Pythagoras and the Theme of Number, by Mário Ferreira dos Santos

“God made the integers, all the rest is the work of men” (Kroneker).

“I am everything that has been, and everything that will be, and no mortal has ever lifted my veil” (Isis, according to the inscription of Sais, reported by Plutarch).

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.

Spiritual Intimacy, by Louis Lavelle

The texts included in this volume are articles written by Louis Lavelle for philosophy journals, communications at conferences, and lectures given at universities in France and abroad. Each of them presents, in summary, one of the essential themes of his doctrine: Spirit, Time, Self, the relationship between Spirit and the World, Essence and Existence, Participation. They span a period from 1936 to 1951, during which he co-directed, with René Le Senne, the collection “Philosophie de l’Esprit” (Philosophy of the Spirit). Through some texts in this volume, one can see the importance he attached to this series of works. It was also the period when he was writing his major work, “La Dialectique de l’éternel Présent” (The Dialectic of the Eternal Present), which was supposed to be crowned by a final part on Wisdom. He was not granted the time to write it. He was preparing it in his final meditations, and when he was invited to participate in the activities of the Society of Philosophy of Bordeaux in 1950, he chose as his subject: Wisdom as the science of spiritual life. It seemed to us that no text could be more suitable for the conclusion of this volume, which contains a summary of his entire doctrine and ends as his work was supposed to end, with the idea of wisdom where he saw the culmination of all philosophy.

—THE EDITORS.

Notes on Symbolism and Reality, by Olavo de Carvalho

In Olavo de Carvalho’s Notes on Symbolism and Reality, from his Philosophy Seminar, he addresses the concept of symbolism and its relation to reality. He critiques the reductionist methodologies often used in deciphering symbols, namely the ethnological, psychological, and esoteric methods. Olavo argues that these methods tend to divert attention from the nature of the symbol itself, and instead focus on the causes behind symbol production. His proposed approach to understanding symbols calls for a suspension of systematic interpretation efforts until a more comprehensive understanding of the nature of the symbol is achieved. He emphasizes the significance of recognizing the distinctiveness between symbolic and non-symbolic meanings ascribed to words, graphics, objects, and entities.

Olavo then delves into what he terms the “rotational perspective,” which underpins the act of knowledge itself. He emphasizes that every step actualized in consciousness implies the virtualization of others, leading to a structure of knowledge that is more akin to a rotating perspective. He adds that this structure is fundamental to the very nature of thought, perception, and the very being of things. He insists that neither abstract thought nor sensory perception can wholly know anything in an instant or as a whole. Rather, our understanding or knowledge of something comes in parts, with some aspects coming to the fore while others recede into the background.

Finally, Olavo confronts the idea of unity in relation to sense and the perception of reality. He posits that the fragmentation of the world into supposedly pre-categorical “data” is a fallacy that is either the result of pathological states of ego division or efforts of imaginative abstraction. Olavo argues that the unity and meaning of the world are given, not constructed, and that the task of philosophy is to record and defend the intuitively perceived world from dissolution. He also addresses the implications of the expectation of continuity beyond death as a necessary condition of human action, asserting that the general movement of the cosmos impacts all human experiences.

Identity and Univocity, by Olavo de Carvalho

Identity and univocity, by Olavo de Carvalho, is a draft for a philosophy seminar on the topic of identity and univocity. It begins with definitions of metaphysics, necessity, critical metaphysics, and dogmatic metaphysics. The author presents a series of axioms, including the idea that self-evident propositions are those whose contradictories cannot be formulated in a logically univocal way. The text then introduces the supreme metaphysical principle called the Principle of Integrity, which asserts that every subject of a proposition that can be the object of an action or the subject of an action by another subject is one and the same. The text explores various forms of suppression and reduction in relation to this principle. It also discusses self-evident propositions and argues that the principle of identity is self-evident because its contradictory lacks univocal meaning. Olavo claims that self-evident propositions are necessarily true and that evidence cannot be hypothetical. The self-evidence and truth of the Principle of Integrity are emphasized. The text provides an example of another self-evident proposition: “I am here.” The self-evidence and necessary truth of St. Anselm’s proof are also discussed. The author argues against the existence of purely formal logical self-evidences and distinguishes between logic and metaphysics. The text concludes with the statement that logic is based on self-evident principles but does not encompass the entire domain of truth. The draft indicates that it is part of a larger work in progress called “The Eye of the Sun” and will be used for an oral presentation in the Philosophy Seminar.

The appendix includes a discussion between a participant named Villiers de L’Isle-Adam and Olavo de Carvalho in the Sapientia Forum. Villiers raises the topic of the principle of non-contradiction formulated by Aristotle and presents a study by Jan Lukasiewicz that examines different formulations of this principle. Lukasiewicz’s analysis focuses on the ontological and logical formulations and explores their validity. Villiers discusses Lukasiewicz’s arguments, including the challenge to the principle of non-contradiction posed by contradictory objects and the distinction between real objects, constructive abstractions, and reconstructive abstractions. Villiers acknowledges the practical importance of the principle in everyday life but questions its complete validity in relation to certain objects and situations. Olavo de Carvalho responds by stating that Lukasiewicz’s challenge is not metaphysically valid and fails to distinguish between logical and ontological aspects. He argues that Lukasiewicz’s arguments actually presuppose the validity of the principle of identity. Olavo criticizes the separation of logic and ontology and warns against drawing ontological conclusions from purely constructive formalisms. He suggests referring to his forthcoming book, “The Eye of the Sun,” for further clarification on the topic.

(The book “The Eye of the Sun” was never published, and might never be published now that Olavo has died.)

Commentary on Cicero’s Topics by Anicius Manlius Severinus Boethius

The Commentary on Cicero’s Topics by Anicius Manlius Severinus Boethius, otherwise known as In Ciceronis Topica (ICT), is a comprehensive exploration and discussion on Cicero’s Topics. Boethius’s commentary is divided into six books, each comprising different aspects and interpretations of logic, arguments, and various topics addressed by Cicero. The commentary was written around 520–523 AD and it overlaps with De topicis differentiis in content and time period. The version transmitted to us, however, appears to be unfinished, missing the end of the sixth book and the entirety of the seventh book that Boethius claims to have written.

The first four books of ICT delve into the nature of logic and topics, providing commentary on different philosophers’ perspectives, including Stoics, Cicero, Plato, and Aristotle. Boethius explores the meaning of argumentation, the structure and role of propositions, and the concept of maximal propositions. There’s an in-depth exploration of ‘Topics,’ where Boethius discusses the division of Topics and the subdivisions of Topics in relation to the matter at issue. The nature and role of related things in the formation of arguments is addressed extensively, with a specific focus on how these relate to the subject at hand. Books III and IV further delve into definition, partition, designation, and the understanding of related things.

In the fifth and sixth books, Boethius scrutinizes the seven Stoic modes of hypothetical syllogisms, the role of causes in arguments, and presents a critical commentary on Cicero’s representation of these modes. A deep analysis is offered on the nature of argument, question, proposition, and terms. There’s also a discussion on the nature of effects and their role in arguments, as well as a focus on comparisons. Additionally, the division of Topics is reviewed along with the reasoning for believing it complete. Finally, the extrinsic Topic from authority and its role in argumentation is discussed, along with the conditions and circumstances that give rise to authority.

12 Layers of Personality, by Olavo de Carvalho

The Twelve Layers of Human Personality, And Their Unique Forms of Suffering, by Olavo de Carvalho, is a comprehensive exploration of the different stages or layers of human personality development and the associated suffering. Olavo views personality as a whole that undergoes transitions between layers, each influenced by new objectives or focal points in life. The layers can be divided into integrative layers, which enclose the personality within a defined framework, and divisive layers, which expose the personality to external influences and trigger a struggle for higher integration. Throughout the text, Olavo delves into each layer, discussing its characteristics, developmental milestones, and the specific forms of suffering individuals may experience within each layer.

According to Olavo, each layer represents a significant shift in the purpose and focus of the individual’s life. These transitions occur when the entire personality changes as a whole, without altering its individual parts. The whole personality can only change in relation to something external to itself, often a new objective or focal point in life that the individual strives to achieve. These transitions mark the progression and evolution of the individual’s personality over time, resembling a scheme of life and temporal development.

Olavo’s theory emphasizes that self-consciousness plays a crucial role in understanding the layers of personality. Each new layer represents a new pattern of self-consciousness, and the transitions between layers involve shifts in values, objectives, and the overall direction of the individual’s life. The layers encompass various aspects of human existence, including physical attributes, temperament, cognition, emotions, social roles, intellectual pursuits, and moral responsibilities. Suffering arises within each layer due to failures, misunderstandings, discrepancies between intentions and abilities, and unmet expectations.

Overall, Olavo’s work provides a comprehensive framework for understanding the development of human personality and the unique forms of suffering experienced at each layer. By exploring the transitions between layers and the changing objectives and focal points in an individual’s life, the text offers valuable insights into the complexities of human existence and the challenges individuals face in their personal growth and self-realization.