ‘beyond…,’ but of its virtuality or its negation. When we actualize this virtualized ‘beyond…,’ we find ourselves facing the antagonism of ideas. (The history of all ideas clearly reveals this monotonous procedure).

In this way, negation acts as the mediator of its own destruction. The overcoming of this situation is the Aufhebung (unifying synthesis), which brings together the extremes of affirmation and negation in a new affirmative-negating tension.

But this, by taking on a different qualitative aspect that includes the polar within a global view, acts again through negations and affirmations, continuing the cycle.

Hegelian categories

To properly understand Hegelian dialectics, whose fundamental foundations we have presented in the previous pages, we need to study some of its categories.

For Hegel, categories are pure, universal, and concrete concepts.

They are not sensed intuitively or represented, as Husserl considers, for example. They are pure concepts, not realized through abstraction made from sensory data, like the concepts of table, book, etc. They are universal concepts; they are simple general concepts like the ones mentioned above. However, they do not represent empty schemata of reality but reality itself; they are concrete schemata.

Contradiction is the universal law, the internal moment of becoming in which being and non-being are negated as independent moments.

Infinity in Hegel

For Hegel, infinity is the moment of pure unity. It is not a transcendent beyond. God cannot be conceived as separate and distinct from the world, and it is through the movement of annihilation, of surpassing the finite, that we can conceive infinite being. To think of infinity, one must think of becoming.

In the Logic, Hegel distinguishes between the good infinite and the bad infinite. The bad infinite is nothing more than the endlessly repeated negation of the finite, whose activity is limited to returning to contradiction without ever transcending it. The true infinite is essentially the act of transcending, through which the absolute idea, God, is recognized, perpetually producing and enjoying itself.

Finitude and an-sich-sein (being-in-itself)

For Hegel, the notion of Being arises when thought takes itself, in its immediacy, as an object. In doing so, it abstracts all determinations of phenomena to retain only the aspect by which it is the being that it is. The idea of Being is characterized by fundamental indeterminacy, which leads it to merge with the notion of Nothingness.

“Nowhere, in heaven or on earth, is there anything that does not contain Being and non-Being” (Hegel), and their transition is the becoming, the passage from the infinite to the finite.

Opposed to Being is existence (Dasein, etymologically, being-there), which is fully determined without this concept requiring the spatialization of existence. It is essentially quality, the background of the real.

Quality, known as “something” (Etwas), is already a transcendence of quality. “Something” is positive reality, but it is this positive reality not in an immediate way like quality but through limitation. “Something” is the negation of negation, for it is the reestablishment of simple self-relation; but, at the same time, “something” is, for this reason, self-mediation. Already in the simple form of “something” and in the most determined way, in being-for-itself, the subject… self-mediation is present; already in becoming, there is totally abstract mediation; self-mediation is posited in “something” just as it is determined as a simple identity" (Hegel).

“Something” requires the presence of another before it and opposed to it. “Something” is what is not another, and the other is what is absolutely external to it. The other is essential to “something,” and vice versa. One “something” is the other of another “something.”

“Something” and the other give rise to being-for-another (sein-für-anderes) and being-in-itself (an-sich-sein). “Something” can be considered in itself (an sich sein) and in its demand for the other. Intellectual thought tends to transform “something” in relation to itself (an sich sein) into the hidden reality of the thing, but this being-in-itself would be ungraspable if it did not externalize itself. The unity of being-for-another and being-in-itself reveals to us that being-in-itself no longer arises immediately but as the negation of being-for-another (ser–para-outro). It is in the category of determination (Bestimmung) that consciousness explains to itself the realized unity of being-in-itself and being-for-another.

“To grasp what is, so to speak, the development, two kinds of states must be distinguished. One is what is known as disposition, power, ‘Ansichsein’ (as I call it), potency, dynamis. The second determination is ‘Für-sichsein’ [being-for-itself], reality (act, enérgeia)” (Hegel).

An-sich is thus the moment of possibility. The seed possesses the tree an-sich; these latent powers, when actualized, move to the stage of ‘für-sich’ [being-for-itself], that is, they realize what already was but was not yet determined, only determined at the moment of actualization. Therefore, actualization does not create anything new; it is immanent to itself. The awareness of one stage to another consists precisely in mediation. An-sich corresponds to the moment of immediacy, and ‘für-sich’ to the moment of mediacy.

However, we would add that there is transcendence here because the adult tree is not just the seed developed in itself but through others and by others. The tree is not only the seed; it is more than the seed because other elements have been incorporated into it, just as the reason of the adult human is not merely a development of infantile spirit but is assimilated from other contributions of experience.

For Hegel, categories are conceived by understanding as something stable, solid, but in reality, they pass into one another, thus containing the moment of mediation. Hegel insists on drawing attention to the movement of mediation within each category and emphasizes the various forms that this movement takes.

Let us listen to him on the topic of Being and Essence.

“In essence, there are no more transitions but relation. The form of relation is not already in Being but our reflection; in Essence, on the contrary, the relation is its own determination. When something passes into another in the sphere of Being, the something disappears. The same does not happen in Essence. Here we have no other true thing, but only difference, the relation of one to its other. Consequently, the passage of Essence is not a passage, for in the passage of the differences of one into the other, the differences do not disappear but replace each other in their relation. In the being of non-being, for example, we have Being that is for itself and non-being, which is also wholly for itself. Totally different is what happens with the positive and the negative. These categories contain the determinations of Being and non-being, but the positive has taken on no sense. The same goes for the negative. In the sphere of Being, the relation is only in itself; in the sphere of Essence, on the contrary, it is posited” (VIII, p. 250).

Identity and Difference

Being deprived of any intrinsic opposition is identical. It is a position opposed to that of difference. Becoming manifests the unity of identity and difference, which is the raison d’être.

When essence reflects upon itself, we have identity.

When essence reflects itself in relation to another, we have difference.

Transforming the former into the ultimate principle, we have what formal abstract logic accomplishes. As the negation of difference, it is a purely formal and abstract identity. It is tautological: A = A.

By negating identity, the category of absolute difference also emerges, which is equally abstract. Both are equally unproductive.

The unity of both constitutes the category of sufficient reason, which is the concrete unity of reflection in itself and reflection in another.

Sufficient reason expresses that a being has its determination in something else and does not consider the thing solely in itself.

This immediate unity of reflection in itself and reflection in another is existence. “Therefore, it is the determined multitude of existents as reflected in themselves, which simultaneously appear in another, which are relative and form a world of reciprocal dependencies and an infinite connection of reasons and consequences. The reasons for being are also in themselves existences, and the existences are equally reasons for being and consequences, successively” (same page, p. 213).

Matter and Form

"Matter, as the immediate unity of existence with itself, is also indifferent to determination: the many distinct matters merge, therefore, into the single matter that is existence in the reflective determination of identity. In the face of matter alone, its multiple and distinct determinations, and the extrinsic relation that we show in it, in the thing, constitute form; the reflective determination of difference; but as existent and as totality.

This single matter, without determinations, is also the same as the thing-in-itself; only that the latter is entirely abstract in itself, while the former is also for another thing, and above all for form" (ibid., p. 128).

Matter and form are the constitutive moments of the thing. Matter is the positive and indeterminate existential element; form is the conforming and determining element.

In simple terms: This apple, without its form, would be matter. It would be indeterminate because it is the form that determines it. Matter, as indeterminate, would have its opposition in form if considered only in itself. And it would not be the thing-in-itself in the Kantian sense because it is different for form if form is also thought abstractly.

Phenomenon and Reality

The appearance of essence is the phenomenon. Essence is neither behind nor beyond the phenomenon. Existence is the phenomenon.

Form is the content of the phenomenon. What is internal to the thing is also external. The phenomenon only shows what the thing possesses, and what exists in essence is manifested in the phenomenon. The phenomenon is, in actuality, the totality of the real, and the real is nothing outside of its manifestation.

The unity between essence and existence, form and content, interior and exterior, is what constitutes reality. This unity does not exclude differences.

“...being is, in general, immediate and unreflective, the transition to another thing. Existence is the immediate unity of being and reflection, and therefore, the phenomenon arises from the reason for being and goes towards the reason for being” (Hegel, ibid., p. 142).

Substance

When the differential determinations are denied in things, we have substance. Substance is the totality of accidents in which it reveals itself as absolute negativity.

Let us clarify: To think of substance, we need to strip the thing of all its accidents. If we strip the apple of its shape, what remains is matter, but it still has quantity, although not delimited. But quantity is still an accident, and if we strip matter of this accident, it would be stripped of all qualities. Only then do we have substance. In Hegel’s opinion, substance is the totality of accidents that we naturally separate by a requirement of our thought. Now, substance is that which undergoes accidents (from ad and cadere, to fall). Substance is immutable, and its mutability would be the accidental, what happens.

Causal Relation

When substance is denied and placed in an extrinsic relation, we have the causal relation.

The entire content of the effect is in the cause. Only in the effect, Hegel says, is the cause real and truly a cause.

The effect is different from the cause in its transition during becoming. But the effect delimits the cause because the cause determines itself in the effect. In turn, the effect is determined by the cause. This mutual determination is what Hegel calls reciprocal action.

Subjective Concept and Objective Concept

The concept is:

  1. Subjective or formal concept;
  2. Objective or real concept (the conceptual significance in itself, or object);
  3. The idea is the unity of subject and object, of the concept as a purely formal and intentional activity of the thinking self, and the concept as the object in itself.

The Three Moments of the Dialectic of Opposites

In Hegel, they are as follows:

  1. Simple affirmation — Thesis;
  2. Negation — Antithesis;
  3. Negation of negation — Synthesis. Negation is always positive for Hegel and should not be considered mere absence.

According to Hegel, the thesis cannot be thought of without the exclusion of the antithesis, matter as the negation of form, being as the negation of non-being. Negation is always positive.

Let us clarify: If existence is becoming, each position (thesis) becomes another, a negation through becoming. The pear seed, taken as a thesis, is in itself a pear seed, that is, it contains the possibility of becoming, of becoming a pear. But the pear is potential and not actual, so it has not yet determined itself; it is indeterminate. By determining itself in the formation of the pear, it negates the thesis; it is anti- (thus antithesis) because by determining itself, it ceases to be indeterminate and becomes determinate. This transition from indeterminacy to determinacy is becoming. When realized as a pear, it is synthesis (with position) because, as such, already actualized, it affirms the thesis (possibility) because it has been actualized, but it negates the thesis because it is no longer indeterminate but determinate; it affirms the antithesis (the transition) because it has actualized becoming, but it negates the antithesis because it has already fully actualized the possibility. Thus, it can be seen that the synthesis is synthesis, that is, the composition of the two positions, the thesis position and the antithesis position; therefore, by affirming them, it affirms the negations of both, which are positive; thus, the synthesis is affirmation and negation. And since it opens up new possibilities, one can start from the synthesis, considering it as a thesis, and be succeeded by an antithesis and another synthesis, and so on.

Negative Judgment

For Hegel, the act of transcendental imagination is the expression of a synthetic activity of the spirit that realizes the unity of transcendental apperception and empirical diversity, which makes it a true plastic mediator.

Recognizing the positive character of negation, Hegel accuses philosophers of giving absolute value to finite categories and of ignoring the immanence of the infinite in the finite, whose connection, with the acceptance of the positivity of negation, is thus established.

Negative Judgment, in truth, is positive, for with a negative judgment, we only reject a presence. It is an act of affirmation. It was because this aspect was not considered that the skeptics failed to understand that their position was still an affirmation; therefore, dogmatic.

Hegel concluded that the philosopher could not think about himself, becoming a particular object, because he would need to apprehend the whole in its relation since nature encompasses an infinity of relations, which definitively hindered the deduction of a particular object, as such deduction would require knowledge of the infinite series of those relations.

Limited in its activity, reason, which can only exercise it by negating the finite, Hegel could confidently respond to skepticism, whose fundamental error lay in its conception of negation by not recognizing in it a positive activity and positive value.

The Syllogism for Hegel

The syllogism is, for Hegel, a synthetic act of the spirit, the passage from the individual to the universal, or from the universal to the individual, in which the middle term functions as a means of transition. Things themselves are syllogisms, and syllogistic reasoning is merely a grasping by consciousness of the movement of the individual into the universal, or the universal into the individual.14

Based on the Hegelian text that states: “What is rational is real, and what is real is rational,” many accuse him of being a panlogist. However, Hegel had already defended himself against such attacks. Haering clearly explained the meaning of these Hegelian terms, which have been used and abused to justify all the violence in history as well.

Thus:

“Wirklich” means active, effective, solid, constant, the actual, as we have already explained.

“Vernünftig” is the deep vital law by which all truth asserts itself; that which is not true disappears.

Only that which is active, creative activity, is real (wirklich), that which is rational (vernünftig).

According to Hegel, every thing is creative tension, and the entirety of the real resolves into an ideal totality, which is the actualization of the absolute.

This passage from Hegel clearly shows his thought, which has often been distorted.

“A misfortune, the death that befalls a dignified individual, is called ‘tragic.’ We speak thus in the case of innocent suffering, of injustice against an individual; it is said of Socrates, who was unjustly condemned to death, and that is considered tragic. However, innocent suffering is not a rational misfortune. Misfortune is rational only when produced by the will of the subject, by their freedom. It would also be necessary for their action and will to be infinitely justified, ethical: thus, the individual must be indebted to themselves for their misfortune; the power that opposes this freedom must also be equally justified from an ethical point of view, and not a natural power or the power of a tyrannical will. In the face of every person, natural death is an absolute right, but it is only the right exercised over them by nature. In true tragedy, it is necessary for the conflicting powers to be two justified, ethical sides” (Hegel, XVIII, p. 48). It can be seen, therefore, that it does not justify any brutality in history. The actual (wirklich) is that which cannot be swayed by circumstances and events. The actual is active and contains its possibilities within itself. Existence will never exhaust the totality of its potentialities.

For Hegel, possibility is not something latent, purely internal, but rather the indeterminacy of being which, in its immanent development, realizes itself through a passage into the other. In contact with others, being becomes enriched with new determinations, for the substance of being is constituted by the relationships it maintains with others. Hegel’s thought of the universe consists in conceiving it as functions (relations of relations, engendering themselves without the need for the idea of a solid support).

Hegel defines the actual (wirklich) as the unity of the real (Realität) and the possible, placing the absolute not as being, but as becoming. The actual is the tensional moment between the possible and the real.

Therefore, for Hegel, the concrete is not an immovable substrate but rather becoming itself. The meaning of this becoming is the great task of the philosopher, according to Hegel, and it is achieved when one discovers the positive character of negation.

In the “Encyclopedia,” Hegel seeks to integrate nature within the idea. It is up to humans to realize the transition from the infinite to the finite through the action of freedom, which asserts itself.

The eternity it seeks is immanent in time; the eternity of the instant, the reconciliation of the relative with the absolute.

Accused of panlogism, supported by the text “was vernünftig ist, das wirklich usw…,” Hegel defends himself by showing that the Logos is merely a particular moment of the real, but supra-rational.

Reasoning reason (Verstand), says Hegel, negates itself. Reason (Vernunft) contains within itself the moment of opposition. Thus, Hegel classifies as mystical (hidden) everything that is rational (vernünftig), which does not mean it is incomprehensible, but rather that it is above reasoning reason (Verstand).

“When people nowadays speak of the mystical, it is considered to have a meaning identical to secret and incomprehensible, and this secret and this incomprehensible are then regarded, according to differences in culture and way of thinking, on the one hand, as what is truly authentic, but on the other hand, as resulting from superstition and illusion… Those who recognize the mystical as the most true consider it to be something simply secret and express, on their part, that thought has only the significance of abstract identity and that, therefore, to attain truth, it is necessary to renounce thought” (Hegel).

We cannot fail to recognize that Hegelian dialectics presents great difficulties. However, during the course of this study, many of the more obscure aspects of his thought will become clear when discussing the main themes. By delving into modern dialectics, we must consider the role played by Hegel. The division of his disciples into right-wing Hegelians (who chose subjective idealism) and left-wing Hegelians (who chose realism), thus unfolding his concrete and dialectical thought into two abstract positions due to their unilateralism, has led to the emergence of many dialectics as well as more accurate studies of his themes. While some aspects have been clarified, others have been obscured and distorted by the intrusion of 18th-century positivist thinking and materialist thinking, both of which are abstract positions, as well as by the exaggerated idealism that has fallen into opposite abstractionism.

This will be highlighted in the analysis of other major currents of dialectics until we can offer a methodological dialectic at the end of this book, drawing on the best elements of all of them to serve as a tool for analysis and study.

After Hegel, dialectics experienced extraordinary development. The world of reality is not a fixed world, an immutable world, an invariant world, but a world of transformations, movement, variations, and mutations. Dialectics delves into this world, examines the contradictions and oppositions that existence presents. However, dialectics not only penetrates this terrain but also the realm of ideas. It examines them, verifies how they form, how they transform, how they are influenced by these mutations, how they also imply their opposites and contradictions. Dialectics thus takes on a very broad meaning in the present because it allows us to analyze not only the existence of real objects but also ideas as ideas and the accompanying psychological process.

Dialectics also considers nature as a set of interconnected facts, interpenetrating and interacting, linked and coordinated. It examines the formation of abstractions, these separations made from universal happenings, not to consider them isolated but to connect them, analyze them, and understand why they are formed and the destiny that awaits them.

General dialectics, as we understand it, is also a true logic of existence, the logic of what is here and now (hic et nunc). It is the logic of nature, things, bodies, of what occurs in time and space, such as psychological facts, which are more temporal, and the objects of natural sciences.

It does not aim, as many believe, to replace Formal Logic, which is a logic of abstractions and timeless, ideal objects, nor does it intend to destroy it. Dialectics does not seek a destructive role but rather to complement what is lacking in Formal Logic, strengthen and expand it, allowing it to invade other territories. By entering the realm of opposites, of contradictions, of conflicts, it is also a logic of antinomies, collisions, and clashes. It seeks to discover their own laws, to show the legality that exists among facts, to observe the universe as a whole, to examine the formation of ideas, to analyze what they affirm and simultaneously negate, what they actualize and virtualize, what they accentuate and inhibit.

Theme IV

Article 1 – Materialist and Historical Dialectic

The doctrine of Karl Marx (1817-1883) has been characterized as “historical materialism” and “dialectical materialism” by Engels (1820-1895), his disciple and collaborator. It is not possible to study the dialectics of Marxist materialism without first making a brief analysis of the foundations of “historical materialism.”

Marx was initially a Hegelian in his youth. After Hegel’s death, his disciples split into various factions. Marx later joined the movement of the “left Hegelians,” gradually developing his own doctrine based on the principles of socialist conception, which had already been delimited in its contours and aspects. To characterize it, we must classify it above all as anti-idealist.

In his criticism of idealism, his position is diametrically opposed to the canon that asserts the primacy of spirit over matter, instead accepting the primacy of matter over spirit. Marx’s entire struggle (and this must be noted primarily) is a struggle against idealism, not against spiritualism.

The metaphysics he opposed is idealist metaphysics. Subsequently, among the followers of Marxism, there is often confusion between idealist-subjective metaphysics and metaphysics in general.

Marx was not interested in resolving the great problems of metaphysics but rather in studying the grand laws of human evolution, the laws of history. He opposed the right-wing Hegelians' idealism (which he judged to be Hegel’s own) that claimed ideas directed the world, and instead emphasized the economic conditions that condition those ideas. These economic conditions constitute the essential structure of human relations, and ideologies form the superstructure upon them. This, at least, is the doctrine of Marx in his truly “Marxist” phase, and it represents his ideas from the phase of the “German Ideology,” one of his best books and least known by his most faithful followers. Let us cite Engels:

“And… it was realized that history is nothing but the history of class struggles; that these social classes that fight each other are, at every moment, the product of the relations of production and exchange, in a word, the economic relations of the era, which increasingly constitute the real base that allows the political and juridical institutions, as well as the ways of thinking religious, philosophical, and others of each historical period, to be explained. In this way, idealism was expelled from its last refuge, the conception of history: a materialist conception of history became necessary; the way was open to explain the consciousness of men by their way of living, instead of explaining, as had been done until then, the way of living by their consciousness.”

According to Marxism, the economic conditions that form the social structure underlie the superstructure—the political, religious, artistic, philosophical aspects, etc. However, it does not deny that the superstructure exerts its influence on the structure, but the economic aspect is always decisive.

As Engels aptly said, “Philosophers have only interpreted the world in various ways; the point is to change it.” These words, more clearly than others, express the meaning of historical materialist doctrine, which, aspiring to be scientific, seeks what science aspires to: action.

Marxism is not a contemplative or purely speculative philosophy but a philosophy of action. Sidney Hook’s words are telling: “Marxism, as the theory and practice of revolution, is the theory of the proletariat class. In this sense, it is a ‘partial’ or ‘partisan’ theory, while still being an objective expression of the interests of the proletariat.”

Thus, it is a revolutionary doctrine. However, while we said that Marxism fought against idealism, primarily on the social and historical terrain, just as positivism fought on the terrain of science and philosophy, Marx and Engels, like Lenin, the most famous disciple, were materialists. As Lenin said, they “emphasized the dialectic more than the materialism when it came to historical materialism and focused more on the historical aspect than on the materialist aspect.”

Although Engels affirmed that “thought and consciousness are products of the human brain,” Marxists take every precaution not to be confused with mechanistic materialists like Feuerbach, Büchner, Vogt. They defend the concept of dialectical materialism, which primarily asserts the primacy of matter over spirit, as Lenin emphasized.

Regarding dialectics, Marx’s work is small. It was Engels who later produced better works that establish its main principles.

We have seen that, for Aristotle, matter is passive and inert, mere potentiality (as possibility), to which form gives structure.

Classical physics itself followed these footsteps when physicists began to assert that matter was essentially dynamism and movement: “Movement is the mode of existence of matter, the way matter is. Nowhere, at any time, has there been or will there be matter without movement. Movement in space, mechanical movement of smaller masses on each celestial body, molecular vibrations in the form of heat, electric or magnetic current, chemical analysis and synthesis, organic life—thus in one form or another, or several simultaneously, every atom of matter in the world exists at any given moment… Matter without movement is also inconceivable, just like movement without matter. To imagine a state of matter without movement is, therefore, one of the emptiest and most insipid ideas that exist, a pure ‘feverish nightmare’.” (Engels)

We have seen that for Hegel, the dialectical process we call objective is merely the work of the idea externalized in the world. For Marxists, the material world exists independently of all spirit, and it is within matter itself that the thesis, antithesis, and synthesis take place. These are provisional and mark the starting points for new theses, antitheses, and syntheses.

“My dialectical method is not only different from the Hegelian method in terms of foundation; it is its direct opposite. For Hegel, the process of thought, which he presents as an autonomous process called idea, creates the reality that in itself is only an external phenomenon. For me, the world of ideas is only the material world transposed and translated into human thought.”

“The mystification into which dialectics led in Hegel in no way prevents this philosophy from being the first to present in a comprehensive and consistent manner the general forms of movement. It must be turned right side up if we want to find within it the rational core.” (Marx)

(It is clear that Marx understood Hegel in reverse, judging Hegelian idealism through the gauge of the right-wing Hegelians.)

For Marx and Engels, Hegelian dialectics “were standing on their heads.” They needed to set them on their feet. This is the work of Marxist dialectics, which thus becomes “the science of the general laws of movement, both in the external world and in human thought,” as Engels defined it.

Article 2 – Analysis of Marxism

Let us examine the main theses of this thought, as presented by Stalin in “Dialectical Materialism and Historical Materialism.”

"The Marxist philosophical materialism is characterized by the following fundamental traits:

a) Contrary to idealism, which views the world as the embodiment of the ‘absolute idea,’ the ‘universal spirit,’ or ‘consciousness,’ Marx’s philosophical materialism is based on the principle that the world, by its nature, is material, that the multiple phenomena of the universe are different aspects of matter in motion; that the interrelationships and mutual conditioning of phenomena, established by the dialectical method, constitute the necessary laws of the development of matter in motion; that the world develops according to the laws of the development of matter and has no need for any ‘universal spirit.’

Let us analyze: According to Marxists, idealism and metaphysics are always considered identical, but it so happens that both metaphysics and idealism are not what they believe them to be. They make metaphysics, like idealism, into caricatures. What Hegel understands, for example, by the absolute idea has been explained in the preceding pages, as well as what the universal spirit and consciousness are. Furthermore, idealism is a current that has several modalities with very distinct differences, which are difficult to include in a synthesis, which dialectically would only be an abstraction of idealism, for the differences themselves must also be considered. Encompassing under the name of idealism what is not strictly idealism, even when considered formally, is not proceeding dialectically because not all idealism is what Marx thought, Lenin and Stalin repeated, and the Marxists proclaim.

Neither idealism nor metaphysics are what they claim to be. If the Marxists, instead of disregarding metaphysical thought, carefully studied it (and dialectics has an ethics just as science does—which consists of balancing opposing aspects and polar valuations of a doctrine to weigh it, compensate for it, and capture the differences in a synthetic view), they would have a different understanding of metaphysics and idealism, which would lead them to a more serious and valuable analysis for dialectics, without the danger of destroying it or the need to distort others' thoughts to justify their own.

Reducing the world to matter, a concept that is now equivocal in philosophy but which for the Marxist “is the substrate of all transformations that occur in the world.” (Marx and Engels, “The Holy Family,” Chapter VI, 3rd), is metaphysical.

“'Movement is the mode of existence, the way of being of matter.” (Engels, “Anti-Duhring,” page 54).

And the fact that the multiple phenomena of the universe are different aspects of matter in motion is also agreed upon by many idealists; that the laws of ‘matter’ arise from relationships would not be new to many idealists; and that the world also develops according to these laws is also not disagreed upon by many others. As for the universal spirit, many understand well that it is constructed from these laws, whose rigor reveals choice, intellect (inter-lec, to choose between, intellect), as they occur in this way and not another, and are sometimes of this nature and sometimes of that nature, but revealing an order that remains and which we can, in turn, capture intellectually. So far, the Marxist opposition is indeed a kind of idealism. A careful reading of idealist authors by Marxists would be beneficial to avoid such naive assertions.

“b) Contrary to idealism, Stalin continues, which asserts that only our consciousness exists in reality, that the material world, being, nature, only exists in our consciousness, in our sensations, representations, concepts, Marx’s philosophical materialism is based on the principle that matter, nature, is being, is the existing objective reality, independent of consciousness: that matter is a primary given, as it is the source of sensations, representations, consciousness, while consciousness is a secondary derived given, as it is the reflection of matter, the reflection of being; that thought is a product of matter when it has reached a high degree of perfection in its development: more clearly, thought is a product of the brain, and the brain is the organ of thought. Therefore, thought cannot be separated from matter without falling into a gross error.”

Let us analyze: The same as we said in point “a” could be said here. Marxists lump together under a single title, formally, as idealism, the subjective and the concrete, without understanding that there are differences between real idealism and ideal realism, and even among the idealists themselves.

Not even Berkeley, who is so frequently cited by Marxists, thought this way. It is enough to read his work to see that Berkeley’s immaterialism does not deny the existence of the external world, which is differentiated from the objective world because it is already related to the human spirit and, therefore, shaped by it. With the exception of Berkeley, to some extent, few idealist philosophers (and truly: the lesser ones) would accept these assertions attributed to them by Stalin and the Marxists.

In general, idealists do not deny the existence of the external world; they only say that the external world is objectified by the subject. This objectification is an intellectual form produced by our knowledge, which is selective. Thus, the objective world (which should not be confused with the external world) is not fully represented in its reality, as it is a construction of human consciousness. Some idealists rationally deny knowing the external world in its entirety since it is known only within the abstract frameworks constructed by reason or intuition, etc. There are still disagreements among idealists on this point, and it would be lengthy to enumerate them. However, all of them, without exception, agree that reflections of matter are in turn shaped by the spirit, meaning that the schemas formed by humans shape their knowledge, as Marx himself partly acknowledged when he realized and affirmed that class perspectives shape the view of facts, and also by recognizing that the superstructure influences the knowledge of the infrastructure.

In general, idealists do not recognize that thought can be explained merely as a cerebral act, reducing the psychological to the biological, which would inevitably lead to reducing it to the physical-chemical level and falling into mechanistic materialism, which Marx always took care to avoid. Under these conditions, Marxist materialism should not be confused with vulgar materialism. Thought is a product of qualitatively different relationships than those of biology.

Indeed, Engels, at certain moments, fell into vulgar interpretation, but the same cannot be said of Marx. This explanation of the psychological through the biological is an explanation that philosophical analysis has already completely discredited, and even science, through its most esteemed individuals, also discredits it. Matter can be understood as a mode of being and not just as the only being, which would lead to an absolutist and less dialectical view of the universe if we were to accept the latter position.

“c) Contrary to idealism, which contests the possibility of knowing the world and its laws, which does not believe in the value of our knowledge, which does not recognize objective truth, and considers the world to be full of ‘things-in-themselves’ that can never be known by science, Marxist philosophical materialism is based on the principle that the world and its laws are perfectly knowable, that our awareness of the laws of nature, verified through experience and practice, is valid knowledge that has the significance of objective truth, that there are no incognizable things in the world, only things that are still unknown, which will be discovered and known through the means of science and practice.”

Let us analyze:

Here again, the same previous words would apply. The idealism that contests the possibility of knowing the “thing-in-itself” is a specific idealism. However, we would then be facing a problem: that of knowledge. It is necessary to determine whether there are limits or not. According to Marxism, there are also limits. On the contrary, the possibility of total knowledge by humans, and consequently absolute knowledge, could only be asserted a priori as a possibility because knowledge will always involve relating, which Marxists cannot fail to recognize. Such a relationship can never become an absolute, except formally. Furthermore, knowledge must be distinguished as either intellectual-rational or intellectual-intuitive, sensory-motor, or practical, which conditions the heterogeneity of knowledge. It is evident that concrete and absolute knowledge would lead to absolute identification, a total fusion between the subject and the object, between the knower and the known. Such a position would deviate from the norms of Marxist dialectics. However, it must be acknowledged that Stalin’s assertion carries a valid meaning, which is that it is possible for us to know. In this case, it opposes the agnostic or skeptical positions of certain idealism, but other positions also acknowledge this. Therefore, considering a specific idealism as generic would be deviating from philosophical truth, which should not and cannot be done without offending an ethics that must exist, at least here.

Indeed, it is a flaw of some philosophies not to consider the lessons provided by science, especially its practical truth revealed in the mastery over things, and to believe that only through abstract speculations will we arrive at more secure knowledge. However, it would also be an unbalanced position to disregard the knowledge offered by intellect. A dialectical cooperation between these two means of knowledge would be useful for humans, not only to expand knowledge but also to construct a more serious analysis of knowledge itself and enable the development of a dialectical methodology that is based on what scientific thought offers.

Science and philosophy, if set against each other, can still cooperate. It is necessary to acknowledge an important dialectical category: that of cooperation between opposites, without which all constructive work of humans is always threatened by one-sidedness and, consequently, by absolutist abstractism.

From the same work by Stalin, let us highlight these important passages:

"The Marxist dialectical method is characterized by the following fundamental features:

“A) Contrary to Metaphysics, Dialectics considers nature not as an accidental accumulation of objects, of phenomena detached from each other, isolated and independent from each other, but as a united, coherent whole where objects, phenomena are organically interconnected, depend on each other, and reciprocally condition each other.”

Let’s comment: This is an important thesis of Marxist dialectics, and truly dialectical. We only disagree regarding Metaphysics because this science does not deny such a thing, nor should the metaphysical term be limited to one opinion or another from this or that philosopher. Metaphysics, as the science of the transcendent, is not abstract, as it is often thought, except for bad metaphysicians. If metaphysics, metaphysically, makes the distinction between the circularity of a tire and the tire itself, it does not consider this distinction as a real—physical separation but only as “metaphysical.” It is analytical and architectonic; not an abstract view of the world. It seeks to achieve maximum concreteness. If it has been understood differently, it is due to the fact that certain metaphysicians have been considered as the embodiment of this discipline. A careful study would lead Marxists to other opinions and certainly to other consequences. In scholasticism, which they always speak of derogatorily, they would find (in the works of its great representatives) what metaphysics truly is. Instead of criticizing the works of great philosophers, it would be advisable for them to delve into and study them to avoid discrediting falsifications for those who make them.

“B) Contrary to Metaphysics, Dialectics considers nature not as a state of rest and immobility, but as a state of perpetual movement and transformation, of perpetual renewal and development, where something is always born and develops; something disintegrates and disappears.”

But who considers nature as a state of rest and immobility?

“C) Contrary to Metaphysics, Dialectics considers the process of development not as a simple progress of growth, where quantitative changes do not turn into qualitative changes, but as a development that transitions from insignificant and latent quantitative changes to apparent and radical changes, to qualitative changes: where qualitative changes are not gradual but rapid, sudden, and occur in leaps, from one state to another; these changes are not contingent but necessary, resulting from the accumulation of imperceptible and gradual quantitative changes.”

“D) Contrary to Metaphysics, it starts from the standpoint that objects and phenomena of nature involve internal contradictions because they all contain a negative and a positive side, a past and a future; they all contain elements that disappear or develop; the struggle of these opposites, the struggle between the old and the new, between what dies and what is born, between what decays and what develops, is the internal content of the process of development, the conversion of quantitative changes into qualitative ones.”

The criticism of these exposed aspects will be developed throughout this book when examining the dialectical categories.

From the above words, we can outline the following fundamental points of Marxist dialectics:

  1. Nature is a united, coherent whole;

  2. Phenomena are organically interconnected;

  3. Dependence of some phenomena on others;

It is an error to consider a phenomenon in isolation from the phenomena that surround it. Lukacs, one of the theorists of Marxism, considers the dependence of parts on the whole as the fundamental principle of dialectics. The category of totality predominates.

  1. Reciprocal conditioning.

Continuing to examine the fundamental points of Marxist dialectics, let’s quote another passage by Engels: For Marxists, “...the world should not be regarded as a complex of finished things, but as a complex of processes, in which apparently stable things, as well as their intellectual reflections in our brains, ideas, undergo unceasing change and becoming, where, finally, despite all apparent accidents and momentary returns, progressive development ultimately prevails.”

So we have:

  1. Everything is in becoming, everything is transformed, both in inanimate matter and in life, including thought itself.

This becoming of phenomena shows two sides: the qualitative and the quantitative. The qualitative aspect is what differentiates objects from each other. “All qualitative differences in nature are based either on a different chemical composition or on different quantities or forms of motion (energy), or, which is almost always the case, on both” (Engels). All objects have a quantitative and a qualitative side, so the object is the unity of quality and quantity. Quality and quantity are in reciprocal action, and “it is precisely in the character of this reciprocal relationship that the cause of the qualitative changes of objects, the transformation of one object into another, is hidden.”

Let’s see how Mark Rosenthal describes this reciprocal relationship: “In the beginning, the quantity and quality of the object constitute an indivisible unity. A certain quality of the object corresponds to a certain quantity. The object has a certain measure. However, in the process of object development, its quantitative aspect changes. There is an unintentional accumulation of quantitative changes that, up to a certain point, do not change the quality of the object. However, this process cannot go on indefinitely. At a certain degree, a situation is created where the measure of the object is disrupted. The new quantitative precision cannot be in unity with the old quality. And then comes the moment when imperceptible quantitative mutations turn into manifest, radical, qualitative mutation. This moment is called the transition from quantity to quality. The qualitative mutation means the disappearance of the old object and the birth of a new one”…

There are many examples in nature, such as that of water. When heated, it boils; or socially, when considering the behavior of one individual, two or three, qualitatively similar, but when the number of individuals increases, the behavior takes on a different quality, becoming a social movement, etc.

So we have a sixth aspect:

  1. In the process of object development, an increase in quantity determines the transition from quantity to quality.

This process is a qualitative leap, a revolution.

Now let’s examine another important aspect of Marxist dialectics, point D.

This is why the dialectical method considers that the process of development from the inferior to the superior takes place through the presence of inherent contradictions in objects, in phenomena, on the basis of a “struggle” of contrary tendencies that act on the basis of these oppositions. Dialectics, in the proper sense of the word, is, according to Lenin, the “study of contradictions in the essence of things themselves.” Marxists often use the term contradiction interchangeably with opposition, antinomy, distinction, etc.

Heraclitus had already noticed that things are constantly transforming: the hot becomes cold; the living becomes dead. Their contradiction resides in all things. The future is the contradiction of the past. Thus, in the egg, its contradiction is in the germ that will give birth to the chick, which is the contradiction of the egg, which it will break when it reaches the cycle of its development. In the egg, there are thus two conflicting forces: the force of the egg that wants to remain an egg, and the force of the germ that wants to become a chick. “The egg is therefore in conflict with itself, and all things are in conflict with themselves,” proclaims Politzer, one of the most famous exponents of Marxism.

The germ in the egg is not the contradiction of the egg, but something else, and we will see why in due course. In the germs, their opposites are present. The germ is different from the rest because it is a unity that is part of the unity, which is the egg.

We will study these aspects later because we will always have to bring up the opinions of Marxists since they have indeed studied dialectics extensively, desiring to construct a solid method with it, which they rarely knew and were able to use properly.

Let us now see how dialectical materialism conceives truth.

It is necessary, once and for all, to stop demanding definitive solutions and eternal truths. We must forever be aware of the necessarily limited nature of all acquired knowledge, of its dependence on the conditions under which it was acquired. Nor should we allow ourselves to be swayed by the irreducible antinomies, always in use in old metaphysics, of true and false, good and evil, identical and different, fate and chance; it is known that these antinomies have only relative value. What is now recognized as true has its hidden false side, which will appear later, just as what is currently recognized as false has its true side, thanks to which it could previously be considered true; and what is asserted as necessary is composed of pure contingencies, and the supposed chance is the form in which necessity is hidden. So we have:

  1. Truth, according to Marxist dialectics, is both relative and absolute.

“Relative to a moment, to a stage of thought, praxis, human history. Absolute through the collective progress of that thought, through perpetual surpassing in a direction, through the dominion and possession of the object” (Lefèbvre).

First of all, by accepting dialogue, Marxist dialectics is subject to its own dialectics and will one day have to be dialectically negated, as it is merely a moment of a larger dialectic that contains it. Engels criticized Hegel for not accepting the transcendence of his own method when he had stated that the evolution of human history would lead to surpassing today’s truths, and that a conclusion accepting a definitive truth would contradict the dialectic itself. In truth, we have shown that Hegel was not so obstinate.

However, in “Materialism and Empirio-Criticism,” Lenin also proclaims: “No fundamental premise, no essential part of this philosophy of Marxism, fused into a single piece of steel, can be altered without departing from objective truth and falling into bourgeois and reactionary falsehood.”

Marxist proponents claim that it provides an explanation for all phenomena, that it is, as someone has already said, “a key that opens all doors,” while others have retorted that “a key that opens all doors must necessarily be a false key.”

Zhdanov stated that with the liquidation of class antagonisms in Russia, the struggle of contrary theses was replaced by criticism and self-criticism. The case of Alexandrov, the notable Russian philosopher subjected to the evaluation of the party leadership, and others, shows how different the reality is from what was asserted in theory.

Marxism is unsurpassable. Let us hear Lefèbvre: "The project of surpassing Marxism perhaps has little meaning or future because Marxism is the conception of the world that surpasses itself. Now, we have seen that the surpassing by Marxist dialectics occurs through negation, which is a term that succeeds, replaces.

There is no surpassing without negation; therefore, there is contradiction.

How to reconcile these affirmations? Marxist dialectics transfers spiritual qualities to matter itself, turning it more into a belief than a science.

Marxists speak of “absolute movement,” of matter that is “infinitely creative,” and they misuse philosophical terms, constantly criticizing metaphysics and confusing idealism with all other currents, etc. The dynamic conception of nature, the idea of surpassing, the transcendence of opposites, have minimized the arguments in favor of ideas in shaping the world and have introduced economic themes into the considerations of philosophers, which were previously given secondary importance, although they cannot fully explain everything as desired by Marxists. The historical character of thought, the influence of the past on it, the influence of present conditions on knowledge, and many other contributions brought Engels and Marx to general dialectics.

While Marxism is not the truth preached by its followers, it does have a role in the history of human thought: the contribution to the impetus given to dialectics, which has taken an entirely new field, rich in remarkable consequences, for the benefit of human thought and culture.15

A is a worker, it is the affirmation, it is the thesis. B is the employer, the capitalist, the antithesis. But A is inseparable from B, and B is inseparable from A, as it is the relations between them, A and B, that form A and B. The person of A is fused into B, so that B, at that moment, becomes the negation of B, which was the negation, and because it affirms A, it thus becomes the negation of negation. Reading Aristotle’s Organon would clarify these aspects of so-called correlative contraries.

Marx would never reason in this way. It is the fate of certain masters to have certain disciples…

If Marxists pondered more on the various dialectical contributions from other origins, they would avoid certain interpretive errors in history that have made them the most accomplished failed prophets of facts. When one delves into socialist thought, it is immediately observed that Marxists, despite all their conviction of truth, have been consistently wrong in their critiques. Read the works of Lenin, Marx, Engels, etc., and one will find an excessive number of instances where words like these are read: “At that time, we were wrong…”

Theme V

Article 1 – Antinomian (Tragic) Dialectic

The antinomistic dialectic is based on the conception of existential antinomic dualism, which we had the opportunity to outline in Philosophy and Worldview when we studied the different and the similar, reason and intuition, and the antinomies of existence exposed by Proudhon in his broad concept of antinomy.

The antinomistic dialectic is also called tragic. Tragic dialecticians were Zoroaster, Heraclitus, Proudhon, Nietzsche.

They accepted a deep antinomy in nature as the foundation of all existence.

This was also the situation of the hero in Greek tragedy, caught between two opposing forces.

Tragic dialectic distinguishes itself from triadic dialectic (like that of Marx) by accepting a constant antinomical opposition in all existence (which, for them, is becoming), while the other admits a third term, synthesis, which we have already clarified. On the other hand, it also distinguishes itself by considering antinomy as fundamental, both in human spirit and in nature, unlike some dialecticians who, in interpreting Hegel, consider it only immanent to the spirit or like the Marxists who proclaim that “contradiction exists in things and not in consciousness and thought, except because it exists in things” (Lefèbvre).

For the antinomistic dialectic (tragic dialectic) that we are going to present, there is a fundamental antinomy of all existence that unfolds in an indeterminate series of opposing processes, which, in turn, generate others, as we will analyze and clarify.

It is not possible to examine it clearly without a precise understanding of the term contradiction, which is constantly used by dialectics scholars.

Contradiction is a concept given to us by both reason and intuition, which we have a rational and intuitive knowledge of, and which we experience both indirectly and directly.

Contradiction is a true category, a general concept to which we can relate our thoughts and judgments. However, contradiction is not even considered as such, and we need to clarify the main meanings that may be of interest to the study of dialectics.

If we accept this statement: “in general, it is said that there is contradiction when something is simultaneously affirmed and denied about the same thing, in such a way that if the affirmation is true, the negation is false, and vice versa,” formally considered, it is evident that this is not properly the concept of contradiction for such dialectics scholars.

And if we examine the various dictionaries that define it, we will always find that the definition does not align with the thoughts of dialecticians.

They affirm that existence is a constant becoming, a constant process. Nothing is static. The process of existence is a continuous transition from one state to another, naturally different.

Whether these constant transformations are caused, performed, or conditioned by an internal position of existence or not is secondary now for the clarification of what we want to elucidate. What, then, does contradictory mean? It precisely means this transition from one state to another state, naturally different. Thus, one cannot statically affirm something about a fact because, being a constant transition from one state to another, the second state, or the successive state, negates the first. This is the meaning of contradiction in terms of alterity.

Some philosophers and critics could accuse dialecticians, as some indeed do, of excessively using a term that has a defined sense in philosophy. They have a valid point, as some dialecticians, like the Marxists, confuse contradictory with distinct, or contradictory with different, contradictory and opposite, contrary, antinomic, and antagonistic, etc.

We emphasize, as mentioned earlier, that Marxists consider what is different as contradictory. However, here we need to make a reservation to avoid confusion.

When Marxists give the example of an egg, in which the germ of the chick is contained, and see in the chick a contradiction of the egg, they are indeed seeing the contrary tendencies of the egg. There is a “difference” present. But if we consider that Marxists also use the word contradictory in the sense of distinct and contrary, everything becomes clear. The chick is thus a contradiction of the egg (at least in this sense). Therefore, the antinomistic dialectic sees an antagonism between the chick and the egg, which is a secondary dialectical process of the existential process because both in the egg and in the chick, as well as in the cells that make up the egg and the chick, there is the fundamental antinomy of existence, a tragic antinomy that manifests itself in many processes, including the most complex process, such as that of the egg and the chick, because it is already a complex of processes. One must never forget that dialectics encompass; it is inclusive, not exclusive like Formal Logic.

We must recognize that the chick replaces the egg, that is, the egg ceases to be an egg through the action of the germ transforming into a chick because for the chick to be a chick, the egg must cease to be an egg. There is thus a transfiguration from the egg to the chick, and the chick, as a chick, is “different” from the egg as an egg, and this fundamental “contradiction,” which takes place in the egg, occurs from the starting point of the germ and the rest of the egg. All dialecticians, with few exceptions (like Gonseth and some right-wing Hegelians), use the term contradiction in this broad sense. And to avoid any doubts, let us clarify it further.

The foundation of Formal Logic is the principle of identity. This principle is one of the principles of reason. What does this principle affirm? What is its classical statement? “What is, is; what is not, is not.”

Thus, a thing is identical to itself. Formally considered, a concept is identical to itself; house is identical to a house; a hat is a hat. But existentially considered, a hat, as the object that is here and now, which we call it, is in its ontic structure (hic et nunc), an object that we distinguish from others and, as a body, is a constant becoming in constant change, and each state that succeeds it is other, distinct from the previous one. Therefore, each state is “contradictory” to the other. We cannot say that existentially considered, this hat is identical to itself because identical is a static concept of reason, and this hat, as a body, is dynamic. So, this hat, as existence, is a contradiction of this hat as a concept, as a form.

Since dialectic is the logic of existence, it is consequently the logic of “contradictions,” or rather, opposites. Now, we have seen that identical has the word different as its antonym, and what we conceive as identical has different as its antinomy.

This divergence occurs in existence between the thing that is (considered formally) and that is not (considered existentially).

Thus, this “contradiction” is not inconsequential for dialectic. That is why we said that, for it, contradiction is a true category, a category of existing (of being and now, of being). Each state is negated by the successive state, which, in turn, is negated by what follows, and so on indefinitely (the antinomistic dialectic establishes another interpretation of the contradiction of existence).

An object, as a unity, as a determined object (this book is here on the table, for example), is in contradiction with its relations (for example, in contradiction when it is on the shelf), but as a unity, this book is not identical to itself at any moment, and it is also identical to itself. Here, reference is made to modals.16

We are facing a paradox or an inconsequence?

That is what we will see next when we study how the antinomistic dialectic responds to and faces this contradiction.

Every existing being presents two dynamic orders: one of intensity and another of extensity. According to the antinomistic dialectic, these two orders are antinomic and irreducible to each other.

But it also affirms that one complements the other, which we will call complementarity.

There is no intensity without extensity, nor extensity without intensity.

Reason and intuition apprehend the two aspects of existence because learning about these two aspects is what stratified these two fundamental functions of the mind. We have already seen that they are fundamental in humans and what elements conditioned them as a structural necessity of existence itself and found their highest stage in humans. We have seen that extensity is homogeneous, static, invariant; and intensity is heterogeneous, active, variant. We are now faced with two important concepts: invariant and variant.

This book, which is here, formally considered as a unity, as a whole, is something invariant, but as a processual unity, it is variant. This book, here and now, and this book later, or up there on the shelf, are formally the same book, considered in terms of extensity. Rationally, we have to call it identical, in the formal sense that reason gives to the term, in any of its states, and existentially as extensity and also as formal structure, it is the same. There are “contradictions” in its relations, as it was on the table at one time and on the shelf at another, but the book is the same. However, as a unity, as a determined body, it is contradictory because it is the combination of two antinomic dynamic orders, intensity and extensity. This “contradiction,” this antinomy, is constant, even if this book undergoes transformations, even if it is consumed by combustion and reduced to ashes, the inverse dynamic order does not disappear because it is constitutive of nature, and it is identified in everything (in a dialectical sense).

This antinomy is not resolved and indicates an oscillation or antagonism capable only of dynamic equilibrium, but this is not achieved by a third term because there is no synthesis in nature, as some Marxists think.

External stimuli are perceived by consciousness. But in every perception, there is a choice and a shaping, so every perception is a “contradiction” of the perceived and a “contradiction” of itself because it is shaped, it is modified. In every knowledge, there is also unknowing. And just as philosophy can construct a theory of knowledge, it can also construct a theory of unknowing.17

What we observe in philosophy is the action of a numerous group that wants to eliminate multiplicity by accepting quantitative monism, to eliminate contradiction by affirming identity. Initiated by Parmenides, it continues to dominate philosophy today, as we have seen, for the most part, it is still under the influence of the great thinker of Elea, although misunderstood.

This imposition of reason, already studied in Philosophy and Worldview, also influences dialectic, especially Marxism, which tends towards identity but in various forms: Hegelian, to attain the Absolute Idea, and Marxism, for a society without class “contradictions.” However, Hegel’s identity is not the same as that desired by Marxism in its assertions because a classless society is a solution in the economy, not in existence, as Marxism recognizes that “contradictions” would continue in other realms.18

Part 3 – “DECADIALECTIC”

Theme I

Article 1 – Analysis of Phenomena – Their Interdependence – Their Antinomic Aspect – Movement, Mutation – Evolution of Phenomena – Antinomic Dualism

Dialectics delved further into the realm of existence when it established that oppositions exist not only in the realm of the spirit but also in things.

However, the great progress made by science allowed for new aspects to be added, liberating dialectics from the dogmatic spirit that had confined it within narrow frames. Scientists boldly applied it to scientific facts, obtaining unexpected results that surpassed the narrow vision in which both right-wing and left-wing Hegelian tendencies attempted to confine it. The great impetus of science completely changed the aspect of the world, now expanded by the revelation of so many new universes.

To grasp the progress of knowledge, it is enough to mention astronomy. If the sidereal world known in 1900 were depicted on a 1-square-meter map, the sidereal world known today, in the same proportion, would require a map much larger than the dimensions of the Earth’s surface.

We have presented only a quantitative aspect of scientific progress, but there has also been qualitative progress. The theory of relativity has given an extraordinary boost to scientific knowledge by opening up new fields of investigation. Time and space, for example, cease to be the qualities cherished by so many rationalist philosophers and become mere abstractions. The chronotopic continuum of physics is not independent of objects or the observer who measures it. Space is not empty but quantitative, and thus it is curved.

The concept of velocity also undergoes modification. What was once considered absolute becomes relative.

Heisenberg’s observations show us the impossibility of a precise measurement of the momentum of an elementary particle and the simultaneous determination of its position in the associated wave. Destouches describes it as follows: “The more precise a measurement of position is, the more unpredictably it alters the momentum, and consequently, the velocity of the particle. The more precise a measurement of momentum is, the more imprecise it makes the position of the particle.”

These are the “uncertainty relations” of Heisenberg. And why is that? Because, as we see in Psychology and also in History, the observed object cannot be separated from the observer. The impossibility of determination gives rise to an indeterministic conception in microphysics. It can only formulate probability. This indeterminism does not imply that physics asserts the “freedom” of matter but rather the impossibility of determining the data.

Mathematics, which begins with sensory experience and reaches total abstraction, works with symbols and penetrates new territories, especially after the development of vector calculus. Soon it will delve into new territories when it takes an interest in the intensist aspect, which vector theory will inevitably bring to the fore. Formal Logic is going through a phase of criticism and analysis, whose fruits are already ripening. The dialectic established by science is more Proudhonian than Marxist, as it establishes, alongside the thesis, the antithesis, which instead of replacing each other, affirm themselves alternately and do not reach a synthesis, except as a connexio (connection, that is, as a unity of opposites). These positive and oppositional affirmations are considered complementary and cooperative. Here, the notion of complementarity introduced by Niels Bohr applies.

Let us explain it: there was a conflict between corpuscular theory and wave theory in optics. “Bohr’s notion of complementarity consists of assigning an equal part of reality to the corpuscular aspect and the wave aspect of phenomena, and declaring that it is always either one or the other aspect that appears when we conduct experiments, and that the two never manifest simultaneously” (Destouches).

Thus, two complementary ideas are distinct, and as such, they oppose each other, but at the same time, they complement each other, so they can be considered elements of concrete reality. When treated in isolation, they are abstractions. What does science conclude then?

Science comes to understand that there is a dialectic in things, and that the dialectic of the spirit is a reflection of that. (Our opinion differs, as we have already shown that the dialectic belongs to all nature, including the spirit). In living phenomena, there is a physical-chemical aspect of things (quantitative, extensive) and a dynamic aspect that transcends physics and chemistry (intensive). To grasp life, it is necessary to examine it from this dual aspect. One is incomprehensible without the other, just as the idea of freedom is incomprehensible without determinism because for freedom to exist, its opposition must exist, so that it may arise, establish itself, and be conceptualized. The absolute conception loses its strength because modern science no longer seeks or operates with absolutes. Even mathematics itself is gradually freeing itself from the aprioristic pressure of the absolute. Scientific dialectic does not seek to achieve a synthesis in which the negation of the thesis would be negated and the contradictions reconciled, but a new representation in which the thesis and the antithesis remain true. Thus, science places itself in the Proudhonian situation where all scientific propositions are “open questions,” requiring rectifications, revisions, and new analyses. Formal Logic is static; dialectics is dynamic, just as the human spirit is dynamic. Dialectics continually transcends itself thanks to the expansion of fields and planes that can be examined and verified.

When studying antinomies, the factors of extensity and intensity that operate in all objective reality, we have seen that all existence is opposition, and that consciousness of existence arises from opposition, the great dialogic opposition between subject and object, the world of the Self and the world of the non-Self. But this dialogue is not only between the Self and the non-Self. This dialogue is highly complex because antinomic dualism is present in all facts of cosmic occurrence, and when one fact opposes another, this dialogue duplicates, as we will see when we explain what we call “decadialectics,” or the ten great dialogues of existence. With the explanation of this great dialectical “complex,” all doctrines and opinions presented throughout the history of Philosophy will take on new and unexpected colors, and our overall view of the world will be the product of the perspective of someone who stands above to examine the complexity of the facts.

“The moral world, like the physical world, rests upon a plurality of irreducible and antagonistic elements, and it is from the contradiction of these elements that the life and movement of the universe result.”

This is the fundamental position of Proudhon, whose dialectics establish the constant opposition of antagonistic elements that form the basis of all existence. He continues: “The question remains whether all these spontaneities that compose creation are in agreement with each other or if they combat each other; whether, by the law of their constitution or by higher order, they form a round dance of perfect love or engage in an immense battle; whether the order that is discovered here and there in this mixture comes from the harmony of coordinated instruments like the pipes of an organ or if it is merely the effect of the balance between antagonistic forces. As for me, my opinion cannot be doubtful: what makes creation possible, in my eyes, is the same thing that makes freedom possible—the opposition of powers. It would be a gross misconception of the order of the world and universal life to turn it into an opera. I see forces in conflict everywhere; I find no place where I can perceive that melody of the grand Whole that I believed I heard in Pythagoras.” Proudhon thus remained in a constant vision of the antinomy of finite existence, unable to transcend it.19

The polemos of Heraclitus, the war, the struggle, was the “category of reason.” Kirkegaard also held this opinion. It is the anguish of contradiction that dialecticians like to talk about when they seek a solution through synthesis. However, Proudhon could not be understood in this way. Nevertheless, if we carefully examine the conception of Marxist dialecticians, they also affirm a constant contradiction through the idea of movement. Being materialists, since they admit that the “essence of matter is movement” and “that movement is already a contradiction,” they accept contradiction as inherent, constant, and eternal. (Note that Marxists consider movement to be eternal, matter to be eternal, infinitely creative, etc., attributing divine predicates to matter).

Movement was not caused by a first mover, God, or a deity; it has existed for all eternity (eternity is always used by Marxists to mean endless time). In other words, movement coexists with matter because matter is movement; therefore, it is not static or passive but active and dynamic. And since matter never had a beginning and will never have an end, being itself movement, movement never had a beginning or will have an end.20

Metaphysics, for Marxists, rests on the acceptance of static ideas, of a stable and motionless world, immovable, unchanging. However, existence is perpetual movement and constant transformation. Let us quote Engels: “Movement is the point of existence of matter. Nowhere and at no time has matter existed or could have existed without movement” (Anti-Dühring), and in “Dialectics of Nature” he says:

“Movement, when applied to matter, is a transformation in general.” It is thus clear that movement is the generator of everything for Marxists. In no situation do they ever ask: is movement something original, primitive, a kind of essence, or is movement the product of other processes in nature? Because by giving matter all creative attributes, the problem is easily solved. Matter is everything, can do everything, makes everything. It is, in short, God.

Materialism cannot escape the religious. It is a religion of matter, which takes on all the divine attributes except for self-awareness, which only becomes apparent in higher living beings, and self-consciousness in humans.

Since everything is matter and everything is dynamically creative, materialism is a kind of pantheism. “Movement is eternal, not transitory, absolute,” exclaims the Marxist dialectician Rosenthal.

However, let us make some simple observations: How do we understand movement? We understand that there is movement because there is more or less movement, that is, some things move faster than others. Therefore, we must conclude that it has intensity; thus, the term movement expresses a variety of movements; it is a general concept. However, to understand them as less than another is not the same as accepting that a body is more or less at rest? Thus, the idea of movement requires the idea of rest. A moving body is also a body at more or less rest.

For one movement to be smaller than another, it cannot be an absolute movement but a relative one. Nor can movement be something simple because then all movements would be the same. And if one is smaller than another, it is because the smaller one contains more rest than the other. How can we conceive of an absolute movement if not as simultaneous?

The idea of movement must also undergo a dialectical analysis: what we call movement is therefore inseparable. Thus, it cannot be the essence of matter; it is not absolute, and to make it unconditional, absolute is to create a new abstraction, to work with ideas alone, to be “idealistic,” and consequently, to be “metaphysical” in the sense that Marxists call metaphysics; it is not being dialectical.

Let us continue our critique so that the concept of becoming (which also encompasses movement as rest) becomes clearer.

In “Dialectics of Nature,” Engels says, on page 35, ed. “Problemas”), “that in the world there is nothing eternal except matter, which eternally transforms itself in eternal movement, and the laws by which it moves and transforms itself.” So there is a legal eternity in nature beyond the eternity of matter and the eternity of movement.

And he further states, on pages 35 and 36: “...no matter how many millions of suns and earths may be produced and disappear; no matter how long it may take for the conditions of organic life to appear in a solar system and only on one of its planets; no matter how many organic beings must appear and disappear before animals with a brain capable of thought can develop among them and find, for a short period, conditions that make their life possible, only to be inexorably destroyed afterward; we are certain that matter, in all its transformations, remains always the same, that it cannot lose any of its attributes, and that, therefore, with the same iron necessity that will destroy its highest flowering on Earth, the thinking spirit will give rise to it elsewhere and at another time.”

Matter remains always the same, that is, identical to itself, through its transformations, and therefore, as such, unchanging. This assertion is quite metaphysical for those who ridicule this science so much. Here we also have the “iron necessity,” the same old necessity of reason.21

Nietzsche liked to juxtapose two opposing concepts or ideas to bring about a new understanding of things. The isolated idea of movement, taken by itself, is a pure illusion, just as the idea of rest is abstractly considered. The conjunction of the two (concept) may give us another comprehension of things.

When we spoke of Niels Bohr’s complementarity, we saw how significant it is that sometimes the corpuscular view and sometimes the wave view appear to us. Neither one alone satisfies us, but both, complementing each other, allow us a more solid position. It is the same here: because rest is something corpuscular and movement is something vibratory (modalities of one and the other). In the notion of a corpuscle, there is a hint of stillness, of rest, and in the notion of a wave, there is a hint of dynamism, of movement.

Everything that is in action is not completely in action, as we have seen. The transition from potentiality to actuality, that is dynamism (like all energy). And because it is dynamic, it is never absolute action, because there would be no further action. The dynamism of existence lies in the transition from potentiality to actuality. What is actualized, what appears, what is a phenomenon is not everything because if it were everything, there would be no transformation, and the dynamism of existence shows us that not everything happens, but there is still something yet to happen.

Every energy implies an opposing energy. Energy, as we know it, is a result and not something simple, as the energists in general believed. It is also a modality. Science did not accept this point of view because it considered energy, unique and positive, in a way that only formal logic could understand, vices employed. Dirac, an English sage, with his famous equations, revealed negative energy (-e), which was later confirmed.

Space, which in classical physics was an absolute space, rigorously homogeneous and infinite, as reason desired, is now relative space, always linked to negative temporality, according to modern relativity. Dialectic is a logic of temporality, while Formal Logic is a logic of spatiality.

The acceptance of a fundamental dialectical principle of energy has completely transformed the old rigid concept of matter, which dissipates in modern physics.

Modern physics does not have the fineness, lightness, and agility of the idea of energy. But energy, as something homogeneous, eternally the same, also does not correspond to the variety of unexpected phenomena revealed by microphysics. However, what is established in a demanding, imperative way is a completely dialectical concept of energy.

It is understood as the result of a struggle between two antinomic orders (one cannot be reduced to the other), vectorially different and opposing. There are two orders, one intensivist and the other extensivist. One tends outward and the other tends inward, which gives the pulsating, centrifugal, and centripetal character of existence, a constant irresolvable antinomy of all chronotopic existence, which manifests itself in positive and negative, attraction and repulsion; in short, in all the qualitative polarizations that human intelligence can comprehend and create. But at this point, we are bordering on the doors of metaphysics in its proper sense, and in this book, we cannot address aspects that go beyond it.

However, we will not fail to examine them within the framework that guides us.

Article 2 – Antinomic Dialectic of Quantity and Quality

We have already established the dialectic of quantity and quality, considered from the perspective of factors of intensity and extensity.

Let us first analyze some aspects of Hegelian dialectic. Pure Being has no determination; it is informed. A determination is a quality because it determines, and what determines, qualifies. Pure Being, as we have seen, is equal to nothing because it has not received determinations.22 When it receives them, it transitions from Being to Existence (Dasein), which is the present, determined being. It is the becoming, the unity between Pure Being and Nothingness, an immediate disappearance of one in the other. Hegel opposes nothingness to something (Etwas) because something is already a determined, distinct being, therefore something other than something. Every determination is finite, hence negation; it negates the “other.”

One of the most obscure points of Hegelian dialectic is the one concerning quantity. Let us begin by discussing what it is not to arrive at what it is. Quantity, already determined, is magnitude; therefore, quantity is not magnitude. Let us strip magnitude of determination, and we have quantity. The absolute is pure quantity, according to Hegel. In this way, quantity is pure Being, the fundamental determination of the absolute as absolute, exactitude without difference (without the different). When quantity is determined, it becomes magnitude. Quantity receives the determination of quality because, as we have seen, quality is a determination, and quantity transitions from pure being to existence, that is, to being determined.

Let us reproduce Hegel’s own words: “It is said that nature does not make leaps; and the common opinion, when it seeks to understand birth or destruction, imagines that it understands them by representing them, as we have seen, as gradual birth or disappearance. But, as we have said, the mutations of being are not the passage from one quantity to another, but the passage from quality to quantity and vice versa, the transition to another, the interruption of the gradual, and a change of quality in relation to the previously determined being. Cooled water does not gradually become hard in such a way as to freeze and then slowly harden until it reaches the consistency of ice, but it becomes hard in one stroke; once it reaches the temperature of ice, it can still maintain its liquid state if it remains motionless, but with the slightest disturbance, it transitions to the solid state”...“In moral life, when considered within the realm of being, we find the same transition from quantity to quality; different qualities appear as founded on a quantitative difference.”

Marxist dialecticians take advantage of this exposition, and some of them seek to avoid considering this leap as essentially instantaneous. It is through a more or less prolonged conflict, through a complex process of destruction and creation, that the leap occurs.

Marxists provide numerous examples, some of which we have already mentioned. But they also accept the transformation of quality into quantity, adhering to Hegelian conception that quality is the determination of Being, for pure Being, as pure, is indeterminate (without forms), while determination (with form, for example) is qualitatively determined. Thus, qualitative transformation occurs through a change in quantity, which, through these increments, changes in quality (changes in form, for example). Since every being in becoming, as a determined being, is constantly changing in quantity, it is also constantly changing in quality. But this change occurs subsequently. First, there is an increase in quantity (as in the case of cooling water), but at a certain moment, when that quantity reaches a certain level (the freezing temperature), the quality changes (from liquid to solid). Thus, both Hegelian and Marxist dialecticians subordinate quality to quantity and vice versa. For example, when the quality of service organization is transformed, it can generate an increase in productive quantity.

We know that it is not easy to navigate through the tangle of ideas of quantity and quality in Hegel, which Marxists have understood well or poorly and seek to apply to their dialectic, which is Hegelian but upside down.

Once we grasp Hegel’s doctrine, it becomes easy to understand what this conversion of quantitative mutations into qualitative mutations and vice versa consists of.

Hegel recognized that fixed being, as distinct from determination, being in itself, would be the empty abstraction of being. Thus, the determined being, which is the other of abstract being, is the very moment of being.

We can grossly exemplify indeterminate being, pure being, as follows: imagine an amorphous substance, like a mass of plastic matter, but colorless, formless. This pure being is pure abstraction, what he calls the absolutely negative, which, in this state, is equal to Nothing, which is also formless, indeterminate. Are these Being and Nothingness the same thing for Hegel? No. To explain them, let us use the example and lesson that becoming gives us. “Everyone has a representation of becoming and will have no problem admitting that it is a representation; moreover, when it is analyzed, it is found to contain not only the determination of being but also that of its opposite, nothingness. Thus, becoming is the unity of being and nothingness.” Hegel provides an example accessible to all: beginning—something in its beginning is not yet, but this not being of the thing is not mere non-being because it already contains its being. So what distinguishes Being from Nothingness? It is not easy to find a distinction because he acknowledges that indeterminate Being and Nothingness are two empty abstractions. The only distinction he finds is in intention; that is, indeterminate Being tends toward being determined, while Nothingness tends toward non-being. Thus, indeterminate Being and Nothingness are moments of determined being, which is concrete being.

With these points distinguished, let us proceed with attention: indeterminate being, which in this state is equal to Nothingness, receives its fundamental determination, which is quantity. By receiving this determination, indeterminate being becomes determined; that is, it transitions from Sein to Dasein (localized being). This determination is called quality because it qualifies, determines. Let us crudely exemplify this: imagine a potter who takes that amorphous substance, the mass (by analogy, indeterminate Being), and gives it a form, limits it, sets terms for it; it ends here, it ends there, that is, it de-termines it.

Every determined being is quality. This determination is one with being, but at the same time, by limiting it, by setting a barrier, it is a negation of Being. With this determination, Being, which was indeterminate, by becoming a determined being, becomes another than it was before. This is what Hegel calls “being other.” The being-in-itself would be an empty abstraction of being. Thus, the determined being, the other being, is the very moment of being, but it is something that is there (Dasein); it is something, and this something is, first and foremost, finite; secondly, mutable, and thus finitude and mutability belong to the determined being of something.

We have already seen that every determined quantity is magnitude, which should not be confused with quantity, for the absolute is pure quantity, and this is the fundamental determination of the absolute, according to Hegel.23

Another Hegelian idea is essential for this study: the idea of quantum, which many confuse with quantity. The quantum (plural quanta) is limited quantity, it is determined quantity, and its development and complete determination are found in number. The quantum is extensive magnitude, as multiple determination in itself, adds Hegel; but when it is simple, in itself, it is intensive magnitude, and we have the degree.

Thus, there are two kinds of continuous or discontinuous (discrete) magnitudes: the extensive and intensive. The former refers to quantity in general, while the latter refers to determinations (the qualitative) of quantity as such. Every extensive magnitude is also intensive, and vice versa; they do not form two species.

Let us try to explain the conversion of quantitative changes into qualitative ones and vice versa, or the transformation of quantity into quality, as others say, or the transition from quantity to quality, as Lenin calls it. “To obtain a quantitative characterization of things, we must find characteristics that are not ‘different’ in the things we want to compare, identical and common characteristics that are not fortuitous or nonessential, but of such a nature that they allow us to determine, through them, their quantitative relations and the qualities that arise from them (Shirokow).” Putting aside the misuse of philosophical terms, we have clearly understood what Shirokow means. Quantity is exactitude without difference. Quantity is the homogeneous, the extensive, what is comparable in all things, as mathematics and mechanics demonstrate very well, especially in their dealings with quantity.

What does not differentiate bodies from each other?

It is quantitativeness. But before reaching that, there was an attempt to consider weight because all bodies have weight.

This was the solution offered in the mechanistic phase of science. Then, velocity, mass, and volume were taken as the simplest and most repeatable aspects of physical phenomena. This tendency led to considering quality merely as quantitativeness. And the reasoning was simple: it is quantitativeness that is present in all things, thus it is the sufficient reason for all things; and quality is merely the apparent aspect of quantity. Formalists, mathematicians, and mechanists rejoiced at the discovery.

In this way, identity would be found in quantity, and the concepts of reason and its principles, as we have already studied, lead to the valorization of quantity, of spatiality.

The examples cited by some Marxist dialecticians aim to show that when there are quantum modifications (yes, because here they refer to the quantum itself and not merely to quantity as quantitatively undifferentiated, as, for example, the idea of matter, which is an indifferent determination of the absolute as quantity), there are corresponding qualitative mutations. Every quantum modification is accompanied by a qualitative modification. This is verifiable by us after reaching a certain degree (note: degree).

What do the above-mentioned dialecticians understand, above all, by quality and quantity? This question is not trivial because in its answer lies the key to the entire difficulty. We have already seen how Hegel thinks about quantity and the quantum.

Quantum is limited quantity; quantity is exactitude without difference, without anything that differentiates it; it is the homogeneous as abstractly considered by reason. Every limited quantity is a quantum, and every quantum is magnitude because, as we have seen, magnitude is determined quantity (the limited is included in this concept).

Let us consider an example of the mutation from quantity to quality as understood by Marxist dialecticians: two men speak out against the government. This fact, due to its small quantity, has no significant meaning. But if this conversation is joined, not by two, but by a hundred, two hundred, three hundred, thousands of people, then the quantitative increase modifies the quality.

What was merely a conversation now takes on a serious political character. Let us analyze: do we have quantity or quanta here? We have magnitudes that are quanta because they are composed of limited quantities (individuals). But it is not merely the gathering of these men, the quantitative addition, that modifies quantity into quality; it is the fact that these men participate, with greater or lesser interest, in the gathering, which gives it a special quality. So, what do we see? We see that in this example, there is not only a transformation or conversion from quantity to quality but also the manifestation of a determined collective state (qualitative).

Here, we have not just a sum of quanta but also a conjunction of quality. Quantity manifests the existing quality, so the transformation does not occur as the Marxist dialecticians believe, even though it reveals the quality that was not perceived until then. Let us modify the example: imagine many indifferent men who, upon hearing the speakers, modify their interest, which increases. Is there a transformation from the quantitative to the qualitative? No. Let us accept that human examples are not suitable because they involve affections, etc.

Let us move on to other examples, such as water cooling. Water, when continuously cooled, reaches its maximum density at 4 degrees Celsius. Cooled down to 0 degrees, under normal conditions, it suddenly freezes. Qualitatively, it changes from liquid to solid, without passing through a constant solidification phase like paste, etc. There is a leap. In this state, frozen, water presents qualities different from ordinary water at normal temperature. It is known that the molecular composition of water is two parts hydrogen to one part oxygen. A volume of water is composed of two volumes of hydrogen and one volume of oxygen. But as we continuously cool the water, it, as a quantum abstractly considered, does not undergo quantitative modifications. It is quantitatively the same water. However, its molecules undergo simultaneous quantitative and qualitative modifications because cooling increases the density up to 4 degrees. It becomes heavier because it is denser, and the gravitational potential is greater.

Now, weight and density are extensive according to Ostwald’s scale, as we have seen, but gravitational potential is intensive (qualitative). Thus, as it becomes denser quantitatively, the gravitational potential, which is qualitative, also increases. Up to this point, we see quality accompanying quantity. By decreasing the temperature (which is intensive) and relates to thermal energy, until it reaches 0 degrees, it suddenly freezes, at least for us, although in cosmic time it is something that lasts. What happens there? Quantitatively, there is an increase in density. By decreasing density, the gravitational potential (intensive) decreases. In other words, the changes that the quantum undergoes in weight, which is quantitative, are accompanied by simultaneous changes in intensity, which is the gravitational potential. What does all of this show us? It shows us that there is contemporaneity between the extensive and intensive aspects, as we understand it. Therefore, the mutation from quantity to quality is also a mutation from one quality to another.

There is no singularly quantitative moment undergoing transformation to give rise to a different qualitative moment. What exists is a quantitative modification contemporaneously with qualitative mutations that are inseparable from it (because, as we have seen, intensity is inseparable from extensity). However, once a certain degree is reached, it appears qualitatively different from the previous state. Thus, there is contemporaneity simply because quantity and quality are inseparable in the process of becoming. If we consider, as we have done, extensity factors as predominantly quantitative and intensity factors as predominantly qualitative, then we can perfectly understand this so-called conversion of quantitative mutations into qualitative ones.24

We only want to say that Marxist dialecticians, for not basing their dialectic on the antinomy of all becoming, which occurs extensively and intensively, simultaneously, seem to want to see (as many really do) a leap from quantity to quality when there is actually a leap from quality to quality, as there have been simultaneous quantitative mutations, or rather, quantum mutations. This is understood by modern science, and in some aspects, Hegel also sensed it when he saw in the quantum the determined quantity as unity, that is, while the general determination (as a general determination) was within it (unity) and that determination was contained within itself and not outside it. Therefore, it was a limit, limited, and as such, it was the quantum, and as unity, it negates what is not itself. The concept of quantum in modern physics arises when considering that energy, as a variant in phenomena, is a discontinuous variation, and the units of that variation are called quanta. Hegel saw that intensive and extensive magnitude do not form two species, that is, that each contains a determination that the other does not contain. Every extensive magnitude is also intensive, and vice versa (Logic § 103).

Quantity, as self-equality, is continuous; when determined, in unity, it is discontinuous. But continuous quantity is also discontinuous due to the units, the quanta, and the quantity considered discontinuous is continuous because it encompasses the units, which are the same as many units. This is the dialectical aspect of quantity, which is continuous and discontinuous. A qualitative mutation, as observed in the examples of Marxists, is a quantum mutation.

But what does this quantum mutation show? It shows a greater velocity (the leap) that is intensive, that is, the energy of movement, as intensity, is greater.

Thus, there is not really a conversion of quantitative mutations into qualitative mutations; there is a conversion of quantitative and qualitative mutations simultaneously, which, when reaching a certain quantum (which is both quantitative and qualitative at the same time), undergo a qualitative leap, which is also quantitative because both are inseparable; otherwise, they would be treated abstractly and not concretely. The Marxists are not mistaken, but they simply did not grasp the profound dialectical aspect of becoming in its mutations of extensity and intensity.

So when Rosenthal says, “an inadvertent accumulation of quantitative mutations takes place, which, up to a certain point, does not change the quality of the object,” he is mistaken because corresponding qualitative mutations already exist, although imperceptible to the eyes. He continues, “This process, however, cannot prolong indefinitely. At a certain degree, a situation is created in which the measure of the object is broken. The new quantitative precision cannot be united with the old quantity. And then comes the moment when imperceptible quantitative mutations become a “manifest, radical, qualitative” mutation. This moment is called the transition from quantity to quality.” It is not only the quantitative aspect that changes (this is inseparable from the other, as shown by all dialectics that do not separate but encompass). These quantitative mutations do not change the quality.

They do not cause any change because quantity, considered in the abstract, is not dialectical. Quantity does not do anything on its own because it is only one aspect of the reality of becoming that our noological constitution unfolds into quantity and quality, as more intelligible concepts.

Quantity does not create quality. The dynamic process of becoming has two orders, the quantitative and the qualitative, but one does not cause the other; they are not factors of each other.

If a gas, by expanding, bursts its container, we must not forget the plastic energy of elongation, which intensely manifests as pressure. And that pressure is intensity. Volume is extensive, but pressure is intensive. The rupture is a consequence of the gas volume, which, expanded by heat (thermal energy), overcomes the resistance of the container through pressure. What happens is a direction, a vector displacement (extensive) of form as elasticity with the corresponding force, which is intensive. If we actualize the extensive, we virtualize the intensive, and if we actualize the intensive, we virtualize the extensive. This is the normal dialectical aspect of our mind, which leads to this evaluative accentuation of quantity or quality.

Marxist criticism had its historical value by definitively putting an end to the prevailing conception in the science of the nineteenth century that saw the process of development of phenomena merely as mere growth processes, mere quantitative processes.

When Engels, in “Dialectics of Nature,” says that all qualitative differences in nature are based either on different chemical compositions or on different quantities or forms of movement (energy), or, which is almost always the case, on both, if the or were removed and the antagonism between them were affirmed, he would have stated what scientific dialectics today cannot fail to recognize.

We do not deny, and no one in good faith can deny, the value of dialectics today when we can no longer deny the immanent contradictions in the world of becoming. Gradually, it becomes a peaceful subject for science, although it does not imply that we have already traveled the path it offers, which is still arduous.

The tensional qualitative leap, which the Marxists partially touched upon, is a topic that we cannot study here, and we will do so in the “General Theory of Tensions,” where the tensional dialectic, which encompasses the one we are currently studying in this book, offers new analytical possibilities.

On the other hand, we can dialectically observe that every ontically affirmed quality is a negation.

Analysis of the dialectic of quality and quantity

When we perceive the qualities of facts, we do so selectively according to our cognitive schemas, as these are always selective because every act of knowledge inherently involves choice. The result is a schema that we assimilate into abstract schemas (hybrids of facticity and eideticity), as we have seen.

In the act of intellectual knowledge, we virtualize what we intuitively know, the ontic. Intellectually, through reason, we actualize what is unknown to us through sensory intuition, the ontological. This car here, gray, is reduced to the abstract schematism of correlated concepts. But the experience of the car, ontically captured, is virtualized in rational knowledge, which is knowledge of the general. In this way, what is known intuitively through the senses is virtualized to actualize what is unknown to them but constructed through abstract schemas by reason.

In mnemonic schemas, the image of the gray car remains, representable or not. This experiential knowledge of the singularity of this car is accompanied by the rational knowledge formed through assimilation, which the image of the car offers to the abstract schemas that reason works with. We now have a hybrid knowledge (experiential-rational) of singularity and generality, which we cannot dissociate in praxis, which is living, but we can dissociate in the analysis of the mind, which is abstract.

If we have to tell someone else that “we saw a gray car here,” we only transmit that generality, which will be assimilated by the abstract schemas of the listener without, however, having any experiential knowledge of the singularity of the car.

In this way, we transmit only what we capture schematically through the assimilation of abstract schemas. We virtualize the heterogeneous aspects of the car to express only homogeneities, even if we do so in as much detail as possible because we always work with concepts, which are abstract schemas.

Therefore, no fact is identical to the concept factually, only ontologically, never factically.

Conclusion: a fact can only be identical to the concept when taken ontologically, that is, regarding the abstract schema, but it is ontically different from the concept and, consequently, ontically analogous, which already encompasses the synthesis of similarity and difference.

Regarding the concept, we can say that it has the essential notes to be classified within a particular abstract schema, but we simultaneously assert that it has more, it has what is not in the abstract schema, what is heterogeneous to the concept, what “contradicts” it.

Thus, we have the dialectic of conceptualization clearly, which, by its characteristics, affirms affirmation and affirms negation regarding the ontic, as it affirms heterogeneity.

In this way, conceptually, everything is and is not; it is homogeneous, and at the same time, it is heterogeneous to the abstract schema that “contradicts” it.

We cannot conceive a factual time-space entity without quality. Every factual existence is quantitative and qualitative. Every quality is revealed through a limit-knowledge because it demands its polarity, its opposite. The quantitative is affirmed by another limit-knowledge. Only by stripping the quantitative of its factuality can we construct a homogeneous concept of quantity, as reason does, making it identical to itself and ultimately transforming it into the abstract concept of space, from which it strips away all heterogeneity to the point of transforming it into nothing.

The idea of quantity and the idea of quality, as categories, present deficiencies that we seek to resolve with the synthetic and dialectical concepts of intensity and extensity, as they are more concrete, while the former is more abstract, as it is merely formal.

Quality presents two problems:

  1. Regarding quality formally, as opposition to quantity and other kinds. Qualis is what defines Aristotle’s third category. The answer to this question is not at all the result of measurement, even in a broad sense.

(Quantities are measured; qualities are compared, it is said.)

  1. It remains to be known what qualitative aspects quantity contains.

Quality can be considered objective and subjective (in humans, for example).

In other words, quality in the thing itself and quality in us. Philosophers have always been suspicious of and even disdainful toward quality because it is tainted by subjectivism.

Husserl, to solve this problem, moved quality to the realm of essences. However, by understanding it as intensity, which does not separate it but rather antinomizes it from quantity, we are on our way to giving it a structure that frees it from the stigma of subjectivism that concerns modern philosophers.

Quantity, as such, is a surpassed and indifferent determination, an indifferent determination.

We often say: how many people have such a thing?

We are faced with indifference. Then we reply: how many what? And then we say: how many meters, how many degrees?

There are qualifications and determinations here, limitations of quantity; that is, the quantum (exclusive determination).

Article 3 – Reciprocity – Antinomic Dynamism of Extensity and Intensity – Contradiction in Unity – Theory of Dynamic Equilibrium – Categories

We know that Formal Logic establishes, through the principle of identity, that what is, is; thus: “this book is a book.” There is nothing to object here against this tautological statement, and dialectics does not intend, as many think, to deny value to this equality, which is fundamental for formal logic. Dialectics recognizes the “contradiction” in things, the “contradiction” in this book as unity, which repeats what happens in all existence. This book, which is this book, is not something static and unchanging, like the concept of book that we apply to it.

This book is something that changes, something that transitions from one state to another, whose being, as a book, is a being of various states that are contradictory. It is a field of struggle between opposing or divergent, antinomic and antagonistic orders.

It is important never to forget the distinction between contradiction and negation. So, if we say, “this book is a book,” we are within the realm of formal logic. If we say this book is in opposition to itself, we are in dialectics. But if we say, “this book is and is not this book,” we need further clarification, as it is necessary to know if we want to refer to the book, declaring that it is not immutable, or if we want to say that it is not itself, but something else.

The “contradiction” of the book is not just the negation of the book. Saying that this chair is not this chair does not establish its “contradiction” dialectically.

Many believe that dialectics is only about negating, taking away, removing, reducing, when, on the contrary, it is about adding, actualizing the virtualized, emphasizing the disregarded, registering what has been forgotten, highlighting what has not been considered. When we are dealing with concrete things, this mode of proceeding does not create major difficulties. However, when we work with abstract objects, ideas, concepts, etc., the confusion between contradiction and simple negation as deprivation leads to dangerous confusions.

Dialectics seeks to give greater concreteness to thought and better adapt it to existence, avoiding rationalistic abstractionism, which has caused so much harm. Negation, in dialectics, is not a privation but an accentuation of what has been inhibited, disregarded. When we say that this book is a being in transition, it is being, we do not want to abstractly consider it as immutable in the formal sense, but individually in transition. In this way, we establish the two opposite aspects of all things: 1) what affirms in them, what wants to preserve itself, what is homogeneous in them, and 2) what transitions from one state to another, what transmutes in them.

Dialectical negation is the negation of the abstracting affirmation. If we affirm that something is, we abstract from it its contradictions; in this case, the affirmation of immutability is an abstracting affirmation. And when we affirm that it is a being with its contradictions, we deny the abstracting affirmation but affirm the heterogeneous side of the object, without denying its homogeneous side, which is affirmed. Negation is thus dialectical and not a privative negation, an entity negation, but a denial of the absoluteness of the abstracting affirmation, therefore an affirmation of the inhibited, disregarded, virtualized. We prefer to use opposition in the sense of what is opposed to the affirmed content, which is also an affirmation of positivity. Hence, Hegel said that dialectical negation is positive.

With this second point clarified, we now need to clarify the third one, which, once perfectly understood, will prevent common errors. There are three terms commonly used that cause confusion. They are: antinomy, antagonism, and contradiction.

We have already examined the meanings of these terms, but we will see that the content of some is smaller than others, and their extensions also vary. Thus, contradiction is not considered absurd by dialecticians.

In any reality, we can find the oppositions that lead it to become.

Contradiction is present in this reality as unity. Therefore, there is no contradiction between this book and this chair as book and chair. As we have already emphasized, the concept of contradiction for modern dialecticians does not have the precision that classical philosophy gave it. For our part, we prefer the traditional use, as we have already exemplified.

However, there are oppositions within the book and also within the chair. Contradiction lies within unity, in everything that forms a unity, in everything that is, as structure, identical. Hence a dialectical principle that states that “everything that is identical (here in the sense of unity) is contradictory; everything that is contradictory is identical.” The necessary coordinates for the constitution of a being are opposed (opposed to each other) and cooperate.

An antagonism is an opposition of two or more contrary directions, as well as of opposing units. There is antagonism in a sports match, between conflicting teams. The “contradiction” between them occurs at the time of antagonism; it is “contradiction” while antagonism, and it is structured as a totality, such as a match, for example. But an antagonism can cease to exist, and in that case, the contradiction also disappears.

An antinomy, in the sense we use it, as we have seen, is the immanent position between two vectors, directions, in which the affirmation or truth of one is not the negation or falsehood of the other.

The antinomy between extensity and intensity does not allow the exactness of one to declare the inexactness of the other.

In becoming, there is an opposition that we prefer to call antinomic because the reality of one vector does not imply the unreality of the other.

Therefore, not all antagonisms are antinomies, but both are oppositions when it comes to structure.

Thus, there are variant “contradictions” and invariant “contradictions”.

Antinomic oppositions are invariant, and antagonistic oppositions are variant.

This clarification is significant for the following reason: in the social realm, Marx and the Marxists criticize Proudhon for asserting the fundamental antinomy of existence and not accepting synthesis in the Marxist sense. Thus, they argue, the antagonisms would always remain in human society, such as those between the bourgeoisie and the proletariat. Proudhon did not think so, and that was what the Marxists did not understand.

The antagonism between the proletariat and the bourgeoisie is solvable because in that antagonism, there is a buyer and a seller of human labor. There is selling because there is buying, and vice versa, and the antagonism is founded there. But the worker can cease to be a seller of their labor, cease to be a wage laborer, through, for example, a social system in which there is no longer any buying or selling of labor.

In this case, the antagonism ceases to exist. In a society of free producers, as Proudhon imagined, there would be neither buyers nor sellers of labor, but fundamental antinomies would continue without certain antagonisms. The synthetic solution of the socialist state, as the buyer of human labor, replacing the private buyer, does not eliminate the antagonism, although it only replaces one of the antagonists and modifies its form for the worse.

Thus, we avoid confusion between these terms, between what is antagonism and what is antinomy, between solvable and insolvable oppositions, between variant and invariant oppositions because dialectics is dialectical even in its own process, and even opposition must be examined under its auspices.

With this explanation made, we are ready to decisively delve into the topic. The fundamental point consists of accepting that in all facts of nature, internal oppositions of various kinds are implicit, and it is the task of dialectics to study and analyze them.

In the development of these oppositions, there is a reciprocal interaction of actions, as contrary tendencies permeate and mutually stimulate each other. This is what is called reciprocity, whose general aspects we will address.

The struggle between these diverse tendencies, which occurs in every fact of reality, is a creative and destructive struggle of different forms and different units, of different quantities that sometimes dominate, sometimes are dominated, sometimes arise, develop, sometimes perish until they disappear and are replaced by others (like living beings), experiencing advances and setbacks, victories interspersed with defeats. And dialectics is the science that studies the struggle of these tendencies, of these opposing sides within the unity of the fact, and correlates them through a constructive connection.25

The opposing sides, the contraries, in addition to the connection that links them, complementarity as we have mentioned, penetrate each other reciprocally, interact, and persist (e.g., the reaction corresponding to the action). Physics shows us this interaction in the pressure and volume, weight and gravitation, mass and velocity, entropy and temperature, etc. In Philosophy and Biology, all functioning affirms this conflict of tendencies.

Reciprocity, the contrary action of opposing sides, is often creative, sometimes destructive, and sometimes achieves a dynamic equilibrium that is more or less stable. This topic will be addressed further. Regarding the creative aspect, it is enough to observe how many people are merely the product of their oppositions, such as artists, writers, doctors, politicians, etc.

The study of these individuals' lives reveals how much the clash of oppositions influences their works. What was Nietzsche, for example, if not that “great battlefield of all ideas and all impulses”? How many are merely their oppositions!

Remove the enemies of certain individuals, and they lose one of their reasons for being.

In the fields of Biology, Philosophy, Physics, as well as Psychology and Sociology, the struggle between opposites is evident in the facts; it is the creator of many transformations.

Some dialecticians seek to distinguish between antagonism and contradiction and use the example of the socialist regime, in which the antagonism between classes should disappear, although the “contradictions” in production do not disappear. The socialist regime, as imagined and utopically dreamed by those who declare themselves the greatest enemies of utopia, is only socialist when it is utopian because when it is not, but rather topical, as we know it today in its manifestations, the antagonism remains, as do the contradictions. It is easy to imagine a society without antagonism, without the “contradictions” inherent in production. But every “contradiction” is antagonistic; the contradiction cannot be resolved as a “contradiction”.

It can generate new forms, as we will see, but the antagonism of contrary tendencies will continue. There are antagonisms of various kinds, and some may give way to others; some may disappear, and others may arise. Antagonism and contradiction are not absolutely the same thing, as Lenin said. Indeed, they are not, but where there is opposition, there is antagonism. The form of antagonism may change, as may the form of opposition, but all opposition is antagonistic.

Thus, the dialectical conception of the universe is an antagonistic conception.

There is no discontinuity between inorganic matter and the biological world. The same principles operate in both, but with inverted function, as we have seen: the predominance of the dynamic order of extensity in the former, and intensity in the latter.

In the biological world, in addition to the predominance of the dynamic order of intensity, there are moments when the inorganic field prevails. Thus, we have:

Inorganic field extensity > intensity

Organic field intensity > extensity

The inorganic field, as a unity, contradicts the organic field in humans, as there are moments when one prevails over the other: organic field > inorganic field.

We use the word “field” here to generalize the aspects, taking advantage of the concept offered by physics, which is magnificently expressive and profoundly dialectical, and serves well to understand phenomena whose sets are qualitatively different. Physics acknowledges that one field can penetrate another. The gravitational field of an object, for example, can penetrate or be penetrated by the electromagnetic field of another, etc.

The inorganic field penetrates the organic, and vice versa, as there is no life where there are no inorganic beings, which are complementary to the organic. But within the scope of each field, there are “steps,” which are energy quanta, as visualized by physics, to make them concretely understandable. These quanta are, for many, like packets of the same energy, unique and identical, whose distribution follows an inexplicable mystery, at least for now. However, others, and this is our thinking, believe that in energetic phenomena, nothing would happen without motion, that is, the “transport” of energy. And these changes are the result of variations in tensional factors of extensity and intensity.

In nature, we are faced with differences and potential drops produced by the antagonistic opposition of these two factors. Otherwise, we would have to admit an energy-in-itself, a sovereign energy, a new and harmless substitute for God, as some have wanted to do with matter. This concept is still a product of the desire for homogenization, inherent to human reason. All movement and incessant transformations would tend towards a return to definitive rest, the dream and desire of certain religious and philosophical ideas. This is why the potential and intensity drop was interpreted as a tendency towards leveling (the dream and desire of the weary), as a factor that facilitates the mission of the extensity factor, instead of an opposition between them.

In the observations of physical chemistry, it was easy to see this victory of extensity over intensity, which led many scientists to have a conception of energy as we mentioned above. In biology, the final victory of extensity also confirmed this conception, as did the phenomena of entropy in thermodynamics.

Everything seemed to give reason the victory over movement. But behold, microphysics and new scientific discoveries support our dynamic, antinomic conception of the universe. The victory was only apparent and equivocal. The struggle continues, but it will always be interspersed with victories and defeats, and the decisive victory will only be desired as a fatigue of negative nihilists, whether passive or active, it doesn’t matter, but negative nonetheless. If we do not admit that these factors are inverse dynamisms, and if these factors are not energy, and energy is a separate, homogeneous reality, the source of all phenomena and action, how could we conceive that it gave birth to this dynamism if we do not accept the “flick” imagined by Anaxagoras or the “clinamen” of Epicurus, the unexpected, the unforeseen, that set everything in motion?

The philosophical idea of scholasticism, for example, also accepts, to some extent, this position because God breathed into the undetermined potential, which was nothingness, motion, making it matter, determinable, therefore potential by the influence of determining act.

The cooperative opposition of act and potential corresponds to the opposition of form and matter, whose cooperation gives rise to the composite. The opposition between the composites and their interaction would explain the relationship of finite beings and consequently their transitions, as we will see later when studying emergent and predisposing factors.

In the corporeal world, there is no proper subsequent state in which the opposition would disappear. The “contradictory” aspect present in the two principles of thermodynamics proves our point.

Lenin said: "The division of unity and knowledge of its contradictory parts… is the essence of dialectics (one of the essential aspects of being, its foundation, if not the fundamental characteristic). This is exactly how Hegel formulated the question.

The condition for understanding all processes in the universe in their “self-dynamism,” in their spontaneous development conceived in their vital and living forms, is knowledge of the unity of their contradictions. Development is indeed the conflict of opposites."

“Unity has its opposites, and they do not form the unity, which is considered homogeneous and heterogeneous, not being inseparable. The unity (coincidence, identity, resulting force) of opposites is conditional, temporal, transient, and relative. The struggle of opposites, which mutually exclude each other, is absolute, just like movement and evolution,” Lenin continues (Vol. XIII, page 324, English edition of “Collected Works”).

It is this unity that constitutes the so-called “law of the unity of opposites,” which, as a law, is an invariant of opposition. Points of disagreement have already arisen, and others will arise when we study the aspects of dynamic equilibrium and the theory of synthesis, the third term that nature does not reveal, to which the Marxists (not Lenin), still influenced by the misunderstood desire for identity, have allowed themselves to be dragged.

Many believe that Hegel did not accept a dynamic and oppositional principle of objective reality, but only in the realm of spirit.

His entire work proves otherwise. And like him, Proudhon also accepted it.

"The truth in all things, the real, the positive, the practicable,

is what changes, or at least, what is capable of progression, conciliation, transformation, while the false, the fictitious, the impossible, the abstract, is everything that presents itself as fixed, whole, complete, unalterable, indestructible, not capable of modification, conversion, increase or decrease, refractory, therefore, to any higher combination, to any synthesis."

But there was a profound distinction between the two. Let’s examine it.

In three essential points, Proudhon diverged from Hegel.

While Hegel accepted three terms, Proudhon only accepted two, but these two constantly faced each other, while Hegel places opposition to “overcome” it later.26

For Hegel, the endpoint is the “synthesis,” while for Proudhon, there is a balance between the oppositions, but a dynamic balance, sometimes broken again, sometimes enduring or not. The third aspect consists of Hegel accepting the Idea as purely immanent to the dialectical process, while Proudhon (it seems through the study of his work) accepted a transcendent principle that dominated the becoming, the action of a superior principle capable of transforming the persistent antinomy into equilibrium, at least in certain aspects (in the social realm), that is, capable of making this antinomy enduringly balanced.

Marx said, and Marxists repeat, that Proudhon learned dialectics from him. However, before knowing Marx, Proudhon had already written in his “Création de l’ordre”: “The ternary facts (which is the case with Hegel and the Marxists)27 borrowed from nature are pure empiricism…” “The Hegelian formula is a triad through the pleasure or error of the master, who counts three terms where, in reality, there are only two, and who did not see that the antinomy is not resolved, but that it indicates an oscillation or antagonism capable only of balance. From this point of view, Hegel’s system must be completely reworked.” And in another work: “The antinomy is not resolved”: “Therein lies the flaw of all Hegelian philosophy. The two terms that it consists of balance themselves, either with each other or with other antinomical ones.” Proudhon fought against these “fanatics of unity” and affirmed that the “opposite terms constantly balance themselves, and balance is not born between them through the intervention of a third term, but through their reciprocal action.”

This led Marxists to see in Proudhon a hesitancy in a perpetual “balancing” between two theses. They called him a petit-bourgeois, as if he actually wanted a middle ground when he accepted the clash of extremes.

For him, the struggle, the clash of opposites, is a permanent category that cannot be suppressed, one of the main categories of our reason that we should not think of suppressing because then it would be the end of the world and the death of thought. Thus, unknowingly, he repeated a Pythagorean viewpoint.

But if this struggle cannot be suppressed, abolished, it can be “transformed.” This peace that can be established is not a reciprocal destruction of the combatants but the production of an always superior order, endless improvement (“War and Peace”). This order transforms into reciprocity. “Just as life presupposes contradiction (he means opposition), contradiction, in turn, calls for justice: hence the second law of creation and humanity, the mutual penetration of antagonistic elements, Reciprocity” (Quoted source).

For Proudhon, reconciliation is the “absorption of one and the other into a more complex formula.” He stated that it was necessary to “discover a higher law, that is, a formula of reconciliation superior to socialist utopias and the truncated theories of political economy. It is not possible to stop at an arbitrary middle ground, unattainable, impossible” (Berthod). Thus, a certain resemblance can be seen between Proudhon’s dialectics and Nietzsche’s, accepting transformation, transmutation[^30], which, in Nietzsche, corresponds to the higher order spoken of by Proudhon.

A fact, as unity, in development, is a set of its oppositions, the struggle of its antinomic opposites in a more or less complex antagonism. But this fact is an isolated fact, unique in itself. It undergoes the influence, the interaction of other units that also have this inner contradiction, but in existence, they either antagonize with each other or not. These complex “contradictions” and antagonisms form the coordinates of existence and give rise to the complexity of universal facts in their development. The transfiguration of one fact into another, its alterity (the becoming of another), is not only the consequence of the action of the internal factors, of their unity in struggle, but also the action and interaction of other external factors that coordinate with it.

To explain the so-called “contradiction” of a seed solely through the intervention of the opposing factors that compose it is to forget the action of the external factors, apart, with their own conflicting factors; it is to transform dialectics into a form of abstract, harmless, and unnecessary reasoning. The transformation of a seed into a tree, which negates it, and from the tree into the production of a fruit and a seed that will subsequently affirm it, is a merely simplistic understanding. The seed is not a homogeneous unity but a processual totality composed of many opposites. In each seed, which forms a whole for us, there is internal multiplicity. In each part of this multiplicity, considered as a unity, its internal struggle is known. The seed is thus a microcosm, a small cosmos of oppositions, multiple, diverse heterogeneities that take varied directions. It is not only the “contradiction” of its core and its envelope, but the core itself is a field of action of multiple “contradictions.” The slow transformation of the seed into a shrub is a complicated struggle, an immense battle of many tendencies, whose result is the product of various clashes, of diverse oppositions that constantly interact, transfiguring themselves in their development into a shrub. The shrub continues to live this opposition in its transformations. The synthesis, here, was a misconception of the dialectical simplism of some Marxists who were never sufficiently Marxists to understand the interpenetration of the quanta (tensions) of opposition, the great discontinuous and continuous struggle of the various quanta in conflict. The Proudhonian and Nietzschean conceptions, not accepting synthesis but the quantitative-qualitative, complementary, and contemporaneous transfiguration of both, were more in line with what science would later show in its great and extraordinary experiments. These complex oppositions, these quanta of “contradictions,” are understood through our decadialectics, the dialectics of ten fields, which we will have the opportunity to explain later.

The equilibrium that Proudhon speaks of (which he called justice) is a “balance in diversity,” constantly unstable, active and dynamic, where “contradiction” moves in tension. This equilibrium, applied to society, is what Proudhon called Justice. "That is why I did not choose freedom as my motto, which is an undefined and absorbing force that we can shatter without convincing; I placed justice above it, which judges, regulates, and distributes. Freedom is the strength of the sovereign collectivity; Justice is its law.

We have referred several times to these supreme concepts that form the categories. We have studied them in “Logic” and in Philosophy and Worldview. The concepts of reason and intuition have been examined in great detail, and we will not return to them here.

A classification of the categories of dialectics has not yet been formulated for the simple reason that, since there is not just one, but many (since all multivalent logic is a kind of dialectics), it is not easy to establish a scale of categories that applies to all.

According to Lenin, “the categories are small degrees of differentiation, that is, of knowledge of the world, the knots in the network that help us know it and master it.” It is very common among Marxists to consider scientific laws as categories. These laws, as reflections of objective reality, are naturally taken as invariants. The categories are not subjective, created by humans to coordinate subjective facts, but they reflect the laws of reality itself, known “based on the practical activity of human beings.” Marxists establish various categories, and there is no uniformity of thought among them. Essence is a category for them, which consists of the “internal side of things,” and phenomenon is the external side, what is on the surface. Thus, a Marxist says, “according to Marx, matter is the essence of all natural phenomena” (Rosenthal). Others say that movement is the essence of matter.

Dialecticians in general consider the historical character of categories, which are formed through long and gradual human practice until they are established as a priori principles that precede experience. There is nothing to object to this statement because it truly represents the history of thought and categories. Recognizing the historicity of categories is a great victory for dialectics, but it also implies the need for studies that go beyond its scope, as they deal with objects that belong to other disciplines.

Accustomed as we are to always emphasize and give validity to what repeats, to the same, to the equal, which leads us to see in facts only the similar that promises us the imminent conquest of absolute homogeneity, identity, we naturally have great difficulty with dialectical reasoning.

It is a march toward the different and its concretion with the similar. Since humans needed to free reason and use it more and more for their development in the world, their non-rational life, the merely intuitive process, was valued at a hierarchical level below reason. However, in four-fifths of our lives, we are not rational. We live irrationally for most of our existence. But this statement does not justify abandoning reason or considering it anti-vital. Instead, we need to, without falling into the unilateralities of irrationalism or rationalism, take advantage of this immense field of intuition and concretize it through a connection, that is, connect it with reason to elevate reason and increase its power of action.

Reason must act a posteriori in capturing connections, the only action in which it is truly powerful, as the scholastics well understood when they opposed rationalistic apriorism.

Theme II

Article 1 – Dialectic of Knowledge and Consciousness28

We perceive according to the pre-coordinated sensorimotor schemas that we already possess, and only afterward do we become aware (through memorization) and subsequently know through assimilation to eidetic schemas.

We only adequately know that for which we have schemas.

Pascal was right when he said that he would not seek God if he had not already found Him.

That is why all our questions already contain something of the answer. Our knowledge, conditioned by our schemas, reveals itself as partial knowledge, and therefore something eludes us.

And what eludes us is what we have not assimilated into our schemas.

This is one of the dialectical aspects of our knowledge.

Thus, the decadialectic is justified since, through it, we are capable of expanding our schematic capacity by combining new orders that we can give to the sets of schemas at our disposal, and with them, achieve more varied and comprehensive assimilations and, consequently, broader knowledge.

In the dialectical understanding of the problem of knowledge, many times those who claim to be dialecticians seek to subvert the “subject-object” relation by simply subjecting one to the other: the object to the subject, as subjective idealists do, or the subject to the object, as objective realists attempt.

In doing so, both the former and the latter evade a truly dialectical examination of knowledge, neglecting to assign the true role to both the subject and the object and understanding the reciprocal relationship between them in the trans-immanent act of knowledge.

Regarding knowledge, there are several possible positions to take:

a) that we know; b) that we believe we know; c) that we vaguely know what we know; d) that we do not know.

But in any of these three cases, which characterize positions such as dogmatic, critical, and skeptical, in all of them, it is impossible to ignore that there is knowledge of knowledge, for we know that we know or we know that we know that we do not know.

From this point on, a problem arises: the knowledge of the knowledge of knowledge. It cannot be denied, for even the denial would affirm it. By positing knowledge of knowledge of knowledge, it immediately transcends itself indefinitely because knowledge of knowledge of knowledge of knowledge can be established, and so on indefinitely, with the subject who knows always receding.

The examination of this point, which implies other problems that will be adequately examined elsewhere, allows, however, in its general lines, an explanation that aligns with dialectical thought.

In psychological assimilation, the assimilated remains foreign, and there is no incorporation into the assimilator, as in biology.

Consciousness would arise through a dialectical process.

A physiological whole, consequently organic, forming a tension, reaches a tensional act that is qualitatively different from the constituent parts.

In psychological assimilation, without incorporation, there is a change in potential, as the accommodated schemas receive a stimulus that either fits or does not fit into them. These assimilations occur according to various schemas, but when they occur through assimilations performed by constellations of schemas that belong to and are connected to the global tensional schema, consciousness would arise.

Now, this global “dependent-independent” nature of the parts (quantitatively dependent, qualitatively independent) presents itself as “other” to itself. When knowing, it “virtualizes the object” (stimulus) in order to “actualize” the schema that is proper to it, activated by the action of life itself.

Consciousness, therefore, is the “actualization of the schema” at a particular point and the “virtualization of the stimulus.”

Consciousness is a knowledge “with,” of itself, a knowledge of a local modification in general, which the total tension assimilates without incorporating it, as a symbol of the very schema that is operating here as the symbolized, the referent.

Since the total tension is an act (which we will still prove), it is not exhausted in this activity because the assimilation itself allows it to be unfolded into subject-object.

And this happens because consciousness, as a global tensional activity, when assimilating, “classifies” and orders.

What one is objectively conscious of is delimited in this way.

It is consciousness of this or that. There we have the explanation for the intentionality of consciousness, which is always objective, consciousness of something that becomes objectified. At that moment, the global tension, as an act, separates and can therefore know the realized knowledge.

Thus, we have knowledge of knowledge or, simply put, consciousness of consciousness. General consciousness that “tends to,” that attends to, something already marks an object to which it is directed.

At that moment, this new knowledge becomes classified, localized, which allows for new objectification, new consciousness of consciousness of consciousness, or broadly, knowledge of knowledge of knowledge, and so on ad infinitum.

As it is always an act, the total tension, while integrated as all tension, such unfolding is always possible, naturally only in humans or intelligent beings.

The emergence of consciousness here is already a self-unfolding; in it, there is always a placing of another that is ourselves. With it, we unfold ourselves; therefore, consciousness is always a dialectical pointing out of the procedural functioning of ourselves.

All affective knowledge is the result of cooperation, and this cooperation occurs through a pronounced commitment between the component terms of knowing.

The act of intellection is the apprehension of knowledge of a choice, of a chosen one, of an actualized difference.

The knower knows himself because he knows something other than himself. If the known were identical to the knower, he would not know, for all knowing is a differentiating act; otherwise, the identical would have to differentiate into knower and known, which would negate the identical. (We have already shown in Philosophy and Worldview that the concepts of identical and identity are grasped by reason, but when taken abstractly, they can only lead philosophy to aporetic states. The dialectical concept of identity-alterity is much more creative and useful for the analysis of knowledge, as we will see later).

But if they are “totally and rigorously” different, how could there be knowledge? How could the knower know the known? Knowing is not incorporating; it is capturing notes. To capture these notes, besides difference, something similar is needed to make a comparison.

Absolute differences would not know each other. Absolute similarities (identical) would also not know each other except through fusion. The dialectical presence of similarity and difference, which are intuitive concepts (absolute identity and difference, as normal and abstract concepts, belong to reason), are indispensable for knowledge because every act of knowing is the pointing to a dynamic synthesis of opposites, but in cooperation, and they reveal an analogy, no matter how remote it may be.

Article 2 – Concepts in Logic and Dialectic

The statement that thought is historical, or at least also historical, constitutes a postulate of current philosophical knowledge. We always give a concept a content.

In truth, we feel that we conjure something when we give it a name because we can only name what we have already conceptualized, and we can only conceptualize what we have already distinguished, and to distinguish is to know, and to know something about something is to already master it. Is it not the genesis of that feeling of security when we can give a name to some new fact that presents itself to us?

When something presents itself to us and we cannot give it a name, is it not because we have not yet mastered it, at least through knowledge?

Concepts are purely quantitative schematic structures in their extension and comprehension; they are therefore, essentially, also numbers. And as we understand numbers, we will understand concepts. We only number what we distinguish, and we number nature because in it we distinguish tensional structures. But to conceive such structures as tensional processes would already lead us to know the world as a process, one of the countless Pythagorean ways of understanding it.

When Goethe said that “function, rightly conceived, is existence thought in activity,” he saw in existence an active process, not a mere quantity. The function, in Faustian mathematics, which is a relation of relation, arises from a dynamic, heterogeneous, dialectical conception of number. It is the first step in bringing mathematics to penetrate the realm of the qualitative, the intensive, which many mathematicians do not even suspect.

Let us briefly examine the psychogenesis of the concept: Psychic schemas are formed through experience, through accommodations and assimilations; once constituted, they serve to accommodate new facts and, through assimilation, include them, through the imago, in the accommodated schema.

The heterogeneities not assimilated by the previous schema, because they escape it, are protean aspects of the fact, not included in the singular schema established earlier.

The ante-concept arises when the abstract schema of the image of the singular serves to generalize what is common in various singularities, as we will see later.29

When these ante-concepts are stripped of heterogeneity to constitute themselves as eidetic abstract schemas (from eidos, form) that contain, as a form, only the indispensable elements stripped of all heterogeneity that differentiates them, then the concept arises, and with it, logical thought.

As we still use ante-concepts today, it can be perfectly understood that humanity knows, according to social groups, periods in which ante-concepts predominate over concepts, and others in which the concepts increase in such numbers as to allow a transfiguration of social thought, from predominantly magical to markedly logical.

Concepts, properly logical, arise from various factors, including economic and aesthetic factors.

Concepts as tensions

The concept, as an abstract schema, as a schema of a series, is invariant.

The individuals that make up the series are variant.

Thus, horse, as a concept (abstract schema), is invariant, but horses, as factual elements of a series, are variant.30

The concept, considered solely eidetically, is invariant, but its factual elements, which symbolize it, are variant. (This assertion is proven in the “Treatise on Symbolics”.)

Invariance can lead to eidetically changing the concept, for example, certain animals that were conceptualized according to their characteristics at a certain time, which are different at another time, come to have a different conceptual content.

We cannot completely separate the factual part from the eidetic aspect when considering the concept from a psychological point of view. There is always a factual element in the eidetic, that factual layer (hyletic layer, for many) that is inseparable from the eidos, whose purity is achieved only through stripping and, abstractly, through more or less difficult and, above all, subtle operations.

On the other hand, it is almost impossible to separate the affective layer, the patency of the concept, which reveals not purely intellectual but affective, experiential meanings. We cannot deny this connection between the concept, a product of intellectual operation, and the experience that assimilates it through pathic schemas, although it is not always distinguishable.

Even the most impenitent objectivist cannot deny the affective influence that words exert.

Therefore, schemas have a life, and that life is not only correlated with an individual but with a social group and a cultural cycle.

Who can be unaware of the typically Greek experiential understanding of alétheia as truth, distinct from our truth, whose term comes from the Latin veritas?

And is not the Greek boulé experientially different from our will?

Can we grasp the experience of dynamis for Aristotle as our potentiality? Or enérgeia as our act?

Does our experience of purpose coincide with Aristotle’s en-telekheia? Can (and who would believe it) our tranquility experientially translate the sophrosyne of the Greeks?

In this way, a concept must be considered as a tension in which three noetic tensional schemas cooperate:

  1. the eidetic (abstract)

  2. the factual (of the object)

  3. the pathic (experiential)

Only in this way can we understand the life and death of words which, as tensions, tend to realize the cycle of tensions whose vectors naturally lead to their tensional disintegration or, through their kinematics, to the dynamism we have already spoken of when discussing knowledge.

Only in this way will we have a concrete understanding of concepts, which come to be understood within the tensional constellations that cooperate with them to give them meaning and life.

Each category of Logic invokes, by implication, the next; the last is presupposed by the first.

Every process of dialectical expression is a convenient means of revealing the successive, which Formal Logic considers simultaneous in the implication of concepts.

Therefore, each conceptualization of a fact affirms the presence of the simultaneity of the logical concept, which has no time, although it occurs in time (for the idea of a horse does not have two or three years of age), as well as the presence of the successive, which is ontic.

In the legality of ideas, as abstract schemas that we construct outside of time, as always present, we must consider their correspondence to the successiveness of the ontic, the factual.

Formal Logic, by actualizing the simultaneous aspect of the legality of ideas, and virtualizing the successive aspect of intuition, errs by abstraction and can lead, as it does when excessively employed, to a false view of reality.

Dialectical concepts

We can conceive the cosmos as in becoming, as in constant change. But if we admit the cosmos as a whole, we cannot conceive this whole as becoming (in alterity), but only as being identical to itself because it is always itself. Otherwise, it would become something else and cease to be itself, and in that case, what would that other be if not itself?

Thus, mutability, which becoming reveals in the part, would not imply the privation, the absence of immutability of the whole as such.

Because exclusive positions have always been taken, mutability has been considered the privation of immutability when both can have positivity, even though they oppose and “contradict” each other without one excluding the other.

In this way, the great tempests of metaphysics, provoked both by its supporters and opponents, would find a good solution to the debate if they understood the positivity of opposites. When one is unilaterally taken, we are led to construct a partial, abstract, and false view, to reduce one opposite to another, to reduce immutability to mutability, with Heraclitus (as it is generally interpreted, which we disagree with, and we will show the reasons for our disagreement on another occasion), or the position of Parmenides (also misinterpreted, even by disciples and scholars), which seeks to reduce mutability to immutability.

While all this was happening in Greek philosophy, Pythagoras had already offered the solution to this controversy, whose echoes have come down to our days.

A dialectical concept of mutability-immutability leads us more easily to understand that both, although opposed, affirm positivities.

Let us consider. If we regard, for example, the cosmos as a product of being, as a cosmos (an organized whole) among many others, as a great cosmic tension among many other cosmic tensions (other different cosmos), in this case it would be a whole that, in turn, would be part of another whole.

But even then, we cannot avoid the same dialectical judgments that we have already presented, for being would become immutability, the origin of all things, necessarily immutable, sovereignly effective and efficient.

If we admit various cosmos, totally and absolutely different, we would consider them either separate or connected to ours.

If connected, they could not be absolutely different; if separate, the same judgments already presented could be applied to each. If similar, they would become part of an order.

In any case, we cannot escape the dialectical concept of mutability-immutability. And a simple analysis of our knowledge, which leads us to see facts ontically and ontologically, allows us to understand the inseparability of opposites, which the selective function of our mind leads us to separate in order to give order to what happens, which we cannot intuitively grasp in its totality.

When I say that jelly is soft, I recognize that it is not only soft but also hard because there is resistance to my action; air is also solid, depending on the speed of a moving object; water is solid for certain beings but not for us.

Every quality is the revelation of a conflict of opposites (of two opposing directions). We classify green, this or that, as green because it belongs to the green series, but it is vibrationally different from another. No concept exhausts the totality of an experience. It always leaves something aside, virtualizes the heterogeneous to consider only (actualize) the equal, the similar, the repeated. Therefore, any concept expressed by a verbal sign, a term, is an abstract schema of a generality, and thus cannot adequately correspond to the reality of a fact, except to a certain extent, that is, from the perspective of its generality and not from the angle of its singularity.

Concepts only classify, they point out what is general, orderly, and serial about the fact, or in other words: facts are given a name, which is the verbal counterpart of a concept, to reveal those indispensable notes for classifying them in this or that order, in this or that series.

Methodologically, dialectical concepts are concrete, concrete universals in the Hegelian sense, as already explained.

Their mere formal placement is a phase of human thought that is antithetical to the ante-conceptual phase, characteristic of symbolic thought, in which representation, referring to an individuality, is applied to generalize.

We have the example of a child who knows the name of a stream (“dog’s stream”) and will call any stream they encounter “dog’s stream,” or the child who sees the shadow of a tree during the day and in the darkness of the room at night says that it is the shadow of the tree that has entered.

We still use ante-concepts, and we see them, although modified, in the individual concepts that serve to generalize: a Napoleon, a Caesar, a Socrates, etc., so commonly used in a metaphorical sense.

After this phase, in which the human being is aesthetically immersed in concretion, as seen in psychogenesis studies, abstract thinking with concepts as abstract schemas emerges, which characterizes speculative thought, still predominant in classical philosophy from its Greek origin until now, followed by the new synthetic phase of concrete-abstract, dialectical thought, because it affirms and negates speculative abstract thinking and affirms and negates primitive symbolic thinking.31

The judicial role of reason, formally considered, ascribes one abstract concept to another. And we have formal judgment.

Dialectical judgment lies in ascribing a concrete concept to another concrete concept, which enriches it. In this way, dialectics includes Formal Logic but surpasses it, preserving it (Aufhebung).

Formal reasoning consists of inferring formal judgments from other formal judgments. Dialectical reasoning consists of inferring them concretely as contained in concretion, that is, identified in the unity, which is examined by the mind but always considered present and physically inseparable from the whole of which they are part, in order to avoid falls into abstractism, which is always deficient and almost always detrimental.

Every fact is a syllogism for dialectics. And the syllogistic process is an analysis of concretion.

Therefore, and for this reason, we must never forget that dialectics is a logic of existence, not merely formal.

Transcendental Concepts

The character of attributes that apply to all beings is considered “transcendental,” not only in what they have in common but also in what is specific to them.

An individual concept refers to a single individual; the universal concept refers to all individuals of the same species and only pertains to the characteristics that are common to those individuals, excluding what is specific to them.

However, a transcendental concept, in itself, is a synthesis of the universal, particular, and individual concepts because it extends to all the characteristics that constitute them, from the highest genera to the ultimate differences.

For example, the concept of “being” is transcendental because it encompasses the entire scope of predication. What is universal “is,” what is particular “is,” what is individual “is,” and even the differences of being are still “being.”

In Metaphysics, the transcendental properties of being are studied, including the concepts of unity, truth, and goodness, which are also considered transcendental concepts. The concepts of “something” and “relation” are also included.

We can say of all things, even before knowing them, that if they “are,” they “are valuable,” they are “something,” they form a “unity,” they are inherently “true,” and so on, as we see in “Ontology.”

However, we could also consider as transcendental those concepts that, within a plane of being, have the same extension in their own plane as being in the total plane or rather the Whole, which is not properly a plane but the unity of planes.

In this case, for example, the categories would be transcendental concepts within their predicamental scope.

Beyond the category of “substance,” which refers to the “form” and “matter” of being, there are the “accidental” categories.

The categories can be classified by the predominance of the quantitative and qualitative aspects (which, in turn, form the categories of quantity and quality, abstractions with real references, as we have seen, pointing to all the categories related to extension and intention). The transcendental concepts of intensity and extensity, which we have studied extensively, resolve the impasses and aporias presented by the concepts of quantity and quality, as we have already seen. The interaction between the factors of intensity and extensity gives us another transcendental concept in the plenary sense, namely “relation,” and the dynamic and dialectical concept of “correlation” (to correlate, to operate with, cooperation, to cooperate), as well as the concepts of opposition and coordination, which are dialectical transcendental concepts. Additionally, there is the concept of “reciprocity,” which is gradual, as all beings relate to others in heterogeneous degrees of reciprocity, interaction, etc. 32

In the tensional plane, other transcendental concepts are justified, such as the aesthetic, harmony, symbol, sign, schema, and also the ethical sense in the immanent sense and efficacy – efficiency (potential and act), all considered dialectically valid, at least in the realm of finite beings.

We can also add the concepts of modality and modality (studied by Suarez), time and space, which taken separately lead to many aporias, but when considered in the dialectical complex of “time-space,” they give us the synthesis of succession-simultaneity, as well as the concepts of homogeneous and heterogeneous.

Thus, when metaphysics studies the convertible concepts offered by Formal Logic, it establishes that being and good (value) are convertible (“ens et bonum convertuntur”), for if good were not a being, it would not be good, and conversely, being is good because every being is desirable to the extent of its perfection. This opinion, inserted in metaphysics, will be clarified by us at the appropriate time.

Every being has value according to the degree of realizability it allows for what is placed upon it. The objects we make use of reveal a positive or negative value depending on the obstacles:

a) Those that hinder or hinder us, as well as facilitate our dominion, apprehension, enjoyment, etc., over it or from it; or

b) Those that enable or prevent our realization, that is, the greater or lesser approximation between subject and object, between what is objectified and what is subjectivized.

And since what functions to facilitate or hinder is constituted of inherent elements, immanent to the object in question, value has a real foundation.

Values, as seen in “Axiology” and “General Noology,” have their subjective origin in affectivity as well as in intellectuality and sensitivity. Therefore, true and false, right and wrong (the first being logical-formal values, the second being values of intellectual intuition), as well as pleasure-displeasure (values of sensory intuition), and pleasant-unpleasant, etc., are values, not excluding the value in the object (“in re”).

Methodology of Decadialectic

Theme III

Article 1 – Contradiction in Decadialectic

Frequently in philosophy, it is considered contradictory whenever something is simultaneously denied and affirmed about the same thing, in such a way that if the negation is true, the affirmation is false, and vice versa.

In Formal Logic, we study contradictory judgments.


A is the universal affirmative, and I is the particular affirmative, E is the universal negative, and O is the particular negative.

Between A and O, and between E and I, when both are affirmed, they are contradictory because we couldn’t say: “All men are mortal (A)” and at the same time “some men are not mortal (O)” because there would be a contradiction, and if one is true, the other is necessarily false.

Similarly, if we say: “No man is good (E)” and “Some men are good,” both are contradictory, and if one is true, the other is necessarily false.

However, if we say “All men are good” (A) and “No man is good (E),” both are contrary. There is contradiction in affirming both, and both can be false, in addition to only one of them being able to be true. For it is possible that all men are good or that none of them are, but it is also possible that only some are good, just as some are not good, and those some are not necessarily the same.

However, dialecticians, when using the terms “contradictory” and “contradiction,” do not employ them in the strict sense of Formal Logic, but give them a broader meaning.

Marxists (and dialecticians in general) consider as “contradictory” that which is different within a unity, the distinction observed within a unity, the diversity of predication it can provoke. As a materialist, the Marxist places the world of existence in the realm of succession, time, becoming. Thus, nothing is what it is (Heraclitean influence), for everything is in a state of becoming. Now, the concept is static, for when we say something is this and that, we also say that it is not. Now, if something is constantly "transforming,"33 it already contains in itself the negation of its current state, which, upon actualization, ceases to be what it was and becomes something else. And since this is constant, everything that is at the same time is not what it is and is what it is not.

In Logic, what is enunciated about a subject is considered a predicate. The predicate is connected to the subject through the copula “to be,” a copulative verb that, due to its other meanings, has opened the field to a series of confusions that need to be clarified.

The verb “to be” can, among its meanings, express the relations between a subject and a predicate, having an ontological and an ontic sense, which we will address shortly. The metaphysical problem of the analogy of being will be discussed in other passages.

Susanne K. Langer establishes five logical senses of the copula “to be.”

  1. “The rose is red.” In this first proposition, being is used as a description of a property.

  2. “Rome is larger than Athens.” Here, being has a mere auxiliary value.

  3. “Barboroxa is Frederico.” Here, identity is expressed.

  4. “To sleep is to dream.” It signifies implication.

  5. “God is.” It signifies existence.

When assigning a predicate to a subject, it is important to distinguish whether the predicate is essential for classifying the subject as this or that, or if it merely receives an accidental attribution, not necessary. There is a clear difference here. In the first case, the subject “has” the predicate, which is merely indicated. In the second case, the predicate “happens” to the subject, without the characteristic of indispensability. There is a significant difference in meaning between the two verbs (to have and to happen) in Portuguese: in the first case, we are dealing with an identity, for the predicate identifies with the being of the thing predicated, composing with it an indivisible and inseparable whole, under penalty of destroying the established scheme. In the second case, the predicate “occurs” to the subject, but it could also not occur, as it is not necessary for it to be so. In the first judgment, stating that the rose is red merely indicates a predicate of this or that rose, without there being a necessary nexus of unity between them, for it is not essential for classifying something as a rose for it to be red. However, redness exists in the existence of this rose, not in the essence rose. In the case of the second judgment, being is auxiliary and could be replaced by another judgment without its presence, such as “Rome reveals itself as larger than Athens.” The explanations are clear for the other three judgments.

But now let us consider an important aspect. In the first judgment, we affirm that there is red color in the rose. But if we observe it from the perspective of the rose, we must affirm that being red is part of its existence, and redness, in that rose, belongs to its existence; it also constitutes its being. It also constitutes the being of Rome, being larger than Athens, for among the many thoughts that I can grasp from its existence, there is the thought of being larger than Athens.

The being of Barboroxa is also the same as Frederico’s, as is the thought of belonging to a class, the class of legendary heroes, in the case of Barboroxa. When I say that to sleep is to dream, the implication is not inherent in sleep, but it is analogous to it and therefore connected to it. In the case of God, being is clear.

And it could not be otherwise because the concept of “being” is the broadest of all, encompassing everything, for being is the subject of all predicates, and in turn, every predicate has some mode of being. Therefore, being is also the predicate of all subjects.

As beings are different, Aristotle understood, and before him, Plato and others, that the concept of “being” is an analogical concept because we predicate it of heterogeneities.

We could simplify by saying that, ontologically, everything is being, homogeneously being. But ontically, everything is being, heterogeneously in becoming.[^39]

[^39] The controversy between Thomists (who affirm the analogy of being) and Scotists (who also accept univocity) can be easily understood through dialectics, for formally being is univocal, but in beings, ontically, it is analogous, as we have shown in “Theory of Knowledge” and in “Ontology.”

But now we come to the fundamental point of dialectics.

The tree, as our objectification, is an abstraction of our knowledge. We call this object a tree because it corresponds to the abstract scheme “tree” to which we assimilate it.

The external world should not be confused with the objective world.

The external world encompasses all existence, but the objective world is conditioned by the polarity of Subject X Object; it depends on the subject’s abstract schemes. However, the external world does not depend on them.

Thus, we say that this object is a tree because it symbolizes the abstract scheme, as it contains all the necessary characteristics to be classified as such, although it also contains what makes it heterogeneous from this abstract scheme, which we disregard at the time of classification, otherwise there would be no classification, only individuals.

But the concept of a tree (abstract scheme) is mentally separated from the outline, as well as from all heterogeneities; it is considered only as a noetic abstract scheme (post rem), intentionally, therefore, of the concrete scheme (in re) of the tree.

But the limits of the tree are not only the formal boundaries we give it through the abstract scheme. For if this tree is such (actualizes itself as such), it is because it is included in a field of coordinates that “are not” the tree, but that also give it being. In another field of coordinates that do not coordinate with what is required for there to be a tree, it does not exist, as for example, it does not exist in the Sun because there are no cooperating coordinates for it to appear. Therefore, if it “is” and “is” a tree, it depends on these coordinates that are also indispensable for it to be such and not something else. Thus, what is a tree, and what it “is,” is also that which we do not classify as such, but the absence or privation of which would prevent its emergence.

It is immediately understood that the concept does not exhaust the “being of the tree,” nor its “being,” and that it, as a being and as an existence, is much more than its concept, meaning it is also the concrete that surrounds and enables it.

Consequently, everything is in a “concretion” according to the constructive coordinates that cooperate in its existence.

Now, if we consider it “formally,” we would only see it in its adequacy to the concept or, in our language, in its assimilation to the abstract scheme “tree.” However, if we want to see it functionally, in its kinematics and dynamics, as well as in its concretion within the field that supports it, we need to consider that which is not contained in the concept, that which is not of the formal concept “tree,” but is indispensable for it to “be” and “exist.”

Formal Logic works only with the formal part, but Dialectics seeks to study the functional nexus. It is a logic that affirms the concept while affirming what it is not, but where what is conceptualized is given, and without which it remains only as an abstract scheme, without symbols representing it. Therefore, the nexus of this functional, active, mobile, kinematic, dynamic, and concrete thought is given by dialectics, for formal logic only deals with the static or freezes the dynamic in order to know it. Thus, dialectics does not deny Formal Logic but completes it to allow for concrete-functional knowledge.

In this way, the being of a thing, ontically considered as existence, consists not only of what is included in its concept, in what is essential, indispensable for us to classify it as such, but also in everything that predisposes its ontic existence, which is not ontologically itself, but which is also indispensable for it to arise.

In other words, the being of something requires its concretion. It is not only its essence, but the outline that allows it to emerge and conditions it. Thus, a man, existentially considered, whether Paulo or João, is not only a man because he has the essence of a man, but he is also ontically a man because he exists, not only the humanity that precedes and shapes him, but also the conditions in which he develops and allows him to be.

Therefore, essentially, “man” is what is ontologically considered indispensable in the concept; but ontically, it is existence itself that gives it existence as well.

Thus, dialectics can only be a logic of “also” (etiam).

When we deal with essences, we cannot help but use the logic of “either… or…,” formal logic. But when it comes to existences, in order to be concrete and not abstract, that is, not to work with existences as if they were merely formal essences, we need to consider what is and what is not, but which leads to being what it is, or rather, that of which something is said to be the opposite, other than what it is.

We thus have the sense of dialectical contradiction (which is actually opposition), which we should not use without the adjective “dialectical,” which qualifies it and prevents it from being confused with formal contradiction. Among the many applications that the term dialectical contradiction has, we can add the following: In every operation, as in every existence, in addition to this opposition, there is, in activity, a dualism whose elements, taken separately by our mind, can predicate attributes that contradict each other. The functions are different, and each one proceeds in the reverse of the other. In movement, for example, the displacement of a body simultaneously performs two inverse functions, that of moving away and that of approaching, or that of moving to the right and moving away from the left, which is easily understandable to an observer. But even without considering the observer of the movement, it is always contradictory because at each moment it is what it is not, affirming a direction and its opposite.34

Therefore, every function implies an inverse affirmation, and the examples we present below will help us understand that existentially, we are always faced with opposition, and that existence itself is only understood and occurs in this opposition, which affirms it and simultaneously affirms the other (alterity).

As a logic of “also,” dialectics seeks to encompass not only the nexus of the homogeneous but also the heterogeneous; it only completes the activity of logic, it does not refute it. Dialectics has no other meaning; it arose from the need to broaden the field of reflection. As long as philosophy does not understand what has already been understood in science, that knowledge does not necessarily exclude the old, but completes it, expands it, philosophy will tread the vicious ground of substitution, which has also been the great evil and great error of aesthetes, for example. Dialectics must be dialectical, and for that, it must overcome while preserving itself (as Hegel very well showed in the concept of “Aufhebung”).

Analysis of dialectical contradictions

When we say something, when we attribute one thing to another, we do not refute, reject the contrary to what is attributed; we only affirm the presence of the attribute that does not negate, does not absent, does not deprive the unity of the presence of its opposites.

And if we say that someone is good, we do not mean that they are only and simply good, nor do we exclude or repeat or refuse or absent other attributes that oppose goodness. What we cannot say, absurdly, is that the “good,” as good, is bad.

When we perceive values in something or from something, we do not reject, repel, refute, or absent opposing values that are hierarchically equal, superior, or inferior.

The absolutist and abstractist exclusivism of our mind has led us to such exclusions and to use only a logic of exclusion, such as formal logic, which is true but does not necessarily exclude dialectics.

And this happens because we continue to confuse negativity (as absence or privation) with oppositionality.35

If we say that A is A and not-A, we reject the being of A, so we say nothing; but if we say that existentially A is A, and also what is not A, we do not reject anything, we only affirm opposites that cooperate in its formation, as we have seen, for example, in what is a tree, formally and existentially.

When dialectics says that something “is” and “is not,” this “not” is not the negation of the first as a unilateral affirmation. It affirms that beyond the first (is), the thing is also another thing that is not the first affirmation. It affirms the first attribution and affirms a second one that is different from the first. It does not contradict when it affirms; it simply does not reduce the thing to just one affirmation.

Dialectic of our senses

Our senses function dialectically: they proceed analytically in capturing external stimuli but simultaneously proceed synthetically in their functioning by grasping only part of what is constructed as a whole, as a global entity.

In turn, these non-analytical totalities will undergo the dialectical action of the mind, which coordinates them into a synthesis according to previous schemata.

The synthesis, as we understand it, is always analogical because it contains and is simultaneous with the thesis and antithesis, unity, and is similar and different from the object of which it is the global expression.

Ernst Meumann states:

“From an observation of the different sensory domains and their relative participation in rhythmic phenomena, we conclude that: 1) each sense participates more in rhythm the more exclusively it is an organ of time perception, which is why hearing is the sense of time par excellence, which has most often inspired the artistic invention of rhythmic forms. Movements participate much less in rhythm because they also serve spatial perception; vision participates even less, manifesting itself as the dullest sense in experiments on time estimation. We can also easily verify that: 2) in the domain of spatial forms, particularly in architectural works of art, we only speak of rhythm to the extent that they offer the occasion for successive contemplation, a kind of periodic alternation between rest and movement.”

The eyes are the senses of space and tend to spatialize facts. With our eyes, we can reverse space. With our ears, we follow the succession of sounds, which help us shape time, which is irreversible because sounds do not reverse.

Thus, we can classify, placing vision and hearing between extremes:


Dialectically, there is only a distinction between time and space, which form the “time-space complex” when space predominates.

In vision, there is still time, as there is space in hearing.

The sense of touch is even more spatial than temporal; in taste, they are balanced; in smell, time begins to impose itself, dominating extensively in hearing.

Therefore, through our organs of intuition, we live between opposites that complement each other and give us, in their combinations, the entire range of our intuitive schemata, the foundation and background of the abstract schemata of reason that strip them of their facticity.

“Vision” reveals its dialectic in its functioning. First, we consider the distinction between its two sensory apparatuses:

  1. The retina, a sensitive surface that receives vague luminous impressions through transparent surfaces. It is responsible for providing extension and color.

  2. The focusing apparatus (mise-au-point), composed of the muscles of the lens, the diaphragm, the periocular muscles, and the eyelids, which provide sharp contours and relief.

Let us add: 3) binocularity, which allows us to see an image in a single vision, and 4) the asymmetry of vision and its functional harmonization, which allows us to perceive depth, planes, perspective, etc., as well as fixate, stop, and staticize the stimulus in order to intuit it.

This asymmetry is revealed by one eye that is attentive, fixed, and one eye that is dynamic, more affective.

Such characteristics of vision’s functioning, always dialectical, favor our understanding of the thesis we have always defended: the fundamental influence of vision on the polarization and construction of reason.

Our focusing apparatus allows us to capture sharp contours, the stereometric form of things. Binocularity has given us fixation, staticity. It is not difficult to understand that from the initial functional schemata we build, we arrive at the formation of the most abstract concepts.

The development and history of this intellectual activity of our mind are explained in our books “General Nooiogy” and “Treatise on Schematology,” and from a gnoseological perspective in “Theory of Knowledge.”

Article 2 – New Aspects of Contradiction

For Formal Logic, the term contradiction is clear. Two mutually contradictory propositions cannot both be true or both be false.

We have the following cases:

a) what is completely negated is affirmed as present; b) what is affirmed as present is completely negated. Consider that formal contradiction consists of affirming the presence of an element and, simultaneously, its absence, or affirming the absence and, simultaneously, the presence, always under the same aspect. The negative is, in every formal position, the absence of…

Now, opposition in dialectics, for dialecticians, is always positive; it is not an absence. What opposes is, therefore, an antithesis, a positivity.36

If within a unity we affirm one positivity and affirm another positivity that stands against it, opposes it, we have “contradiction” in a dialectical sense, for we state one positivity and contradict it with another. It is only in this sense that the term contradiction can be used in dialectics.

Contradictions that can arise within facts can be internal or intrinsic and external or extrinsic. Internal contradictions are those that are included within the immanence of the object being discussed; external contradictions are those that, in any way, do not belong to the considered unity but are coordinated with it, acting as conditioning factors, such as the earth, air, water, etc., for the formation of the unity of a tree.

Therefore, we have:

dialectical contradictions

  • internal — those that are part of the unity.
  • external — those that condition the presence of the unity or cooperate with it or not.

For dialectics, every contradiction is antithetical and therefore positive. Since Dialectics does not exclude Formal Logic, as it is never exclusive but inclusive, there are also the following dialectical contradictions:

dialectical contradictions

  • by privation

  • by alterity

Contradiction by privation, dialectically considered, is rejected, as in Formal Logic, because contradiction (as opposition) is always positive, has formal and real presence. Dialectically, one cannot affirm a positivity and negate it, that is, affirm the presence of the absent, whether in formality or in unity. This goes against human understanding and is absurd.

This is the aspect that opponents of Dialectics do not understand, and they think that Dialectics affirms the presence of an absence, thus transforming it into a logic of absurdity, which is another way of negatively considering it.

Contradiction by alterity is the result of the process of becoming, of the transitivity of being in its existence.

With the concept of “contradiction” clarified for dialectics, we can now establish ten opposing aspects that an entity can present:

  1. within unity, through the orders of intensity and extensity;
  2. formally considered, in the opposition between its formal generality and its material singularity (form and matter, for Aristotelians, for example);
  3. as part of a whole: every unity exists within a structure that is part of it and opposed to it (e.g., a nerve cell in tissue);
  4. in alterity (in the development of its internal process, becoming);
  5. in the formation of its totality (influence and reciprocity with the environment in the development of its process of externalization);
  6. in the intrinsic principles of being, such as actuality and potentiality, and extrinsic principles, such as predisposing factors, which we will study later;
  7. in global concretion — opposing vectors of the structures that contain it (a cell belonging to nervous tissue, which in turn belongs to the innervation of an organ, and that, in turn, belongs to the nervous system);
  8. in the planes to which it belongs — (a cell is not only a biological entity but also a physical-chemical entity, as it is included in the psychic plane, whose functions are diverse, contrary, but positive);
  9. considered as a unity, in relation to other entities that affirm it through opposition (existing as opposition);
  10. as a unity, it is a whole composed of parts but, at the same time, it is part of a structure; it is simultaneously a whole and a part, although for different reasons.

With these ten dialectically opposing aspects present in any chronotopic being, we are on the path to construct and understand the methodology, which we will soon present, in order to make practical use of decadialectics.

On Opposition

Dialectically, opposition can be:

opposition

  • antagonistic: when the opposition can be resolved;

  • antinomistic: when it is not resolvable (irreducible);

  • cooperative: when the opposites contribute to the construction of the same order in which they operate together.

In addition, the oppositions already studied in logic, such as contradictory, contrary, and subcontrary oppositions, are included, which refer to logical judgments.

To clarify these logical terms, let us make the following observations:

Both contradiction and contrariety imply oppositionality.

Oppositionality implies the positionality of at least two antagonists.

This oppositionality can occur in two ways:

a) that the affirmation of a positionality necessarily implies the negation, by exclusion, of the opposite positionality; b) that the antagonism can occur with the position of the antagonists.

In the first case, we have exclusion; in the second, presence within unity. Example of the first case: contradiction in the formal logical sense: Either it is or it is not… In the second case, the presence of contrary predications in the same unity, dialectical contradiction, as what is formally not is existentially. This book is formally a book; existentially, it is an object in becoming, which ceases to be what it is, accidentally or modally, what it currently is, and through substantial changes, it will decay, etc. Being a book does not prevent it from also being what is not a book. Therefore, it is a “contradiction” that includes, contrary to formal exclusion.

In the first case, we have formal contradiction, as we have already said. In the second case, we have contrariety (dialectical contradiction), which is also opposition.

Goodness, as such, excludes badness because it is only formally considered. Goodness in this man does not exclude the presence of badness, which antagonizes it and dialectically contradicts it because Dialectics is the logic of existence, while Formal Logic is the logic of ideal forms (of eide).

Two contrary propositions in Formal Logic cannot both be true, but they can both be false.

Existentially, through dialectics, both can be true because they refer to actualizations of the unity that contradict each other, not as such, but as tensional schematic components of the being in question, as they refer to the unity and not to the formality of this or that.

Dialectically, there is no exclusive contradiction in saying that this man is good and that this man is bad when we consider goodness and badness as constitutive of the unity of “this man.”

But badness, as such, excludes goodness as such.

When considered formally, concepts are rigid.

The facts that symbolize them are therefore analogous to those concepts because that is the characteristic of every symbol: to be analogous to what it symbolizes, according to various modes of analogy that we have already had the opportunity to study in “Ontology and Cosmology.”

In this way, as form, the idea of goodness (as an abstract schema) excludes any and all traits of badness.

But the goodness of this man is analogical because it is a symbol of the concept (abstract schema) of goodness. This goodness in this man, being analogical, includes the traits of goodness when abstractly considered, but in him, it coexists with other traits that constitute his character. Among these traits, we will find others that are included in the concept of badness (the concept, abstract schema of badness). Therefore, this man, when formally considered, has goodness. Goodness, as such, formally considered, excludes badness. But existentially, in this man, there is also badness. Consequently, there is also formally considered badness. If badness formally excludes goodness (when considered as abstract schemas), it does not exclude, however, the presence, in this man, of the corresponding traits. Therefore, we can assert that in him there is goodness and badness without these concepts, as abstract schemas, transforming into one another, which would be an absurdity on a formal level. However, they do not prevent the presence of traits that, without dialectical absurdity, allow us to affirm that in this man there is goodness and badness in contradiction but as parts of his unity, this man.

Where there is formal incompatibility, there may not be dialectics. Formal Logic is the logic of either… or… (exclusive).

Dialectics is the logic of etiam (also); therefore, it is inclusive. One does not negate the autonomy of the other. Dialectics acknowledges the validity of Formal Logic, as it belongs to its order, its sphere, which is that of abstractions, but it seeks to realize another truth in the realm of concretion.

From the cooperation between the two, with their clearly defined activities, decadialectics emerges.

Article 3 – Intrinsic and Extrinsic Principles

There are certain topics in metaphysics that are important for a clear understanding of dialectics, especially for the construction of its methodology, which makes it practical for a more in-depth analysis of facts and ideas. In this part, we wish to examine and outline these topics.

It is not possible to define being as being because we cannot reduce it to a genus. It is the subject of all predicates and the predicate of all subjects.

“Actus secuuntur esse,” say the scholastics. Action follows being; being is active, both created and creator of all things because what creates “is,” the creature “is,” and the action of creating “is.”

But finite beings, being delimited, are and are not, as while they are, they pass to other modes of being and cease to be what they were before, as delimitation, and being as they are in becoming, they are as they were before, “being.” Being is thus immutable as being because otherwise, we would have to accept that being comes from nothing, as absolute non-being, as the absence of all efficacy. Now, if nothing could create being, it would cease to be nothing, the absence of all efficacy, in order to have the efficacy to create. Consequently, the empty idea of an absolute nothing can only give us the total and absolute absence of efficacy and being. Therefore, being, and only as such, can create, can be by being, can become. But in becoming, it ceases to be a limited, finite being to become another limited, finite being, while infinitely remaining being through all forms of being as becoming because it is being that generates itself or, rather, it passes through all its mutations, which are only from finitude to finitude, never ceasing to be. Thus, there are no interpolations of nothing between beings, but rather interpolations of finite non-being between finite beings. The verb “estar” in Portuguese, absent in many other languages, clearly gives us the difference between when being “is” and when being “is.” Being, as being, “is”; being as a finite being, “is.” It moves from one state to another in constant becoming; it moves from one delimitation to another, not from an absolute nothing to a being, but from a limited non-being to another limited non-being, always being being through moments of “estar.”

The becoming of being, of being and “estar,” is revealed to us through principles that metaphysics classifies as:

Principles

  • Intrinsic principles of being

  • Extrinsic principles of being

Principle means beginning, what is found at the start of something, what consequently explains it, gives it its reason.

Metaphysics distinguishes three orders of principles, which are presented according to formal philosophy and find a correspondence in dialectical philosophy. Let us analyze:

a) Logical principles, already studied in Formal Logic, are laws of formal thought.

They are:

  1. Principle of identity;
  2. Principle of non-contradiction; and
  3. Principle of the excluded middle.

To these principles correspond others in dialectics.

To the statement of the formal principle of identity: “What is, is; what is not, is not,” we respond with the dialectical principle of identity: “What is, formally is; concretely, it is and is not; what is not, formally is not, but concretely it can be or not be.”

For the formal principle of identity, “this object is a tree or is not a tree,” dialectically we would respond: formally considered, this object either is a tree or is not; but concretely considered, this object is a tree, but to be a tree, it requires coordinates that are not itself, but without which it could not be a tree. Being a tree implies the concretion where it occurs, and what is not a tree is in it.

It is not justified to confuse here the verb “ser” (to be) used in two different senses because when the formalist states that this object is a tree, they state it as existentially such. Furthermore, dialectics does not exclude Formal Logic; it just does not stay within the formal realm as it is interested in the concrete. And as beings are not static in concrete terms, dialectics is concerned with outlining the dynamic and concrete aspects of being, which we will soon examine.

To the statement of the principle of non-contradiction, which says, “The opposite of true is false,” dialectically we respond: “Formally, the opposite of true is false; but concretely, there is gradation between the extremes of exact and incorrect, which correspond to the formal concepts of true and false, which do not admit degrees.”

This is understandable because Formal Logic is exclusive. Formally, when we say that this object is a tree, we either state truth or falsehood, but dialectically we say that this object is a tree, but what is not it, what is essential for it to be, is existentially excluded from its formality.

To the statement of the principle of the excluded middle, “Of two contradictory propositions, one is true, and the other is false,” dialectically we can respond: “Formally, it is so, but dialectically we can enunciate from the same fact two opposing propositions, as long as they refer to what is opposite in its concretion.”

We can say that this object is a tree, but we can also say about it what it is not, but what is indispensable for it to be, which also gives it being. We can enunciate propositions about the dynamic and kinematic aspects of its internal contemporary oppositions and its oppositions in alterity, in succession.

Physical principles should not be confused with the principles of physics or with the general laws of science; they refer to the elements that make up the material world, such as atoms, electrons, etc., which are the principles of the material world.

They are constructed or obtained by reason; they do not have a physical real distinction, like that of carbon and nitrogen; they are entis quibus, whose existence is in beings but does not exist (entis quae) in themselves, as the scholastics have shown. Many dialecticians believe that all philosophers give metaphysical principles an independent existence, completely separate from existence. These metaphysical principles are those of act and potency, matter and form, essence and existence, etc., which are properly studied in our book “Ontology and Cosmology.”

The ontological, formal, fundamental principles of the formal logical principles, which are based on them, also receive a dialectical statement corresponding to them.

Thus:

  1. "Every object is identical to itself"- ontological-formal principle of identity.

Corresponding to it is the dialectical principle: “Every object is opposed within itself, and in its unity, its oppositions are identified.”

  1. “No object can be both itself and not itself at the same time” – ontological-formal principle of non-contradiction. The dialectic responds with the dialectical principle of contradiction: “Every object is itself, formally, and what existentially does not belong to its formality.”

  2. “Every object is what is clearly predicated of it and what we can logically and dialectically predicate of it in opposition.” Dialectical principle of inclusion.

a) Dialectical principle of sufficient reason: “Internal and external oppositions are reasons for the being of that which ontically exists,” or: “Everything that ontically exists has a dialectical reason for being and non-being.”

b) Dialectical principle of chronotopic existence: “Every ontic existential chronotope is in becoming.”

c) Tensional dialectical principle: “Every tensional structure is quantitatively equal to its component elements, and qualitatively and specifically different from them.”

A being moves from possibility to actuality through the action of effective, extrinsic agents, such as the effective agents that allow a seed to transform into a tree. Without these extrinsic elements, encompassed in water, heat, etc., it would not be a tree, nor would it be without the incorporation of what it is, which is identified within it through biological assimilation. These are the extrinsic principles, which receive the general name of causes, that predispose its development, allowing the emergence of latent potential.

Thus, we have predisposing causes and emergent causes.

The intrinsic principles are the constitutive ones, which are captured by the analysis of the mind, although not by experimental analysis. However, it is the data of experience that provide us with the points that enable us to capture them, such as act and potency, physically inseparable but metaphysically distinct: essence and existence, form and matter, studied and analyzed in “Ontology.”

In a methodological application of dialectics, such distinctions in metaphysics are important for a clear understanding of the factors, as well as to facilitate decadialectical reasoning, which we will study shortly.

An example clarifies the agreement, cooperation, or subordination that can occur between causes and intrinsic principles.

We could consider, although justifying this would require the analysis of other metaphysical topics, that emergent causes, included in the immanence of ontic being, result from its internal form, which must be distinguished from its external form (its first essence and its second essence, as metaphysics would say), and from external coordinates, which allow emergence through the predisposition they offer. There is thus reciprocity in action, as we will see further.

An apple seed contains within it the germ of the tree. But the tree is not the development of the seed. The seed, possessing its internal form, in the relationship of its oppositions and its tensional structure, has the possibility to actualize an indefinite number of possibilities, which environmental conditions (environmental coordinates), external predisposing causes, can facilitate or hinder, and which oppose, antagonize, and cooperate with it.

We thus have the internal dialectic of the seed considered in its contemporaneity and the dialectic of its alterity. It is determined as a seed, but as a potentiality to become an apple tree, it is an indeterminate being. With the cooperation and antagonism of environmental coordinates (external causes), which in turn act dialectically upon it, it can thrive, following its first essence, existentially considered as a seed, this seed, and its second essence, its species (apple), which form a set of apple schemas. It can assimilate corporeal elements from the environment that are not, but that, in it, cease to be what they were to be, now, the apple tree, which, in turn, ceases to be the seed it was by being the apple tree. This becoming is a negation of previous states but also an affirmation because by actualizing its possibilities, it negates possibilities as possibilities since they are now actuality, but it affirms possibilities because having been actualized, they are confirmed as possibilities and actuality, which would be properly synthesis, composition. But this synthesis is not the only one possible to construct because it, the seed, now the tree, formally considered as a whole, separated from the environment (coordinates), is negated by it, but as a tree, it affirms the seed (as thesis) as it negates it because it is already a tree (antithesis), and as synthesis, composition, it affirms and negates the thesis and the antithesis, affirming the seed and negating it through the tree; affirming the tree, but negating itself because as such, it is the actualized seed, which, in turn, is, as a tree, the possibility of being a tree, which negates it, and so on. Similarly, in relation to the environment, there is the same unfolding of thesis, antithesis, and synthesis. But everything that happens with the apple seed also happens with the apple tree, that is, conditioned to the apple structural scheme, which emerges its internal form thanks to the external causes that coordinate with it to form the concretion of the apple tree, which is not only formally an apple tree, but concretely also the coordinates that predispose its emergence.

In this way, any body is acted upon by external causes (predisposing) if it has the possibility (internal causes) of being acted upon. This way of dialectically visualizing entities in their concretion prevents us from recognizing the presence of factors that contribute to realizing the entity in its kinematic and dynamic development.

Thus, one could call the internal factors emerging factors, and the external factors predisposing factors. As for the latter, by integrating into the entity, they form its concretion (identification in a dialectical sense) and, therefore, they are altered in it and, in turn, alter it.

It is easy to conclude from here another dialectical ontological principle: the principle of alterity, whose statement could be: “Everything in becoming is a constant alternation of internal factors in coordination with external factors, that is, concretely.”

And concretely because “concrecionar” comes from “crescior cum,” to grow with. And entities grow with the coordinates that are them, without which they do not exist, essential for the constitution of their being, as we have seen.

Methodologically:

To carry out a dialectical study, of anything, the studied object can only be mentally separated for analysis from its internal oppositions, from its internal form, as well as from the external coordinates that predispose its emergence, its development, which leads us to consider the three modalities of knowledge, which taken separately are abstract.

Phases of knowledge

Based on F. Houssay’s morphological classification, we can establish that the most comprehensive knowledge of a fact requires considering it from these angles and aspects:

  1. Static knowledge: considering it in its tension at a precise moment of its process (e.g., of the mechanics of a mobile device isolated from the action of forces and time).

  2. Kinematic knowledge: capturing the variations of that fact over time.

  3. Dynamic knowledge: when studying what acts upon the fact (external influences), which do not constitute its tension but rather its contour.

And finally:

  1. Concrete knowledge: achieved through decadialectical analysis, including the synthesis of the previous three, as the final concretion.

Theme IV

Article 1 – Decadialectic Reasoning

We can classify the various logics and dialectics according to their valence. We have seen in Logic how certain logicians (such as phenomenologists) reduce judgment to a value judgment.

When we say “this book is red,” it is possible to replace that statement with this: “it is worth for this book to be red.” And within Formal Logic, it is only acceptable to say of this book that it is red or that it is not red. That is, it is worth for this book to be red, or it is worth not being red. Therefore, it can be concluded that Formal Logic operates with bivalence, that is, two valences can be attributed to the book. If one is accepted, the other is inevitably rejected.

This is why Formal Logic is said to be a bivalent logic. Based on valence, can we classify the various logics and dialectics? Yes, they can be classified based on valence, without exhausting all possibilities of classification, because they also allow for determination based on other aspects. We offer a synthetic classification of the various logics:

  1. Monovalent Logic, that is, the one that accepts only one valence. It can be stated as follows: “Only this is valid for this.” An example of this is the logic of classical, pre-relativistic science. It is the Logic of YES.

  2. Bivalent Logics are those that accept more than one valence, but they are mutually exclusive. They fall into three categories: a) This can be stated as follows: “This is valid for this thing or it is not.” It is the Logic of Yes or No, this or that; it is Formal Logic.

    b) A relativistic logic, as an aspect of Formal Logic, could establish bivalence, basing valence on conviction rather than certainty, and it could be stated as follows: “For this thing, we are convinced that only this is valid, or it is not valid.” It is the logic of maybe yes, maybe no. It is a relativistic bivalent logic, and its statement would be: “This is only valid for this, in this situation; in another situation, maybe not.” It is a logic that conditionally affirms and accepts the possibility of negation.

  3. Polyvalent Logics do not rely on the principle of non-contradiction of Formal Logic and accept the excluded middle while excluding the fourth possibility.

    Thus, Marxist and Hegelian dialectics are polyvalent logics, but they could be better classified as trivalent, as they accept the triad: thesis-antithesis-synthesis. They can be stated as follows: "For this thing, this is valid, but its negation is also valid, and subsequently, the negation of its negation. Thus, we have the thesis, the antithesis, and the synthesis. Three affirmed valences.

    b) Polyvalent logic with a hierarchy of valence. It can be stated as follows: “For this thing, this is more valid than this or that.”

    c) Polyvalent logic similar to the previous one but without a hierarchy of valence. It can be stated as follows: “For this thing, this is valid, but also that, and that other one, etc.”

    d) Polyvalent, antinomic dialectical logic. It can be stated as follows: “For this thing, this is valid, but also its successive, current, and potential oppositions. ‘Yes and no,’ not just yes, nor just no.”

    We can see that dialectical reasoning is predominantly polyvalent, while formal logical reasoning is either monovalent (in pre-relativistic science) or bivalent (in classical Formal Logic). 37

In everyday life, these logics are not pure. They are influenced by a powerful element that shapes them, modifies them, and penetrates them. This element is also dialectical and is inevitably present in reasoning. If we examine the history of human intelligence, we see it always present, always influencing: it is the contribution of affective logics.

Through affective logic, there are valuations of valence. There are valences that receive the influence of the conviction of evidence and are considered evidence when, in reality, they are only convictions. This logical fact is historically powerful.

There are principles that are considered axiomatic in a certain era, and no one dares to question them. If someone does, their opinions do not find resonance.

Under the influence of created interests, affections construct a valuation of valence, in addition to value valuations, lending evidence to convictions. Affective logics are individual (when it comes to human singularities), particular (when it comes to groups, classes, estates, etc.), and general (when they represent an era, a culture).

Affective logics always operate alongside the others, no matter how much logicians, scientists, and philosophers may not want to accept it.

These affective logics require a study that goes beyond the scope of this book.

In each era, geniuses perceive the affective nature of so-called evidence and accepted axioms. They denounce them. Naturally, they are not heard because their affirmations stand against affections and the convictions based on them. After a certain time, the affective foundation, which is always mutable, changes, and convictions lose their strength. When they lose strength, it is discovered that the evidences are not as evident as they were thought to be. Then, there is room for the resonance of what had been previously affirmed. Only then are the genius’s opinions understood, and they are considered a genius, and homage is paid to the past. No genius has triumphed against dominant convictions. Their victory is always the result of the defeat of convictions.

Thus, geniuses do not triumph on their own but merely survive or persist after total defeat. This is the tragic aspect of genius. Therefore, the masses cannot be accused of not understanding geniuses. They have to be misunderstood.

Nietzsche said that the value of an era would be measured by the ability of the masses to recognize their true great men. A humanity that could analyze dialectically, using polyvalent logics to examine affective logics as well, may be an ideal but not a reality.

Without any trace of pessimism, we believe that such a fact will not occur. Only a humanity of geniuses could understand their own geniuses.

Having established this introductory basis for the significance of valence in logic and dialectics, it is not difficult to understand that there is not just one dialectical method, but many. Does this possibility indicate the weakness of dialectics?

In part, yes, and in part, no. Dialectics is a new discipline, still in the formative stage, still in its adolescence, and therefore subject to many experiments and errors.

Dialectics (which is generally a polyvalent logic) does not come to create confusion and disorder in thought. We are in an era of value revision, a time of great new experiments, where principles considered evident (which were merely convictions of evidence) are threatened in their supreme and apparently immutable position. Dialectics enriches logic.

It is natural that many attempts are made, many new errors are added to the old ones, but the diligent and careful work of philosophers will allow us to separate the wheat from the chaff.

What generally terrifies us is not having a solid foundation, a point of support that can make us feel secure in examination and choice. Classical formalism had that Archimedean point in the principles of reason.

Dialectics follows the same path as the current relativistic science when analyzing them. Relativistic science replaced the fixed point of support, which was absolute space and time, with relative space and time.

Dialectics does the same, replacing the Archimedean point of support with a relativistic point as well. Relativism, in its general sense, is always a transient position in the history of human thought.

It arises in times of crisis when the highest values are threatened with transmutation and overthrow. Let us not think that it is possible to halt the history of human thought. What we have today as the best is not yet the end. Perhaps we will never have an end. Perhaps this eternal search, this eternal unveiling, this eternal progress through unknown regions, belongs to humanity alone. The universe of thought has no goal other than the ideal. Our desire to reach an end may only be a great desire for an end, for termination, for destruction, for annihilation, and not for the absolute truth dreamed of by all.

Parmenides' painful cry when he addressed his prayer to the gods, offering everything for just one certainty, however meager, may be merely a longing for security, for solidity, even though that security and solidity may seem empty to many.

Let us remember Schiller when he told us that the beauty of the journey lies in the journey itself and not in the point of arrival. Let us be tireless travelers, yearning for certainty. Let us not make our impossibilities our anguish. Let us live the beauty of the paths we travel and not interrupt our journey because we do not know where we will end up. Let the unforeseen be our yearning. Perhaps the unforeseen awaits us in the folds of the road. And what more could it give us? Perhaps everything that doubt often denies will be ours.

The decadialectic reasoning is structured on what is firm in classical logic, without abandoning what is useful in dialectics, but it avoids falling into the infertile, slippery terrain of inconsistency.

Practical rules

It is always worth remembering:

a) The law of alternation – Examples of vibrations – Action and reaction – Positives and opposites.

b) Every affirmation excludes, and the excluded, if concretized with the affirmed, must be remembered.

c) Everything that exists chronotopically occurs in time, therefore it changes (law of alterity).

d) Everything that is, has within itself dialectical reasons for being and not-being. Examples: benevolent and malevolent impulses; impulses of death and life – Centrifugal and centripetal – Intensity and extensity.

e) Everything that is, to exist, requires what opposes it to achieve being.

f) Everything that is in act is indeterminate in potentiality, and this potentiality, when actualized, reveals new possibilities.

g) Always keep in mind the polarizations of values and epithets.

Decadialectic (deka in Greek means ten) is the dialectic of the 10 fields of reasoning. These ten fields combine with each other and make dialectical reasoning complex, heterogeneous, like the heterogeneity of existence itself.

Let’s establish them synthetically, and then try to apply them in examples.

  1. Field of subject and object.38

This is the first major dialectical field that we can emphasize, which is fundamental for humans and for all philosophy. But we would be on a narrow ground if we confined ourselves to a subjectivity and an objectivity only correlated with humans, that is, if we circumscribed it to the dualism, often called antagonistic, between the Self and the non-Self. That is not the dualism we want to emphasize here. It is the dualism between subjectivity and objectivity, and these terms have a much broader sense, as we will see shortly.

When we say, “We have a book in our hands,” it is easy to analyze that the subject is us and the object is a book. But when we say, “This book is red,” in analyzing this judgment, grammarians will say that this book is the subject. The book that was an object in the first proposition becomes the subject in the second.

Do not think that grammarians, in making such an analysis, are as far removed from reality as some philosophers think. Let us assume that one of us is handling the book and begins to reason: “I see this book, I have it in my hands. It is a red book, and it deals with philosophy.” In the first proposition, the I that speaks about the book is actualized; in the second, the actualization is of the book, and the speaker remains virtualized.

In the first proposition, the attention of the speaker is entirely focused on oneself, on one’s actions of seeing and having. In the second, the attention is diverted from oneself to focus on the book, examining one of its aspects. The book then occupies the central point, with everything else revolving around it, surrounding it. If one continues to say, “It is a deeply written book, it deals with important themes,” the entire actualization remains focused on the book. But if one says, “Therefore, I must read it because I can learn a lot that interests me,” there is a shift in attention from the book to the person speaking, who becomes the subject. Common language, like classical language, perfectly reflects this mechanism, this constant shift from subject to object, and vice versa. In this way, we can conclude that everything is subject when actualized by thought because it receives the ject, and object, which is partially virtualized. The concepts of actuality and virtuality come into play here, forming the second dialectical field that interpenetrates with the subject-object field.

Thus, there is a dialectic of the subjective and the objective, considered as the Self and the non-Self, whose reciprocity we have already studied, and in relation to actualization, a variability of objectivity and subjectivity: the fact that one is sometimes subject and sometimes object. Therefore, everything that is subject can be object, and vice versa, depending on the actualizations and virtualizations of our mind.

  1. Field of actuality and virtuality.

We have already examined Aristotle’s doctrine of act and potentiality on several occasions, as well as the various opinions formed about actuality and virtuality.

This field is the broadest and penetrates all the others that we will examine. Everything that exists in act is not yet fully realized because there is something in potentiality, something that has yet to be accomplished, actualized. But what is in potentiality must be specified: a) as potentiality, and in this case, we adopt the concept from physics, for which what is in potentiality is not merely nothing. Here we must distinguish potentiality from possibility. Thus, the opposition between potentiality and actuality is not the same as that between possible and real.

Potentiality is (being-in-potentiality), and the possible is what does not formally contradict it. Potentiality is being while it has not reached its totality (perfection), while it has not received all the determinations or forms it entails (Globot).

Potentiality is the power to become the contrary and even contradictions. In potentiality, contrary determinations merge because any being, in potentiality, is everything it can become, and in act, it is everything it is. In act, contradictions are distinguished and excluded. The seed of a tree is not only what it is in act (a seed), but also what it is in potentiality (a tree, a seed, etc.).

Thus, what is in potentiality has its possibilities, which, to be more precise, we should call probabilities, in the sense of what is admissible but also what “satisfies the general conditions of experience,” what does not contradict any fact or empirically established law. Therefore, all phenomena have their possibilities. But if we examine them closely, they may have a greater or lesser basis of reality.

For example, it is possible for the Moon to collide with the Earth. It is possible for it to rain today and have good weather tomorrow. The first possibility is less real than the second. Thus, what is in potentiality can have real possibilities, with probability, and non-real possibilities when subjectively (by humans) considered.

The reality of a possibility is grasped through the degree of potentiality. Thus, “any young person can become a pianist” has the possibility for it. But Mozart, as a child, had more than potentiality, he had virtuality to become a pianist. In this way, potentiality encompasses a dialectical field formed by its possibilities, and then we have:

  1. Field of real possibilities (virtualities) and non-real possibilities.

These possibilities are in an indeterminate number (n possibilities). When examining the possibilities, we must see the degree of reality they possess in order to classify them as real or non-real. And this degree of reality is given to us by the knowledge we can have of their potentiality. (We said can have, and here the dialectical field of potentiality enters the field of knowledge, which we will soon reach).

  1. Dialectical field of actuality and the antinomy between intensity and extensiveness.39

What is in act possesses intensity and extensiveness, which can be real or abstract. If what is in act is a body, the antinomy between intensity and extensiveness is contemporaneous and irreducible, in addition to being necessary. If what is in act is an abstraction, such as an idea, then we have an intensity and an extensiveness that are also contemporaneous and complementary, in the abstract, because as we have seen, a thought requires being thought and, therefore, the act of thinking.

The understanding of the concept is analogically intensive, and its extension is extensive.

Outside of this, thought is merely possibility. We have already examined intensity and extensiveness in the chronotropic. We have seen how heterogeneous the former is and how homogeneous the latter is. Because it is heterogeneous, intensity has its inherent and immanent oppositions, which vary according to the alterations of what it encompasses since the alterations, being qualitative, are intense. Thus, we have here the

  1. Field of oppositions of intensity and extensiveness in actualizations.

We have already seen the first ones, which refer to intensity. The second ones are found in the oppositions of the various actualizations that are successive, such as motions, mutations, and movement in bodies.40

These actualizations are also of an indeterminate number, and when they are qualitative (intensity) or quantitative (extensiveness), they have reciprocal actions that we have already studied when dealing with the transitions from quantity to quality and vice versa, reciprocity, etc.

  1. Field of oppositions of the subject: Reason and Intuition. We will not repeat what we have already studied regarding the oppositions between Reason and Intuition as important functions of the human mind and the reciprocity exercised between them.41

  2. Field of oppositions of Reason: Knowledge and Unknowledge.

We have already seen that reason provides us with knowledge of the general, while intuition provides knowledge of the singular. But in all knowledge, there is selection: to know is also to unknow (consciousness and unconsciousness) because when we know certain aspects, we unknow others.

Rational knowledge can be a priori or a posteriori, but there is always a reciprocity because there is no a priori knowledge without a posteriori knowledge and vice versa, which we have also studied in detail.

In knowledge, the oppositions between the object and the subject arise, indicating that this dialectical field penetrates the field of rational knowledge. There is also a virtualization from the singular to the actualization of the general. When rationally knowing this book, we inhibit the singularity aspect of the book from being this particular book, a singularity, and we know it as a book, a conceptual and general knowledge.

Hence, reason exhibits dualisms such as concrete-abstract, objectivity-subjectivity, and consequently, their antinomies in the Kantian sense, such as time-space, finite-infinite, etc. The categorical knowledge and conceptual knowledge should also be considered. The former is a classification of the known by categories and is a knowledge that disregards the most specific aspects, such as conceptual aspects. In conceptual knowledge, the known is only classified within concepts. In this field, Aristotle’s analyses of the categories are of great value.

Furthermore, it is important to consider value judgments, which assert values and not just facts, as in the case of the phenomenologists we have studied (where there is valence and not strictly value), and existence judgments.

In the former, evaluative and ethical influences penetrate, while in the latter, there is only the affirmation of facts as they occur, stripped of any evaluation or valuation.

When dialectically examining a line of reasoning or an opinion, one must search for the opposition between value judgments and existence judgments that constitute them. This search reveals very important aspects and enriches the dialectics of this field, as it shows us how reason knows and how it unknows.

These are important corollary subfields of this 7th field.

All these oppositions give rise to the

  1. Field of oppositions of Reason: rational actualizations and virtualizations (intuitive actualizations and virtualizations).

Reason actualizes or virtualizes, as we have already seen, either the singular or the general because reason rationalizes the work of intuition.

From the singular, intuitive aspect, it induces the general (induction) or from the general, it deduces the singular (deduction). Reason does not dispense with intuition; both are contemporaneous. They are separated only in an abstract sense. As for actualizations and virtualizations, we will not discuss them as we have studied them several times.

There are also actualizations and virtualizations in the intuitive process. What is actualized does not exclude what is virtualized because attention is given to what is actualized while what is virtualized remains in a state of potentiality. This opposition in the intuitive process is analogous to that of reason.

  1. Field of oppositions of Intuition: knowledge and unknowledge.

We have already studied the concepts of reason and intuition and their opposing conceptualizations. Intuition, as knowledge of the singular, and therefore of the different and heterogeneous, is both knowledge and unknowledge. We do not know the entire content of a singularity. But other fields come into play in this selection. The same applies to reason as it does to intuition. If we know this book as an exemplar (as singularity) and apprehend its red color, the unique and exclusive marks it bears, the paper it is composed of, we do not know everything, but we also unknow because knowing something also means unknowing something, and paying attention to something means disregarding everything else.

  1. Field of the variant and the invariant.

This is an observable antinomy in all facts: what is repeated and what presents itself as new.

There is no fact that is completely different and does not repeat something from something else, at least formally. However, certain facts exhibit a certain constancy in the repetition of aspects, such as sociological and economic facts, to give a few examples among many, which reveal an invariance of notes coordinated with other co-variant aspects. In this case, for example, the calculation of Einstein’s tensors is a manifestation, in mathematics, of this field’s dialecticism. For instance, gravitation, as a state, is an invariant. All bodies are subject to it. But the act of gravitation is covariant, variant, and thus it is accompanied by its corresponding coordinates. We have thoroughly examined the sense of variant and invariant on multiple occasions, and we do not believe that difficulties would arise in understanding how important it is to seek the invariant and variant in all facts along with their coordinates, i.e., the co-variant, which allows for a broader dialectical field of vision.

This field interpenetrates with the fields of the subject and the object.

Thus, we have observed the great polarity of the entire dialectical process, which unfolds in 10 interpenetrating fields, interacting in constant reciprocity and generating many other fields that participate in them. However, it should not be assumed that we must always work with these ten fields to have any reasoning. We can reason formally by only considering actualities (as we usually do in practice), or we can reason with two, three, or more fields. But for a reasoning to realize our greatest possibilities, in our view, it should include all ten fields.

Next, we will provide examples of dialectical reasoning. One example will follow the Marxist dialectic, another the Hegelian dialectic, and finally, one within the framework of decadialectic. We will see how reasoning can be enriched for a more concrete perspective.

The greatest contribution of decadialectic is its ability to order each fact, studied in all aspects that, taken individually, are abstract, allowing reasoning to achieve the desired concretion.

In all of this, we have seen a polarization of all processes, a polarization that always manifests itself at all levels of knowledge, and which, in turn, arises in valuations, as seen in physics between positive and negative electricity, between concrete and abstract, between deduction and induction, polarizations that stand out in chemistry between analysis and synthesis, attraction and repulsion, negative and positive, and we could cite hundreds of examples.

What is never seen is synthesis in the sense of a third term, except as composition (syn and thesis), the genuine sense of the term, but rather a concretion that encompasses the fundamental antinomic dualism of all existence, taking a position that stands above the abstract extremes.

Methodologically: a fact or theme, considered as a whole, can be placed in 5 planes:

  1. as unity – that is, studied in itself in its inner process, and descriptively;

  2. as totality – forming part of a whole, of which it is an element;

  3. as series – that is, as part of a totality that would be, along with other totalities, in the formation of a new structure or scheme;

  4. as system – that is, as part of a totality and structure that belongs to a conjunction of serial structures, enclosed in a tensional scheme;

  5. as universe – that is, considered in all the previous aspects, but being part of a system that, together with others, belongs to a tensional universe, or merely abstract-noetic scheme.

These are the five planes in which any tension, any structure, can be placed, and the search for these planes during the dialectical examination of what is intended to be studied allows the expansion of the concrete field of dialectical analysis.

We could exemplify: the neuro-muscular cell, as such, is unity; as totality, it is part of nervous tissue; as series, we have it in the innervation of an organ; as system, in the nervous system; as universe, in the living individual. In society, the individual can be seen as unity, as totality in the family, as series in the social group to which they belong, as system in the cultural cycle that includes them, and as universe in humanity.

We can also start from universes as units and search for their totalities, series, etc., as a tensional constellation can be part of many others to constitute an existential plane, such as the fields of Physics, Chemistry, Biology, Psychology, Sociology, etc.

In each of these planes, we must seek the ten dialectical fields and cross-reference a comprehensive analysis, considering the interactions, the reciprocity of planes, and the influence they can exert on each other in the formation of attitudes, such as the human perspectives that vary according to the planes to which the individual belongs. This forms the object, in certain aspects, of the sociology of knowledge and the study of ideologies.

Just as we can dialecticize a theme according to the fields, we can also pentadialecticize it according to the planes. As examples of these processes, we will examine a philosophical theme, Aristotle’s concept of substance, and an economic theme, the concept of value, at the end of this book.

Many may argue that this method requires a lot of time and care because it involves the presence of so many heterogeneities. But let us look at the natural sciences and observe how heterogeneous and complex the methods of verification are. To do philosophy without effort may be the desire of many who think they can reach the deepest understanding without the burden of intellectual work. Look at the works of men like Aristotle, Thomas Aquinas, Duns Scotus, Kant, Hegel, and you will see how much effort, how much work, is involved because genius is undoubtedly “a long patience” and also great and tireless work, as talent alone is not enough. The same is true in science: Pasteur, Newton, Osvaldo Cruz, Edison, Siemens, Mauá, etc., were tireless workers.

Article 2 – Practice of Decadialectic Analysis in Philosophy and History

Let’s examine some examples of dialectical reasoning according to different doctrines to show how we can adapt them in practice.

Let’s take the French Revolution as an example. First, let’s see how Hegel interprets it according to his method:

“The French Revolution has its beginning and origin in thought. Thought, which considers universal determinations as supreme and finds that what exists is in contradiction with them, revolted against the existing state. The supreme determination that thought can find is that of freedom of will. All other principles, such as happiness and the good of the State, are more or less indeterminate; freedom of will, on the contrary, is determined in and by itself because it is nothing more than self-determination.”

According to Hegel, the will is free when it wills itself and nothing more than itself; otherwise, it would be dependent. Absolute will is the will to be free, and will, which only exists through will, is the will to be free. Man is only free through will. The State was in the hands of injustice and corrupt oppression. The revolution was the result of the clash against organized injustice that prevented the development of the spirit of freedom. From this contradiction, the French Revolution arose.

Now let’s see how the Marxist interpretation is dialectical. The causes of the French Revolution were based on the nature of social relations, whose ultimate cause lay in the state of productive forces.

The relations of production in France and the established economic regime were in contradiction with the political regime. It was necessary to replace the old political institutions with others that would harmonize with the new economic regime. The bourgeois class, which was developing, aspired to power. The revolution paved the way for them.

These reasonings are undeniably dialectical, but both are abstract because they actualize certain aspects of French society at that time and virtualize others. Hegel sees the struggle between oppression and freedom; Marxists see the economic “contradictions.”

Marxists reduce the first to the second, explaining the ideal through the real; Hegel would explain (partially, as a thorough analysis would not be completely like this) the real through the ideal. If we accept contemporaneity, and in this case, we are already reasoning with our own dialectic, both interpretations touch on one aspect.

We cannot say that there is a priority of the ideal over the real, nor vice versa, simply because we cannot say that there is an a priori knowledge without a posteriori knowledge, and vice versa.

Man does not detach his mind from the events that happen to him. While it may seem chronologically posterior rationally, it is understandable because every rational process requires a pause, a fixation of what one wishes to examine. To reason about something, speculation, reflection, and analysis are necessary. Reasoning is posterior to the facts but not as intuition. However, in this posterior (mediated) reasoning, there are also a priori elements, based on previous experiences and formed ideas. If people feel restrictions on their movement, they do not just feel them as restrictions; they idealize them, form ideas about them.

If someone is prohibited from going here or there, they do not merely have the intuition that they are prevented from going here or there. The inability to go here or there is complemented by the universal idea (scheme) of not being able to go, of experiencing a restriction on their freedom of movement.

The occurring event has its ideal complementarity. Economic situations alone cannot be causes, but rather factors, and there are both real and ideal factors. If the economic factor alone directed people, there would never be processes or human transformations because they would not resonate in the mind.

Because there is a mind, they resonate, and because they resonate, they are more powerful. A real factor by itself does not generate social changes.

Mind is necessary. Man would never have created technology if he were not intelligent, if he did not have the power to create because animals that lack this power do not experience progress. If real factors influenced the outbreak of the French Revolution, ideas, in dialectical reciprocity, also helped to inflame the spirits. Suffering alone is not enough; one must have moral awareness of suffering for revolt to arise. This is what we call resonance. When an idea has no resonance in reality, it is purely abstract and does not lead to anything on its own.

But an idea that resonates with real facts is a force.

The ideals of freedom did not originate with the French Revolution.

They have existed since man has been man. When real conditions are oppressive, ideas of freedom and resistance against oppression find justifications based on facts, making them more powerful. And in turn, ideas exacerbate the actualization of real injustices, creating a growing reciprocity where a spark can be enough to set a people in motion.

To think that the French Revolution was only the result of ideas is an abstraction, just as it is to think that it was only the result of economic conditions. One supported the other; one found its basis and justifications in the other. But what was the decisive factor in the outbreak of a people wanting to destroy the existing order?

As we have explained in Philosophy and Worldview, causes and factors are distinct, and confusion often arises between the two.

If a people rise up to destroy an existing order, first of all, it must be accepted that this people must know in advance that it is possible to destroy the existing order. They must be conscious of a possibility. If men, throughout history, undertake transformations of their way of life, it is because they know that these transformations are at least possible. If they did not have this consciousness, they would accept the existing order as fate. If they revolt against oppression, it is because they always have an awareness of what freedom is.

The emerging and decisive element in the uprising of peoples lies there: the consciousness of the possibility of transformation, the awareness of transformative power.

But more is required: a resolve to abolish what oppresses them. And for that, a psychological act, a deliberation, a choice between conforming and rebelling is necessary. Indignation is required. The contrast between what is and what could be, comparing one’s current situation with the potential situation, makes one feel the injustice of what is. Thus, in an act of social eruption, real and psychological factors emerge and predispose.

The French people lived oppressed under a corrupt and unworthy court. That was a fact. They had to feel it as an injustice, to have the concept of justice, the consciousness of what is just and unjust, in order to be indignant, to be dissatisfied. They had to actualize this injustice, elevate it to the maximum, give it value to feel indignation. What did the intellectuals do if not this work? But this work would be useless if there were no real conditions to make it justifiable, to make it evident.

They had to believe that everything could be better, to believe in a possibility. That possibility had to have the force of reality to launch them into the experience of struggle; it had to have or present reality. The conditions in France were actualized by the revolutionaries, only in their reactionary and unjust aspect. It was necessary to accentuate social differences, to live them as stronger, to exaggerate them as much as possible. In the struggle, the antagonists stubbornly hold on to what interests them and justify themselves through a logic that is more affective than cold. The reactions of the antagonists exacerbate the divisions. In the midst of these clashes of interests, obstinacies only serve to increase the separation and deepen the abysses. All these contradictions are powerful, and it is from the conjunction of all of them that the eruption can arise. Just as the expansion of gas is the cause of an explosion, of which fire and the fuse are only factors, the belief in possibilities and the will are the causes of revolts, while oppression, injustice, and social conditions work as factors. This does not imply the absence of a hierarchy among the factors. However, as the economic factor gains power, the accompanying ideal factor gains power as well.

Real facts have their complementarity in psychic facts.

They are contemporary. One does not precede the other, because here precedence is only a misconception.

Let’s look at other examples:

According to Marxists, Descartes is the philosopher of industrial civilization, a prototype of manufacturing. His interpretation of animals as automata is just a transcription of machines onto living beings. His famous “Discours de la Méthode” is simply the manifesto of the rising bourgeois and liberal individualism, individual initiative. Descartes reflects all of this, and without that historical period, he would not be Descartes.

Marxism is not wrong in its assessments, which only fall short because they are partial. Looking from one angle, their critique is dialectically well formed, but it lacks comprehensiveness because it does not grasp other angles.

The contemporaneity of the mind with facts is thus shown: we are faced with a fact that we have a sensory intuition of. Let’s say we are at home and a government official comes to collect a certain tax from us. Up to that point, there is only a singular fact. But we label the collection of that tax as injustice and declare that the state is exploiting us. We could not call it injustice if we did not already have the concept of what is unjust. In this case, in the face of the fact, the formed idea may be posterior, not the ideation it provokes or the ideality to which it is connected (scheme). The idea of injustice, in this case, precedes it as it precedes our capacity to compare it to what we understand as unjust and assess that this fact fits into that idea (assimilation). But here comes the one who accepts the anteriority of the fact and says: but this capacity to judge and conceptualize is produced by the sequence of a series of facts, whose images, etc., etc. There is no need to repeat all the well-known arguments.

However, would the facts themselves have the possibility of creating that ideal capacity to conceptualize and organize concepts into ideality (ideality being the legality of ideas, that is, the principles that govern the connection of ideas with each other, coordinating them) if humans did not have the potential for it? Because if that were not the case, animals would also be capable of reaching the conditions of ideation and ideality like humans, which is not the case.

If the anthropoid, when descending from the trees, became erect, and because of this erect posture, there were so many physiological transformations that allowed for the development of the brain, etc. (which can be considered a well-ordered hypothesis), such conditions allowed for the emergence of intelligence, and that intelligence preceded the knowledge of production forms and production relations, which were conceptualized later. Now, if one wants to start from the anteriority of the object over the subject to subsequently substantiate the Marxist doctrine, we can respond as follows: the object is not anterior to the subject because there is no object without a subject. Secondly, the opposition between object and subject (in the case of the Self and the non-Self) is the product of a differentiation between two inverse dynamic orders: that of the living being and that of the environment when it is not an entitative part of the living being. Human intelligence is not a consequence of this or that. The anthropoid descended from the trees as such, and after many modifications, it only became human when it was capable of constructing tools to make use of them. To assume that it first made tools and then had a notion of them would be an incomplete assertion. Well, when primitive man threw a stone and understood what it meant, he would not have understood it if he did not have the intellectual capacity to understand. No one denies that facts exert influence in developing human intelligence. On the contrary, external facts shape intelligence, just as intelligence shapes facts. There is reciprocity. But such facts, by themselves, do not create intelligence. Ideality, in humans as humans, is always contemporaneous with facts because, otherwise, they would not resonate in ideas and would not create new schemes.

Next, let’s give an example of dialectical reasoning, following some methodological rules. Let’s examine the personality of Napoleon.

We cannot separate him in any way from the historical environment in which he lived. Developing through the French Revolution, he never had the ardor of the revolutionaries for it. As an actualized subject, he is a defined psychological type shaped by social conditions. He is constantly in contradiction with the environment around him. The era belongs to the “citoyens,” but he keeps his distance from the people. His life as an officer proves this. Once the revolution is victorious, he accepts it as an accomplished fact and puts himself at its service without loving it. He could have been on the other side if circumstances were different.

Elevated to a high position, at that critical moment when he is appointed commander-in-chief of the troops in Italy, he encounters opposition from older generals who refuse to accept his leadership. Given his personal conditions, Napoleon imposes himself with the persuasiveness of his attitude. Everyone obeys him. His subordinates are ragged, famished soldiers. He motivates them, incites them when they are discouraged with skillful proclamations. He directs them to fight. He is in Arcole, where he could have been killed by an enemy bullet. That does not happen; he emerges victorious. The situation in France is chaotic. Siyès realizes that France needs a sword to impose order. They think of Jourdan, but he had fallen in battle.

If Jourdan had not died, would he have been the providential man of France instead of Napoleon? And would history have taken the same course?

Napoleon is elevated to power without love for the people or the republic.

“France needs a good sword,” Siyès said. That sword could have belonged to many others. The invariance in history is this struggle between the forces of renewal, the dissatisfied, the oppressed of all kinds, against the oppressors, those who wish to maintain the status quo of their exploitation. These classes are called patrician or plebeian, noble or peasant, proletarian or bourgeois, it matters little, as they are variants of history, but the struggle between oppression and freedom is an invariant. France needed a providential man. This is the invariant in similar cases, where this kind of man is always sought. Napoleon was that man, just as it could have been someone else, with different ideals, being more sincere towards the republic. These factors are outside the scope of economics, purely economic contradictions, because Napoleon could have been different psychologically without any modification in the economy.

We may disregard the possibilities that his entire history offered. It is natural that today, when it is not possible to reverse history because it belongs to time, everything seems to us as necessarily having happened. An actualist, someone who only values actualizations, sees destiny in Napoleon. But we know, for example, that when Hannibal was at the gates of Rome, he was in control of the situation, and the fate of the world would have been different. However, he hesitated, waited, and let victory slip away. Such possibilities of a different course of human events are found in the pages of history. However, an actualist does not see it that way.

But a “potentialist,” someone who values possibilities, will see it differently and notice that there are decisive moments that a person’s will can resolve. When Caesar reached the Rubicon, he had to make a decision. What followed afterward was the consequence of that act, whose significance he fully understood. Others in history miss opportunities. Not recognizing possibilities and not giving them value leads them to not accept such facts.

But let’s objectify Napoleon: he is no longer the subject but the object. Here, we weave comments, opinions; we judge his actions, interpret them. But Napoleon is not just an individual; he is also the era, which is a whirlwind of antagonisms and conflicting interests, in opposition and bloody clashes. Napoleon encounters a people yearning for the expansion of their ideals. He energizes them, inflames them, leads them to fight against almost the entire Europe because the governments of that time were fighting against revolutionary France. This opposition stubbornly persists in both opposing groups. The French people actualize the injustices of other nations and see themselves as liberators. They virtualize countless aspects that oppose them. The social contradictions of each European nation, internal struggles, conflicting parties find in the movement that comes from France a reason for their revolutionary struggle or their reaction. What an assemblage of antagonisms in all of this! How is it possible not to consider all these fields in which various interpenetrating and stimulating oppositions are elaborated?

These are brief analyses, but they show us how immense the dialectical possibilities are when applied in all fields. A simple subjective interpretation is not sufficient, nor is an objective one. It is necessary to consider, amid this clash of antagonisms, the interpenetration of opposites, of opposing fields, and their reciprocity.

Article 3 – Decadialectic of Substance in Aristotle

As substance is not a being of experimental observation but a philosophical concept, the first step is to ideologically classify it: substance, once classified, is a predicamental property of being; therefore, it is what being has; a category of being, which is the supreme genus of being (kategoreyn).

As we already know, categories are the generic modes of being in philosophy. Therefore, categories do not divide being. And since being, if it were indeterminate, would be, as Hegel shows, pure nothingness, and since we know determinations, the generic determinations of being are precisely the categories. Among them, the first one is substance, and consequently, by determination, quality, quantity, etc. According to Thomists, substance undergoes these determinations that occur, happen to it, which are the accidents. Thus, Aristotle’s categories are accidents of substance, such as quality, relation, action, passion, place, etc., whose mutability does not imply the mutability of substance.

Becoming is the realm of accident, and accident has its being in substance; that is, it does not have its own being.

To carry out a decadialectic analysis of substance, we only need what we have presented, both in this book and in Philosophy and Worldview. We will dispense with certain discussions that take place about subtle distinctions, which scholasticism has examined so skillfully but which would not fit within the scope of this book.

In Philosophy and Worldview, in the study of the concepts of Reason and Intuition, we had the opportunity to show the genesis of this concept, which is highly valued by formalism as well as abstract rationalism. Assuming that the reader has already examined it, let us decadialectically analyze other aspects, making a quick reference to what has already been examined.

Let us examine the theme of substance in Aristotle.

If we consider the theme of substance as unity, it is structured within a totality, which is the connection of categories, which in turn forms part of the structural series of Greek theoretical thought, belonging to the system of the Greek cultural cycle, structured within the universality of the era we call pre-Christian.

So we have the theme of substance placed in its five planes:

  1. as unity – the theme of substance according to Aristotle;
  2. as totality – within the categories, in Aristotle’s thought;
  3. as series – structured in Greek theoretical thought;
  4. as system – structured in the Greek cultural cycle;
  5. as universality – structured in the general context of human culture in the pre-Christian era.

From the interaction of these planes, it is clear that Aristotelian thought on the theme of substance cannot and should not be considered apart from the sets in which it is structured, from which it receives influences and which explain, delimit, characterize it, and naturally give it boundaries.

Although we can study substance in Aristotle through analysis, we cannot, for example, leave it in a state of separation without returning it to the culture from which it arises, whose structural thought and historical conditions play an important role in its gestation. The pentadialectical placement already allows us to conduct a good analysis.

The second step for the decadialectical examination is to specify Aristotle’s statement about substance, that is, what the Stagirite thinks substance is, so that the analysis can be carried out.

Let us listen to Aristotle: "Substance is considered, if not in a large number of senses, at least in four main ones:

  1. it is believed, in fact, that the substance of each being is the essence (to ti én emai, literally: the era of being);41

  1. the universal;

  2. the general;

  3. the subject."

We present Aristotle’s words schematically for greater clarity. We can then summarize: substance for Aristotle is:

a) what a thing is; b) that which the thing is;

As a category, substance is ousia, the essence of the thing, that which creates the thing, since ousiô in Greek means to give being. The origin of this word comes from haveres, the goods of which we have ownership. Things that possess something not accidental, something permanent, properties that are fixed, with which one can operate, have ousia. Ousia is the fixed, the firm good of the thing, what a thing is. Physically, substance is what supports (sub portare, sub stare, to be under appearances) in Greek hipostasis (from hipo (under) estasis (to be), hypostasis), what can also be hylê, matter.

Metaphysically, it is what the individual possesses as the cause of its being and its independence. It is no longer hylê or ousia as essence, but the concrete of the individual as primary substance.

Hence, Aristotle simplifies and clarifies substance by reducing it to two:

Ousia prote (substantia prima of the Scholastics, first substance) formed by essential and accidental predicates; substance is the individual being (substance of this book, of this apple).

Ousia déutera (substantia secunda, second substance) of unity, of characteristics, the quiddity for the Scholastics, which answers the question quid sit? What is it? This object is a book (essence, form, in the Thomistic sense; this is the second substance).

So, when we speak of substance according to Aristotle, it may refer, for example, to matter or form, or both when combined in a concrete being (to synolon) (the only whole (holos) with (syn) together).

Third step: Placing the thought to be analyzed dialectically.

We have, then: thesis – substance as support, matter, etc. (ousia prote); antithesis – substance as form (ousia déutera).

There is an antithetical situation between the two, because if we start with the second substance as the thesis, the first substance becomes antithetical to it. Epistemologically, we can consider them contemporaneous, and they oppose each other, that is, place one before the other, with distinctions that make them contradictory, dialectically speaking. The same Hegelian thought of concrete universal and abstract universal could be applied here.

Synthesis: it is to synolon, the composition.

Fourth step:

Now we can analyze Aristotelian thought on substance in a pentadialectical manner. Since this analysis requires decadialectics, we will only provide a general outline.

  1. as unity, already discussed;
  2. as totality – In Aristotelian thought, substance is the supreme category that supports accidents. Therefore, it is structured as the totality of the mutability of accidents, which are the occurrences of substance, which is invariant; and accidents, which are variant. In turn, the presence of variant accidents is an invariance because there is no substance without accidents, just as there are no accidents without substances. Thus, dialectically, substance is, for Aristotle, theoretically immutable but antithetically mutable due to the presence of accidents: they are theoretically invariant in terms of the presence of the accidental, but antithetically variant in terms of their occurrences.

In both cases, the synthesis is, in the realm of substance and in the realm of accident, the composition of variance and invariance, which separately allow for abstract views of both.

Substance, when considered synthetically, and accident, when considered synthetically, are combined in to synolon, the synthesis of these two syntheses, which can be approached both theoretically and antithetically.

Aristotelian doctrine of substance is structured within the predicamental totality of being, with which it is coordinated. There is no need for a detailed study here, as doing so would require analyzing the work of the great Greek philosopher, which would go beyond the scope of this concise exposition.

  1. As series, Aristotelian conception of ontology is coherently structured in Greek theoretical thought.

The theme of substance is present in all theoretical speculation of Greek thought, from the pre-Socratics in search of the arche, the first principle, the source and support of all accidental occurrences. This first principle would be substance, that which sustains all mutable and variant accidents, for by varying, it is the variation of something that varies. Therefore, behind everything that varies, there is the subject, the recipient of the object, and it is always itself, for what remains is one being, and the being is substance, the hypokeimenon of the pre-Aristotelian Greeks (from hipo, under, and keimai, to lie down), that which consists, that which gives consistency to the thing, an invariant thought among the Greeks.

In Greek thought, since Hesiod, the ontic structure is that of an arche from which other beings emerge, finding their consistency in it, their hypokeimenon, the chaos, a principle not yet determined in the form of determinations of the cosmos. Chaos, for our cosmos, is order in itself, not order for our order, a dialectical characterization of chaos that, being chaos, indeterminate, negates itself in the possibility of being cosmos. When it actualizes itself as such, it affirms its possibility and denies it because it actualizes it, thus realizing the synthesis in the Hegelian sense, the first being of our being, pure temporal structure, as time arises when it actualizes its possibilities of cosmos. Time (Chronos) is thus what negates itself because time is becoming seen from the angle of succession, and as chaos orders itself into a cosmos that creates and negates it through time, for it is before time, while time is after it. In the dialectic of alterity, time, becoming, actualizes the possibilities of chaos, which affirms chaos and denies it by ceasing to be chaos. All Hesiodic thought affirms this anterior substance, which becomes accidental in becoming, always remaining itself (invariant), but which negates itself in the accident and is, in existence, concretion, synthesis.

“Hegel says, 'The first is pure being because it is immediate, undetermined, and uncompounded.’” And we have Hesiodic chaos, the very first being of everything (pánton men próstita).

In Empedocles, the one and only (hen e monos), the hen realizes the diastema, extends itself, and creates multiplicity, but it is still one (monos). The whole is “everything” (the multiple) and is “alone,” solitary (hólos, alone). Quantitatively unique and qualitatively diverse, substantially one, accidentally diverse, therefore supporting all diversity, it is placed dialectically.

Let’s consider Parmenides. There is a separation between the “being of things and the things themselves and the appearance of being (pros dóxan), the being of doxa, common opinion.” To strip things of what appears (accidents) is to reach their aletheia, their truth, the support of everything that happens, immutable, eternal, homogeneous, and unique.

This aletheia is revealed only to the eyes of the spirit (noein) and not to the eyes of the body, which only show us the phenomenon, what appears.

And Heraclitus exclaims: “from all comes the one, and from the one, all” (frag. 45). “It must be conceded, not precisely to me, but to reason, that all things are one” (frag. 92). “The hidden harmony is superior to the manifest (that of being is superior to that of the phenomenon) because in the former, by virtue of a divine mixture, differences and diversities are implicit and in decline” (frag. 40).

The unity of substance is virtually multiple because it can vary, and the actuality of multiplicity is virtually one, unity.

“All things are exchanged for fire, and fire for all things, just as goods are exchanged for gold” (frag. 49). Substance is always the same dialectically, invariant, but the creator of variance, whose fluidity finds the best symbol in fire. According to the order of symbolic thought, still strongly present in the Greeks, Aristotle chooses the fire of the concrete world to express an idea.

The substantial arche of everything is also present in Plato’s thought.

For him, things in our ontic world only repeat small forms (eidola) of the first forms, the archetypes. Behind all things is the truth, aletheia, eidos, form, for the eyes of the spirit, and these forms constitute a cosmos, an order, a connection. It is this order that shapes things, which are merely mass (massein, to make mass) and the sensible, perceptible by the senses, and merely an ekmageion (from ek e mageion, from massein, mass of), but ekmageion amorphon, without form, but capable of receiving form (eidos, idea, as commonly said of Plato but which we prefer to call form, to avoid confusion with the term “idea,” which has already been definitively compromised by the confusion between Platonic “ideas” and Hegelian “ideas,” etc.). These forms are the being of things. The mass is shaped by the forms, but this mass, which is inert (from in ars, meaning without autonomy to create form), is not static, stationary, immobile, but rather agitated by seismos, constant vibrations, yet it submits to the shaping form. Thus, the matter would be mass in seismos, but malleable by forms.

The apple has its form (eidos), and this apple here imitates the form of an apple, which gives it the being of an apple. Thus, the being of things lies in the forms of things, for if this thing is an apple, it is because this mass, this ekmageion amorphon, has received the form of an apple, which has given it this being. The form of an apple is not present and is present in the apple. It is not present because it would also be present in another apple. Now, the form (eidos) “apple” is the same here and there, so it would be simultaneously here and there, and how could it be simultaneously here and there if it were temporal and spatial, if it belonged to the ekmageion amorphon? Therefore, the form of an apple is unique, and every time the ekmageion amorphon assumes the form of an apple (relating its structural elements, according to modern language, to achieve a specific form of relationship, we then have an apple). In this case, number (and here the true Pythagorean sense, which has nothing to do with the misinterpretations of apprentice disciples still in the stage of paraskeiê, but rather with the disciples, already of the third and fourth degree, in the stage of teleiotes and epiphania, but unfortunately, they are stubbornly repeated in textbooks and schools), number, we repeat, is form (and let’s not forget the Pythagorean thought in Plato), and this number is one, which things copy and imitate. Now, such forms are the essences of things, for this matter is this or that according to the form it has. A heap of clay, in this state, is merely what it is because it has the form of a heap of clay, but when it is molded, assuming the form of a vessel, it ceases to be what it was to become a vessel. It is the form it received that gives being to the vessel. Plato thus actualizes eidos, form, as the principal substance of the thing, and all forms are, in turn, copies of the supreme form of the Good, the form of forms, for everything aspires to the good. It is the forms that qualify things and give them their “names.”

Aristotle defines substance as “tóde ti ón kaí koriston” designating the being and delimitation, possessing defined boundaries. Therefore, substance is limited, and Aristotle synthesizes Platonic thought, giving substance a dialectical role as first and second substance, as ekmageion amorphon with an external form here and now (temporal-spatial), and as eidos, form, second substance, whose synthesis is synolon.

Analyzing Aristotelian thought on substance in this way, its coherence becomes evident, especially in Greek theoretical thought.

  1. As a system, it is structured within the Greek cultural cycle, Aristotelian thought allows for another dialectical analysis.

From a historical perspective, his thought is influenced by the conditions of Greek society in decline, the rise of the popular classes, the clash between Greek democracy and aristocracy. To synthesize in this sense the ekmageion amorphon of the popular masses, the first substance, with the form, the second substance, of the aristocracy, which is actualized in certain aspects in the Macedonian Empire, would be an interpretation with a Marxist flavor, but it would not be entirely incorrect. It would suffice to consider the idea of finality, perfectly suited to giving an important role to the aristocracy, an idea always exploited for the philosophical justification of the ruling class and especially the conservatives, who always take advantage, albeit falsely, of Aristotle’s genuine idea. It cannot be said that he had this intention, but it is understandable that he was influenced by his era.

To conclude this outline, we can say that Aristotle’s concept of substance as to synolon, as a compound of form (morphê) and matter (hylê) hence hylomorphism, is perfectly aligned with the thought of the Greek cultural cycle, and naturally, his conception, taken as a unity in this context, cannot be understood without the influence and interaction exerted by the other planes we have studied.

  1. Within the universal plane, Aristotelian thought on substance is influenced by the thought of the time, the search for an Archimedean point of support, but it is also influenced by the Persian threat to Greece and the desire for unification of the Greek world. This work on ideas is realized in Aristotle, especially in his hylomorphic conception, which seeks to reconcile the opposing theses of matter, the democratic mass, and form, the aristocracy, whose unity was necessary to confront external threats to Greece.

That Aristotle’s ideas were influenced by the universal plane cannot be refuted since such positions arise at moments analogous to this and resonate in cultured society only when they find real factors to corroborate ideal factors. Here, the dialectic of factors applies.

Having presented Aristotle’s thought on substance in its different planes, and if we were to emphasize the reciprocity among them, it would naturally lead to much more extensive studies. However, what we have gained is sufficient to demonstrate how dialectics can be applied in this field.

Fifth step.

Subjectively, we can consider Aristotle or the Aristotelian idea of substance. If we examine Aristotle in this case, we do it psychologically. Intuition revealed variability to him, while reason, due to its stabilizing functionality, directed his attention to invariance. In the face of Greek thought objectified for him, when he knew and focused his attention on substance, which escaped the eyes of the body, he only knew what the intellectual schemas allowed him to assimilate.

By actualizing the invariant, he virtualized the variance, which would then become an accident, thus antithetical to substance. Greek spirit reveals a desire for solidity, security, corporeality, which is evident throughout this cultural cycle. Therefore, by focusing on the firm, the solid, and disregarding the flowing, the becoming, the Aristotelian dialectic of knowledge and unknowing is revealed, which rationalizes everything that stabilizes, stops, and staticizes, and virtualizes everything that dynamizes, moves, and transforms. In the knowledge of matter, he accentuates the static nature and ignores the dynamism because matter is either inactive for him or a virtual activity, not actualized, requiring a motor, the prime mover, God, to move it because it is incapable of motion. Thus, he actualizes the static and, in his intuitions, sees, in the dynamism of things, not an order of the being of things that he virtualizes, but an order of the being of form that gives them actuality. Consequently, his conception of substance could not help but be built on a synthesis of thesis, act as active, and antithesis, potency, passive matter, whose actuality only occurs through to synolon, composition.

With Aristotle as the subject, and substance as the object under study, he considered the actual intensity of matter to be virtual, actualizing only extensity in this field, which is more static. And he actualized virtuality in the object, lending activity to another, to form, which, by synthesizing with matter, by composing with it, would provide the missing activity. In this way, inactive matter contained only a possibility of activity if actualized by another, leading to a dualistic position from which it would hardly be able to escape, and consequently, his thought would fall into all the aporias that this abstracting position generates.

When substance is taken subjectively, the field of the subject and intuition becomes the author of the conception, and substance as such becomes objectified, which would allow for new analyses, but within the framework we have already outlined schematically. A more complete analysis would require many pages, which is not difficult to achieve if we follow the providential steps outlined and always keep in mind the dialectical frameworks we have provided, which synthesize what has been beneficial so far, as we believe, in the studies of this discipline, which is now beginning to bear its first fruits and structure itself more solidly.

The sixth step, and final one, the synthesis of Aristotelian thought on substance, is a task that we refrain from doing as it would be merely a synthetic re-exposition of various statements.

With these examples (alongside others scattered throughout our books), we aim to show how dialectical thinking allows us to construct a clearer vision of our universe, achieving a new stage of logic without destroying it, but surpassing and preserving it (Aufhebung).

Deeper analyses can only be carried out through the coordination of symbolic dialectic with noetic tensional dialectic, which is presented, the former in our “Treatise on Symbolics,” and the latter as the architectural whole of the connection between ideality and reality in our “General Theory of Tensions” and in “Dialectical Methodology,” where we provide methods for the practice of integral dialectics.

Article 4 – Decadialectic Analysis of the Theme of Value in Economics

As an example, only in the object field, we will now present a dialectical analysis of the theme of value in economics in order to demonstrate its analytical-dialectical effectiveness.

We will begin with an exposition in the economic field to provide some data and, finally, partially carry out a decadialectical examination.

We will not proceed here according to the order of the six steps already studied in order to simplify and avoid repeating what the reader has easily grasped in the previous pages.

Theories of Value

Observable price variations occur in a market as a result of variations between the quantities of goods offered and the quantities demanded.

Now, these variations in the value of a commodity naturally led economists to a series of questions. Among them, we can highlight the following: Why is one commodity worth less than another? Why does a commodity have a fluctuating value, sometimes more, sometimes less, depending on circumstances?

To answer such questions, they analyzed the facts and concluded that for each commodity there are:

  1. a normal value, which is based on its cost of production;
  2. a current value, which fluctuates according to the variations in the market, corresponding to changes in supply and demand.

Thus, the law of cost, the law of supply and demand42 would be the fundamental principles of the theory of prices or, to speak in the language of the topic we are addressing, of value.

This way of presenting the theme of value is, with some variations, the approach taken by Ricardo, Adam Smith, Mill, and considered by the latter as a definitive acquisition of economic science.

Based on these analyses already made, we can already visualize two aspects in value:

  1. there is a value that is connected to the good, which is immanent to that good;

  2. there is a value that depends on exchange.

The first is often called use value, that is, the value of usefulness, the utility that a good offers; and the second is called exchange value, that is, the value given to a good in exchange for it, or its onerousness.

Regarding the first value (use value), it is presumed from the outset that we can observe various variations in it, corresponding to the appreciation that individuals may have for a good. One could call this aspect subjective value, and the second one objective value, that of exchange.

An immediate question arises that seeks to understand the relationship between these two values, their interaction.

a) To find a buyer at a certain price, it is necessary from the outset that a product or service meets a need, that is, it is useful;

b) The seller does not want to sell at a loss, so they fundamentally consider the cost.

Therefore, two important concepts are formed, as we have seen: utility and cost.

It is evident that in the field of Economics, as in all disciplines studied using formal methods, when faced with two vectors, there is a natural tendency to reduce one to the other, that is, to explain one in terms of the other. This tendency towards reducibility is driven by the impulse of identification inherent in human reason, which seeks to explain, that is, to say what something is, by comparing it to another thing or saying that it is another thing. It gives its consistency, in what it consists. In this explanatory process, reason tends to reduce everything to a single, unique foundation that can define what things are. This impulse of reason is structured in philosophy under the name of law of identity or principle of identity. To this end, reason reduces everything to an absolute likeness and explains it through it.

Thus, economists, influenced by this same impulse, sought to explain one by the other. But there are economists who did not proceed in this way. This divergence among them gave rise to a series of theories on value, which we will summarize since it is impossible for us to examine them in all their individualizing aspects, which are typical of each theory.

How do the “reductivists” proceed? For example, we have the Ricardian theory that reduces value to labor, which leads to extremes, as well as the Marxist theory, whose aspects and reasons we will study more analytically shortly. For others, value depends only on the degree of utility. We clearly have two unilateral positions here because they focus only on one side.

Let us make some comments.

It is observed that some commodities have a “high value” despite requiring little labor to obtain them; others are highly useful, such as wheat (bread), and have a modest place in the scale of values, while others offer satisfaction to merely accessory needs, such as diamonds, and yet occupy a high position.

For a synthetic exposition of the theory of value in economics, as presented by Marx, let us take advantage of the succinct explanation given by Lenin, which we reproduce:

"A commodity is, firstly, a thing that satisfies any human need; secondly, it is a thing that can be exchanged for another. The usefulness of a thing constitutes its use value. The exchange value (or simply value) is, firstly, the relationship, the proportion, in the exchange of a certain number of use values of one kind against a certain number of use values of another kind. Everyday experience shows us that millions and billions of such exchanges continuously establish relations of equivalence between the most diverse and dissimilar use values. What is common to these different things that are continually compared to each other in a specific system of social relations? What they have in common is the fact that they are products of labor. By exchanging their products, people create relations of equivalence between the most diverse kinds of labor. The production of commodities is a system of social relations in which various producers create diverse products (division of labor) and make them equivalent to one another at the moment of exchange. Therefore, what is common to all commodities is not the concrete labor of a branch of production, but rather the abstract human labor, indeterminate human labor, which is not the labor of a particular quality but the general human labor. In a given society, the total amount of labor represented by the sum of the values of all commodities constitutes a single and unique human labor force; millions of examples of exchange demonstrate this. Each commodity, considered in isolation, is therefore represented by only a certain portion of socially necessary labor time. The magnitude of value is determined by the quantity of socially necessary labor or the socially necessary labor time for the production of a given commodity or a specific use value.

“By establishing the equal value of the various products exchanged with each other, they (people) affirm that different labors are equal to each other as human labors. They affirm this without realizing it.”

"Value is a relation between two persons, said an old economist; one should simply adjust it: a relation concealed beneath a material appearance. Only by understanding the system of social relations of production in a specific historical formation, that is, relations that appear in exchange, a mass phenomenon that is repeated millions and millions of times, can one comprehend what value is.

As exchange values, all commodities are small definite measures of crystallized labor time."

Now, let us examine the proudhonian theory of value, which predates Marx’s theory, and in the end of the exposition, we will provide a synthesis and a differential parallel of both.

Proudhonian Theory of Value

In the field of social themes, the desperate struggle between Marx and Proudhon is well-known. Both represented: the former, Prussian-style socialism, authoritarian, absolutist, and the latter, Latin-style socialism, libertarian, humanistic, comprehensive, and pluralistic. Proudhon published “Economic Contradictions or the Philosophy of Misery” in 1844. Marx, who had hailed Proudhon as a “scientific socialist,” broke with him because Proudhon did not want to participate in the organization of a group to direct and dominate workers' organizations, which he always wanted to be free. Marx then wrote “The Poverty of Philosophy,” a polemical book full of accusations against Proudhon.

While Proudhon was alive and his memory still fresh, Marx’s work had no effect. It was received by the proletariat worldwide as a work of infamy. However, as years passed, new workers who were unfamiliar with Proudhon and some ignorant literati started reading Marx’s work without reading Proudhon’s. They idolized Marx, the Prussian philosopher of socialism, and believed that everything he had stated in that book was true and refuted his adversary forever.

Years have gone by, and today Proudhon is being read, meditated upon, and followed again. Many socialists exclaim with sorrow: “What a mistake it was to have distanced ourselves from Proudhon for a hundred years! Why did we stop reading his works? His criticisms, made centuries ago, are still relevant. Socialism has degenerated, taking the path of brutality and absolutism.”

It is understandable that we will not show passage by passage from the works of both authors to analyze to what extent there is good faith and to what extent Marx’s work contains falsifications and lies. We will only explain, in general terms, Proudhon’s theory of value, which, like Marx’s, is based on Ricardo but diverges in taking a dialectical rather than a formal aspect, as Marx’s theory does.

Before his death, Proudhon spoke about Marx’s book and his critique using these words: “The true meaning of Marx’s work is that he regrets that I have thought in the same way everywhere, and that I said it before him. It is up to the reader to see that it is Marx who, after reading my work, regrets thinking like me!”

For Proudhon, use value and exchange value are inseparable and form a unity. But within this unity, they are in perpetual struggle. Supply and demand are constantly in conflict, diametrically opposed, and tend incessantly to cancel each other out. Supply and demand serve to bring use value and exchange value face to face, to reconcile them, and this reconciliation is reflected in the price, which should and must, although it does not always do so, express true value, be the fair expression of value.

But up to this point, we are only discussing expression. What constitutes value? What element, what means do we have to have a concrete view of value that combines both antinomies: use value and exchange value?

The constituted value is value conceived as the proportionality of products and presupposes the unity of exchange value and value of use.

“The value conceived as the proportionality of products, in other words, constituted value, necessarily presupposes, in equal measure, utility and marketability, indivisibly and harmoniously united. It presupposes utility because, without this condition, the product would lack the affinity that makes it susceptible to exchange and thus converts it into a wealth element. It also presupposes marketability because if the product were not exchanged, at all times and for a determined price, it would be merely a non-value, it would be nothing” (Proudhon).

Proportionality has a law, and the force that produces it is labor. “Labor differs from producer to producer in quantity and quality. The same happens to it, from this point of view, as with all the great principles of nature and the most general laws, which are simple in their action and in their formulas but infinitely modified by a multitude of particular causes that manifest themselves in an innumerable variety of forms. Labor, and labor alone, produces all the elements of wealth and combines them even down to their smallest particles according to a law of variable but certain proportionality. Finally, labor, as the principle of life, stirs the matter of wealth, mens agitat molem, and gives it its proportions” (Proudhon).

Labor is the only thing that fixes the importance of a good. Variations in labor will cause relative value to fluctuate. Thus, for Proudhon, value varies, but the law of value is immutable. In our words: labor is the variant because it can produce more or less, with greater or lesser effort, but it will always be labor that determines the measure of value (the invariant). This opinion of Proudhon is partially found in the doctrines of Adam Smith, Rodbertus, and Ricardo.

According to this analysis, value, considered in the society formed naturally among producers through the division of labor and exchange, is the relationship of proportionality of the products that make up wealth; and what is specifically called the value of a product is a formula that indicates, in monetary terms, the proportion of this product in the general wealth. Utility establishes value; labor determines its relationship; the price is, except for the aberrations that we will have to study, the very expression of this relationship."

It was through gold and silver that the establishment of value among all commodities was achieved, although they are subject to dependencies regarding abundance or scarcity, which Marx did not understand when criticizing Proudhon. “The distinctive characteristic of gold and silver comes, I repeat, from the fact that thanks to their metallic properties, the difficulties in their production, and especially through the intervention of public authority, they early on acquired, as commodities, stability and authenticity” (Proudhon).

“Therefore, I say that the value of gold and silver, especially silver used in the minting of coins, although this value may not yet be calculated in a rigorous manner, is no longer arbitrary; and I add that it is not susceptible to contempt like other values, although it may continuously vary” (Proudhon).

“Finally, since the successive establishment of all commercial values implies an infinite progress of labor, wealth, and well-being, we already know our social destiny from an economic perspective: to produce incessantly, with the smallest possible amount of labor for each product, the greatest quantity and variety of values, in such a way that each individual achieves the greatest physical, moral, and intellectual well-being, and for the species, the highest perfection and infinite glory” (Proudhon).

In summary, for Proudhon, value contains within its unity the inherent (antinomic) contradiction between use value and exchange value. Exchange value is marked by labor, which binds it to use value, i.e., it constitutes and concretizes both. This constituted value received its most accurate and fixed expression through gold and silver, chosen among all other commodities that served as currency.

Marginalist Theory of Value

It was after 1870 that a new theory emerged to explain value, developed by various authors based on the ideas of marginal utility, final utility, or marginal utility (including Stanley Jevons, Carl Menger, Leon Walras).

This conception “allows us to overcome in advance the objection drawn from a necessary antinomy to the idea of a hierarchy of utilities based on needs and the observation of a price scale that sometimes seems to be at odds with this hierarchy. Thus, a diamond is worth more than an ample supply of bread” (Nogaro). While this may be true, this observation does not necessarily contradict the idea of value in general and exchange value in particular, based on utility. Menger gives an example: after a meal, someone desires a cigarette. They prefer it to an additional roast. They will assign a price to the cigarette that they would not assign to an unnecessary roast. However, the need for meat surpasses the need for a cigarette. The same can be applied to a collective. In this way, it is explained why a diamond holds such value. Those who acquire it belong to a scale of people whose most urgent needs are already fully satisfied, and those needs have lost their significance.

“Thus, we find in the theory of marginal utility a possible explanation for the apparent contradiction that facts seem to pose to a theory of value based solely on the consideration of utility. From there, we understand that something quite useful can occupy a modest position on the value scale due to its abundance, and the need to which it responds is already largely satisfied” (Nogaro). “Furthermore, in the preceding observations, we will also find the elements of a method to construct a scale of utilities that can be validly compared to the price scale: it will be a scale corrected according to the degree of satisfaction of the corresponding needs. It is the utility of the last useful unit of each considered good that allows for comparisons between the utilities of different goods or services. In other words, it will be a scale of limit utilities or marginal utilities.”

When man produces goods, he considers not only their utility but also the effort employed and the cost it entails.

This effort is manifested in the work required to accomplish what is necessary.

Thus, the economic agent weighs the satisfaction he wishes to achieve against the effort, the burden, it costs him to obtain the necessary good.

Even in cases of subjective value, it is rare for the classification of goods to be based solely on utility. Each valued objective gives rise to a double estimation: that of utility and that of cost.

It has been impossible to establish a strict relationship between these two values.

The reason for this impossibility lies in the fact that they are antinomic, of different orders, and in our final analysis, we will have the opportunity to show, in light of everything we have said, the reasons for this difficulty, which can only be overcome through a concrete conception of both, rather than through an abstract characterization, as has been attempted thus far, by reducing one to the other, subordinating one to the other.

In a planned economy, exchange value can be established by authority, compensating for differences with the exchange values of other products. In such cases, the authority seeks to consider the satisfaction of needs, the availability of products, demand and production, in order to establish a dynamic equilibrium. However, this practice has not always yielded the desired results, which could have been imagined aprioristically.

In the study of money, it can be seen that it is a sui generis commodity because it is not primarily used for consumption but only serves as a signifier of an undifferentiated utility applied to any good. Otherwise, it would not fully fulfill its intended purpose.

Now, the purpose of money is to serve as a medium of exchange, and it serves no other purpose. This exchange can be actual or potential. Therefore, the quantity of money has its effects on exchange.

Our position on the theory of value

The concept of value is both philosophical and economic in nature. A precise analysis of value cannot be established without considering its place within the field of philosophy. In this field, which is still controversial, it presents problems that have not yet found peaceful solutions. Problems such as the essence of value, its consistency, its origin, its objectification, its relationship with the antagonism between subject and object, its interaction with other values, its hierarchy, the possibility or impossibility of creation and consequently, the annihilation of values, its ontic and ontological character, its affective and logical basis, its function in the mind, its presence in judgments, etc., are among the many topics belonging to a discipline called Axiology (from curiós, in Greek, meaning value, and logos, meaning treatise), which is the discipline that has value as its object.

However, in economics, value cannot, in its foundations, do without the peculiar philosophical studies, but it can still be placed within the economic field, under aspects that are only general and specific to that field.

To begin the dialectical analysis, let us outline a framework and then establish comments based on it:


Let us analyze, therefore:

The value must be viewed from two generic perspectives: (1) that of extensity, which gives it a quantitative character, exchange value; (2) and that of intensity, use value, that is, the capacity of a good to satisfy needs, and in proportion to that capacity, it has value.

It is estimated in relation to this effective capacity to satisfy needs. Looking at it from this perspective alone, the good is evaluated based on its capacity to satisfy needs.

Now, intensity has degrees. A good can satisfy a need more or less, therefore, it can be evaluated here on a scale, that is, scalarly, but only as more or less, without the possibility of exact, mathematical measures because intensity, to be quantitatively measured, must be reduced to extensity, thereby ceasing to be intensity and becoming merely extensity. In this case, it loses its peculiarity to be considered abstractly.

However, the intensity of the value of a good is not something that can be considered statically, but dynamically.

Thus, we can dialectically place it in two fields: the variant field and the invariant field. We have seen that everything that happens in our cosmos can be seen from its variant aspect or from its invariant aspect, that is, we can only visualize what varies, changes, becomes heterogeneous, and what does not vary, remains constant over time, the homogeneous.

Now, the use value is not always the same over time or among people. The good that satisfies a need today with a certain intensity may satisfy it tomorrow with greater or lesser intensity. On the other hand, there are subjective variations at the individual, class, group, people, race, and even era levels. The use value for one individual may vary more or less over time. What is valuable to one person may not be valuable or may be less valuable to another. These variations can occur among social groups of various constitutions, as well as in different eras of humanity. Goods that would satisfy the needs of Greeks, Assyrians, Babylonians, Egyptians may not satisfy the needs of others (taken here intensively, that is, satisfying to a greater or lesser degree).

These variations depend on historical and technical covariants and the discovery of new goods that can better satisfy needs, making the previous ones less desirable. Exhaustion of these new goods may occur, making the previous ones valuable again. On the other hand, someone who is satisfied with a good has a different level of satisfaction than another person. The same good may satisfy to a greater or lesser extent depending on the individual, class, group, etc.

However, these variations do not imply the invariance of use value, which is its normal utility. If a new good is preferred for satisfying a need, it does not mean that the precluded good has lost its utility, which remains normal, and its use may return if the new good is lacking, as we have stated. On the other hand, this use value of a good must be considered in its actual utility, in action, that is, in relation to our knowledge of its capacity to satisfy needs. But a good may have unknown capacities for satisfaction, that is, capacities beyond those known. Therefore, it must be considered both in action and in potential (its possibilities). A good that is currently applied to satisfy a particular need may contain, in potential, the capacity to satisfy other needs that are still unknown but later become known. These possibilities may be revealed through analysis and experience or not, but they cannot be ignored as inherent to use value, although not yet actualized for us because they are still potential. Examples of such cases are easy to find because they occur daily in economic experience, such as certain plants, fruits, minerals, etc.

However, a purely intensivist view of value would lead us to abstractly consider it, separating it from its reality, which is also extensive. Only a dialectical view, a holistic one, would allow us to have a concrete understanding of value.

A good that has the capacity to satisfy a need or needs requires effort, work, a burden.

These aspects are more measurable because we can more easily compare them, using a more spatialized scale, that is, based on extensive dimensions.

This value is called exchange value because it accurately reflects exchange. To obtain a good that satisfies a need, we have to give effort, service, or other goods that also require effort.

Now, in life, we evaluate things based on what they cost us. What we obtain with difficulties, we do not easily let go of; what we obtained with great effort, we value more.

Thus, in this extensive aspect, we can see both a variant aspect and an invariant aspect. Let’s see: the variant aspect is the expended work, the cost, as one good may require more effort, more labor, than another. And obtaining a good may require more effort today than yesterday, and the circumstances and means employed to obtain it may make the acquisition easier, avoiding the need for greater effort. What is invariant is the burden. In any case, an economic good is burdensome. However, the burden varies according to circumstances, means, employed techniques, etc.

Exchange value is realized in price because price is like the sum of all the efforts employed, no matter how varied they may be. And those who expend this effort want to be compensated, that is, they want to receive what they consider fair in return. Therefore, price reflects this sum.

But this price is not fixed; it undergoes changes. This happens because a series of obstacles or facilitations may occur.

These possibilities, derived from market fluctuations, supply and demand, and the relationship between currency and existing goods, reveal the potential side of exchange value. They should be considered by those who have goods for the market because they can influence variations in exchange value.

Now, exchange value and use value complement each other and together form the concrete understanding of economic value. Considering one aspect in isolation, neglecting the other, is to treat the problem of value in an abstract manner. Considering one as reducible to the other is an attempt to reduce what is irreducible because intensity cannot be reduced to extensity. One is more qualitative, and the other is more quantitative.

They are antinomic (irreducible) but necessary for the understanding of each other. They oppose each other in eternal opposition because this inherent contradiction, as we have seen, arises from the fact that a good is capable of satisfying needs but also requires effort because of it.

This contradiction is manifested in society, in the separation between consumers and producers. Those who consume primarily look at the use value but consider the exchange value as a difficulty, a burden, an obstacle, which primarily concerns producers. This clash is natural in a society where consumers and producers are separated and have opposing interests.

Goods that have a higher use value and are more universally applicable, such as basic necessities, naturally require the least amount of effort, that is, the minimum exchange value. What is economics if not, in its general aspect, the science that teaches us how to make what we need less costly?

Therefore, the use value, in proportion to its intensity, plays a stimulating role in the production of the good and forces it to decrease in exchange value (except in cases where it is still technically impossible). This dialectical aspect is important because it reveals the opposition between both values and explains why goods of greater necessity tend to be less costly.

Thus, an increase in use value (we have already seen its variant aspect) obliges, or at least demands, a reduction in exchange value. An increase in exchange value can lead to a reduction in current use value, as consumers may seek substitutes when they cannot afford it.

From this perspective, Proudhon’s assessment was more scientific than Marx’s, as well as more dialectical. Proudhon considered the struggle, the insoluble antagonism between use value and exchange value, as contemporary, while Marx sought to reduce the former to the latter by considering that use value was already encompassed within exchange value since production would not be directed toward what is not intended for consumption.

A concrete understanding of both is a true synthesis achieved by the mind, a synthesis that is possible in the true sense as employed by Hegel, in the sense of justice as employed by Proudhon, which is completely different from the Marxist conception that, in negation, confused alterity with deprivation and considered synthesis as a third element that replaces the others, while still preserving the characteristics of the thesis and antithesis. However, this critique pertains not to economics but to philosophy.

In this way, we have presented, from various angles, a glimpse of the usefulness that the application of our dialectics can offer, avoiding unilateral and primary positions that are true manifestations of philosophical barbarism.

  1. For a better understanding of this point, it is advisable to read Philosophy and Worldview, written by us.↩

  2. Like Article 1, this should be reread after reading this volume for better understanding.↩

  3. The ontological argument is presented in “Man before the Infinite,” when discussing proofs of the existence of God.↩

  4. In truth, Hegel never fully understood the formal sense of the principle of identity. In “Concrete Philosophy,” we studied it in its true aspects. What Hegel says here was already said by the Scholastics, and they did not understand identity in this way.↩

  5. In our forthcoming work, “Hegel’s Logic,” we restate his fundamental ideas, making certain passages that are intentionally obscure by Hegel clearer.↩

  6. The dialectical naivety of certain Marxists is manifested in reasoning like this:↩

  7. The mode is absolutely inherent to the modified thing. A car in motion is modally different from when it is stationary, but in both states, the car is substantially identical. Understanding this, as the scholastics did, is more dialectical.↩

  8. We consider it unnecessary to change the conceptual structure of the term contradiction, whose classical content should be preserved. The frenzy of novelties (which has bourgeois influence) leads many modern thinkers to the use or abuse of ambiguous terms. Philosophy needs secure and unambiguous terms to avoid ambiguities and, above all, Dialectic.↩

  9. Marxist dialectic is a dialectic of alterity. Soon, we will see that this aspect is just one of the many that can be used to construct this discipline.↩

  10. In “Pitagoras e o Tema do Numero,” we explain how the philosopher from Samos understood harmony. Proudhon, in no way, knew anything about Pythagoras except for what he heard from uncategorized authors.↩

  11. The affirmation that being is the supreme genus or rather the genus raises a significant problem. Since its discussion requires other knowledge, we leave it for future works. Regarding the demonstrability of axioms, we should not forget that if they are not demonstrable, demonstrable by others, they are nevertheless self-evident. This is what we justify in “Concrete Philosophy.”↩

  12. This does not mean that we accept that matter is extended being. We do accept, however, that being extended is being matter, but this can be considered in another way, as we see in “Concrete Philosophy.” We used the above statement only as an example, without it signifying a metaphysical standpoint.↩

  13. Only a clarification of the differences between value, worth, and valence—which can only be done in “Axiology”—will allow us to resolve this problem. In addition, the topic of meanings is clarified in our “Treatise of Symbolics.”↩

  14. As a complement to these rules, in our book “Theory of Knowledge,” we present the method of suspicion, which offers a useful set of measures to prevent the occurrence of common errors.↩

  15. The discussion on the topic of judgments and on space and time as pure forms in Kant will be presented in our upcoming work: “Kant’s Three Critiques,” where we will explain his thought and the synthesis of the critique it provoked.↩

  16. Alétheia is a word formed by the privative alpha (a) and lethes (forgetfulness). Literally, it is the un-forgetting, what has been remembered again. When it illuminates us, truth appears as something we had forgotten and now remember. In this sense, it proclaims an experience (affective, therefore), as in the face of illumination, we feel that something we had forgotten is returning to us. This conception affirms that we have a virtual possession of truth, which is important in “Theology.”↩

  17. The dialectic of Pythagoras, expressed through Platonic dialectic, is especially examined in our book “Pythagoras and the Theme of Number.”↩

  18. This is what we do in “The One and the Multiple in Plato,” authored by us.↩

  19. The material in this article should be reexamined after handling this book for better understanding.↩

  20. This thesis is easily refuted in “Ontology” and “Theology.” Furthermore, movement is always translational, the topological transport (the motus loci of the scholastics, which corresponds to Aristotle’s phorá). But there are other motions that we will study at the appropriate time.↩

  21. As materialists, Marxists tend to consider movement (motus loci) as fundamental. But movement is just a modality, a way things behave, but absolutely inseparable from them. It is being in another and not in itself. It lacks density, permanence (per se). Movement does not have an independent existence but subsists in something else. Its absolute inseparability and its presence in corporeal things are Aristotelian and scholastic theses, predating Marxism.↩

  22. Here, nothingness is relative and not absolute; it is the non-being of this or that.↩

  23. This statement sounds absurd because quantity is an accident, and if the absolute is pure quantity, it is a loose accident of a substance, or without substance, which would be formally contradictory for an accident and, therefore, an absurdity.↩

  24. The topic of intensity and extensity was studied by us in Philosophy and Worldview.↩

  25. The opposition of internal vectors is sometimes stimulating, sometimes destructive. Their interaction can be observed in the generation and corruption of beings, which is examined in “Aristotle and Mutations,” where we study, while commenting on the Aristotelian text, the dialectic of mutations.↩

  26. The problem of the triad in Hegel (thesis, antithesis, and synthesis) is more complex than it seems at first glance. Both right-wing and left-wing Hegelians have constructed an interpretation that we do not accept. In future works, we intend to show the errors we believe such interpretations are tainted with.↩

  27. Our parentheses.↩

  28. This article, as it deals with aspects that involve the understanding of “tensions” and “schemas,” may appear obscure for now, but it will become easily understandable as we examine the next topics.↩

  29. The ante-concept is still a hybrid of memorized facts. It is in the imago, that is, it is still a rich image of the facticity of the object, with the capture of notes provided by sensory intuition, such as those we keep in the images of new singular facts.↩

  30. The form, which in the horse is a concrete schema (in re), is tactically the essential schema of the horse, which singularity imitates, as seen by the Platonic conception. Here we touch upon the controversy of universals, which we examine in “Theory of Knowledge.”↩

  31. Decadialectics aims to realize, on the logical level, the Aristotelian opposition of aphairesis-prosthesis (separation or abstraction, and reuniting of positivities or concretion).↩

  32. The dialectical transcendental concepts apply to finite beings. Regarding God, these concepts would have a distinct ontological structure.↩

  33. In reality, there is only transition, for if a transformation is a transition, not every transition is a transformation, since alteration does not necessarily imply substantial mutation, from one form to another (trans).↩

  34. It would be enough for us to ponder over time, which is while it is not and is not while it is. Everything in becoming is in time, in a constant negation and affirmation. As long as we look at the facts from the perspective of temporality, we would see them “contradicting” in succession.↩

  35. What is formally this or that in something cannot, under the same aspect, be considered not-this or not-that, as Aristotle demonstrated and logic accepts because otherwise, we would fall into absurdity. But the presence, in a unity, of a formality does not exclude the presence of a different formality, even if it is put within the unity. This is a formal “arithmós” of diverse formalities, just as of diverse real things that cooperate in their formation, which can be symbols of formality that even oppose each other when they are only distinct. Dialectics, as we understand it, is only the concretion of formal logic, which was already implicitly present in Aristotelian and scholastic thought, in opposition to the excesses of modern rationalism.↩

  36. The term contradiction is only valid in the sense of Formal Logic. Dialectics, as we understand it, is ultimately a method, always inclusive, whose scope is interconnected with Formal Logic.↩

  37. The ontological dialectic we present in “Concrete Philosophy” is monovalent because it is reduced to apodictic judgments; that is, necessarily valid.↩

  38. Before we develop this point, we must keep in mind that the term field is used here in analogy to the term used in physics, the concept of which we have already explained.↩

  39. In Philosophy and Worldview, we studied in detail the distinctions between intensity and extensiveness.↩

  40. Motion is any transition in the Aristotelian sense. If it pertains to substance, it is mutation (generation or corruption); if it pertains to the accidental, it is alteration or increase or decrease; if it is modal, it is modification, along with movement, which is topical and is an accidental modality.↩

  41. Distinctions between Reason and Intuition were examined in Philosophy and Worldview.↩

  42. The so-called law of supply and demand must be divided into the law of supply and the law of demand, for reasons that we cannot explain here, which we do in our “Decadialectical Treatise of Economics.”↩

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