On Division, by Boethius, is a logical work that explores the different forms and principles of division. The author discusses division of genus into species, division of a whole into its parts, and division of a word into its meanings. He emphasizes the importance of definitions, the distinction between univocal and equivocal terms, and the criteria for determining which differences should be included or excluded in a division. Boethius also covers the division of speech into significances, highlighting the need for clear determination in communication.

Furthermore, the work delves into the division of a whole based on its composition, distinguishing between continuous and non-continuous wholes. It explores division based on matter and form, as well as division of universal wholes and wholes consisting of virtues. Boethius emphasizes that division should be understood as a mental and rational process rather than a physical separation. He provides examples, guidelines, and cautions throughout the text to aid readers in understanding and applying the principles of division effectively.

Preface.

How great the benefits that the knowledge of division brings to the students and how this knowledge has always been held in high esteem in Peripatetic philosophy, are taught by Andronicus, whose diligent old man published a book on division[;] and this same is approved by Plotinus, the most serious philosopher, and repeated in the commentaries of Porphyry’s book, Plato’s Sophist, and praised by him through this introduction to Categories. For he says that knowledge of genus, species, difference, property, and accident is necessary, not only for many other reasons but also for the maximum utility of dividing.

Therefore, since the greatest use and easiest teaching, I have also handed this down like most things to Roman ears, with an introductory manner and a treatment that is both suitable and subtle and of moderate brevity, so that neither the anxiety of decisive speech and incomplete sentence is imposed on the minds of readers;

nor does the inexperienced, crude, and unusual think that it is fitting to have an equal mind towards the verbose talk of these matters,

nor does any envy obscure with oblique bites of detraction that which is both hard by nature and unknown to our people, but to us is arranged with great labor and usefulness for readers, finally rather paving the way for studies, sometimes forgiving, sometimes even approving, than tightening the reins on good arts, while they reject anything new with imprudent obstinacy.

For who does not see that it greatly contributes to the decline of the good arts if there is never any despair of displeasing in the minds of men? But this is enough for now.

Division of Divisions.

Now the name of division itself must be divided and according to each division term, the properties and parts of each proposed must be dealt with, for division is said in many ways. For there is a division of genus into species, there is again a division when a whole is distributed into its proper parts, there is another when a word signifying many things receives a section into its proper meanings.

Besides these three, there is another division which is said to happen according to accident. This has three modes: one when we separate the subject into accidents, another when we divide the accident into subjects, a third when we cut the accident into accidents (this happens if both seem to be inherent to the same subject). But examples of all of these must be provided so that the entire reason of this division may be illuminated.

We divide a genus into species when we say “some animals are rational, others are irrational; of the rational ones, some are mortal, others are immortal” or when we say “some colors are white, others are black, others are in between.” But every division of a genus into species must either be into two parts or more, but there cannot be infinite species of a genus nor less than two. However, why this happens must be demonstrated later.

A whole is divided into parts whenever we resolve each thing into what it is composed of, as when I say that a house is one thing being the roof, another the walls, another the foundations, and that a human is joined by soul and body, and when we say that the parts of man are Cato, Virgil, Cicero and each one who, although they are individual, nevertheless combine and compose the force of the whole human; for man is neither a genus, nor are individual men species, but parts by which the whole human is combined.

The division of a word into its proper meanings occurs whenever a single word signifying many things is opened and its plurality of meanings is shown, as when I say “dog”, which is a name and designates this four-legged barking creature and also the one in the sky that twinkles sickly at the foot of Orion; there is also another, the sea-dog, which growing into an excessive body size is called blue.

But this division has two modes, either one name signifies many things or a sentence is already composed with words and names. And indeed a name signifies many things as the one I proposed above, a sentence, on the other hand, designates many things as in: I say to you, Aeacida, that the Romans can win.

And indeed the division of a name through its proper meanings is called partition of equivocation, but the distribution of a sentence into its proper meanings is the distinction of ambiguity, which the Greeks call amphiboly, so that a name signifying many things is called equivocal, but a sentence designating many things is called amphibolous and ambiguous.

But of those things that are divided according to accident, the division of the subject into accidents is as when we say “all men are either black, white, or of a medium color”, for these are accidents to humans, not species of humans, and man is the subject of these, not the genus.

The section of the accident into subjects happens as in “all things that are desired, some are in the soul, others are located in bodies”, for what is desired is an accident to the soul and the body, not a genus, and the goods that are located in the soul and body are not species but subjects.

The division of the accident into accidents is as in “of all the white things, some are hard”, like a pearl, “others are liquid”, like milk, for the liquid and the whiteness and the hardness are accidents, but the white is separated into hard and liquid. So when we say this, we separate an accident into other accidents.

But this kind of division is always alternately changed into the other, for we can say “of the things that are hard, some are black, others are white” and again “of the things that are liquid, some are white, others are black”; but we divide these again conversely: “of the things that are black, some are hard, others are liquid”.

However, this kind of division differs from all that have been said above, for we cannot divide meaning into words, since a word is distinguished into its proper meanings, nor are parts divided into a whole, although a whole is separated into parts, nor is species divided into genus, although a genus is divided into species.

As for what was said above, that this division is done in this way if both were seen to be inherent in the same subject, if looked at more closely, it is clear. For when we say that of the things that are hard, some are white, others are black, like stone and ebony, it is clear that both are inherent in ebony, both hardness and blackness. The diligent reader will find the same in other cases.

For those to whom the highest operation of truth is sought, they should first understand what is the common property of all these and by what individual differences they are separated from each other. For every division of a word and of a genus and of a whole is called a division in itself, but the other three are placed in the distribution of accident.

The difference of this kind of division in itself is as follows. The division of genus differs from the division of word in that a word is always separated into its proper meanings, but a genus is not divided into meanings but is separated in some way by a kind of creation from itself, and a genus is always a whole to its own species and more universal in nature, but equivocation is said to be more universal in the things signified, only not also a whole in nature by the word.

It also differs from the distribution of a word in that the things that are under that word have nothing in common except the name alone, but those things which are placed under a genus receive both the name of the genus and the definition.

Moreover, the distribution of a word is not the same among all: what is called a dog among us when its many meanings in the Roman language are perhaps simply predicated in a foreign language, when those things which are called by one name among us, they perhaps signify by many. But the same division and distribution of a genus remains among all, hence it happens that the division of a word pertains to position and custom, that of a genus to nature, for what is the same among all is nature, but what is changed among some is custom. And these are the differences in the distribution of genus and word.

The division of a genus is also separated from the distribution of a whole because the division of a whole is made according to quantity, for parts joining the whole substance are actually or in the reason of the mind and in thought separated, but the distribution of a genus is accomplished by quality. For when I have placed man under animal, then the division has been made by quality, for what kind of animal a man is, therefore, because it is formed by a certain quality, hence when asked what kind of animal man is, he will either answer “rational” or certainly “mortal”.

Furthermore, every genus is naturally prior to its own species, but a whole is later to its own parts; it is the parts that join the whole, they precede the perfection of their compound in nature only, also in reason of time, hence it happens that we dissolve genus into what comes after, but a whole into what comes before.

From this, it is also rightly said: if a genus is removed, the species immediately perish; if the species is destroyed, the genus, not destroyed, remains in nature. On the other hand, it happens in the whole, for if a part of the whole perishes, the whole will not exist, of which one part has been destroyed; but if the whole perishes, the parts remain distributed, as if someone took away the roof from a whole house, he seizes the whole that was before, but with the whole perishing, the walls and foundations will stand.

Moreover, a genus is matter to species, for just as bronze, having accepted a form, passes into a statue, so a genus, having accepted a difference, passes into a species; but the multitude of parts is matter to the whole, and the form of these parts is their composition. For just as a species consists of a genus and difference, so a whole consists of parts, hence it happens that a whole differs from each of its parts by the composition of the parts, but a species differs from a genus by the conjunction of difference.

Moreover, a species is always the same as a genus, as man is the same as an animal and virtue is the same as a habit, but parts are not always the same as a whole, for neither is a hand the same as a man, nor is a wall the same as a house. And in those things that have dissimilar parts, this is clear, but not in the same way in those things that have similar parts, as in a rod of air, whose parts, because they are continuous and of the same air, seem to be the same as the whole is, but falsely; for perhaps parts of this kind are the same in substance, not also in quantity.

There remains to give the differences between the distribution of a word and of a whole. They differ in that a whole indeed consists of parts, but a word does not consist of the things it signifies; and the division of a whole is made into parts, but the division of a word is made not into parts but into those things which the word itself signifies, hence it happens that if one part is removed, the whole perishes, but if one thing that the word signifies is removed, that word signifying many things remains.

Division of Genus.

Now, therefore, since the differences of division in itself have been spoken of, let the distribution of genus be dealt with. First, what a genus is must be defined: a genus is that which is predicated of several species differing in what they are, but a species is that which we place under a genus, a difference is that which we propose to distinguish one thing from another.

And indeed a genus is that to which it is appropriate to answer when asked what each thing is, a difference is that which is most rightly answered to the question of what kind. For when someone asks “What is a man?” correctly “Animal”, “What kind of man is he?” conveniently “Rational”, is answered.

However, a genus is divided sometimes into species, sometimes into differences if the species by which the genus ought to be divided lack names, as when I say “some animals are rational, others are irrational” - rational and irrational are differences. But since there is not one name for this species which is a rational animal, therefore we put a difference in place of a species and join it to the superior genus, for every difference coming into its proper genus makes a species, hence it happens that a genus is somehow matter, difference is form, but when species are called by their proper names, a straight division of a genus is not made into differences.

From this, it follows that a definition is gathered from several terms. For if all species were called by their proper names, every definition would be made from only two terms; as when I say “What is man?” why would I need to say “Rational mortal animal” if “rational animal” was called by its proper name, which, together with the remaining difference, that is, mortal, would complete the definition of man with the most truthful reason and full conclusion? But now, division of species is necessary for complete definitions, and perhaps the reason for division and definition lies in the same place, for with divisions joined together, a definition is composed.

But since some things are equivocal, others univocal, and those that are univocal we ourselves take into sections of genus, but those that are equivocal, in these, division is only of signification, it is first to be seen what is univocal, what is equivocal, lest, when these have deceived us, we resolve an equivocal name as if into species, so into significant things. Hence it happens that again, a definition is necessary for division, for we gather by definition what is equivocal, what is univocal.

There are differences, however, some in themselves, others by accident, and of these, some are consequent, others immediately leaving. Immediately leaving are such as sleep, or sit, or stand, or watch, but consequent are as curly hair (if not lost) and blue eyes (if not disturbed by some external weakness). But these are not to be taken for the division of genus, for they are not suitable for definition; for whatever we rightly gather for definitions is apt for the division of genus, but only those things that are in themselves are apt for the division of genus, and these inform and perfect the substance of each thing, as man’s rationality and mortality.

But how we might prove whether they are of the kind that immediately leave, or are consequent, or remain in substance, it seems to me to be seen in this way, for it is not enough to know which we take in division unless it is also known, how we may rightly know those very same ones which are to be taken and which are to be rejected.

Therefore, it must first be seen whether the proposed difference can always and in every way be in the subject; if it is separated either in act or in reason, this is to be separated from the division of genus. For if it is often separated both in act and in reason, it is of the kind of those things that immediately leave, as sitting is more often separated and is divided from the subject by the act itself.

But those things which are divided from the subject by reason alone, these are of the consequent differences, as we separate the condition of having blue eyes from the subject by reason, as when I say “It is an animal with blue eyes, like any man”, and if this man was not of this kind, no thing would prevent him from being a man.

Again, there is something else that cannot be separated by reason, and if it is separated, the species is destroyed, as when we say that it is in man to count alone or to learn geometry. If this possibility is separated from man, man himself does not remain; but these are not immediately of those things which are in substance, for man is not because he can do these things, but because he is rational and mortal. Therefore, these differences, because of which the species exists, they themselves are placed both in the definition of the species and in the division of its genus that contains the species.

And it can be said universally, that whatever differences are of such a kind that not only can the species not exist apart from them, but they exist solely because of them, these must be taken either in the division of the genus or in the definition of the species.

But since there are some things that differ which should not be set against each other in divisions, as in a rational and bipedal animal (for no one says “Some animals are rational, others have two feet” because rational and bipedal, though they differ, are not separated by any opposition from each other), it is clear that whatever things differ from each other by some opposition, only those differences placed under the genus can separate the genus itself.

There are, however, four kinds of opposition: either as contraries, as good is to evil, or as a habit and privation, as sight is to blindness, although there are some things in which it is difficult to discern whether they ought to be placed in contraries or in privation or habit, such as motion and rest, health and sickness, wakefulness and sleep, light and darkness – but these are for another time, now we must speak of the remaining oppositions. The third opposition is according to affirmation and negation, as: “Socrates lives”, “Socrates does not live”. The fourth is according to relation, as father is to son, master to servant.

Therefore, it must be shown by the most correct reason according to which of these four oppositions the division of the genus should be. For it is clear that there are four oppositions, and species and genera are separated by opposites. Now, therefore, it must be said according to which of these four oppositions or in what way it is fitting for the species to be separated from the genus.

And the first indeed is the opposition of contradiction, and I call the opposition of contradiction that which is proposed by affirmation and negation.

In this, therefore, negation by itself makes no species, for when I say “man” or “horse”, and something of this kind, these are species, but whatever one has put forth in negation does not declare a species, for not being a man is not a species. For every species constitutes being, but negation separates whatever it proposes from being, as when I say “man”, as if something exists I have spoken, but when I say “not a man” I have destroyed the substance of man by negation. Thus, by itself, the division of genus into species lacks negation.

But it is often necessary to compose a species with negation when the species we want to assign by a simple name is not called by any word, as when I say “Odd numbers are either prime”, like three, five, or seven, “or not prime”, like nine, and again “Some figures are rectilinear, others are not rectilinear” and “Some colors are white, others black, others neither white nor black”. Therefore, when a single name is not given to species, it is necessary to express them by negation. This, therefore, is sometimes forced by necessity, not by nature.

In the same way, whenever we make a section with negation, either affirmation or a simple name should be said first, as is “Some numbers are prime, others are not prime”, for if negation is spoken first, the understanding of the thing we propose is slower. For when you first say that some numbers are prime, after you have taught what prime numbers are by example or definition, the listener will soon understand what non-prime numbers are. But if you do the opposite, either both will be understood suddenly or both will be understood more slowly, but the division which is found for the sake of the clearest nature of the genus should rather lead to more understandable things.

Moreover, the prior affirmation is, the later negation, but what is first in division must also be ordered primarily. It is also always necessary for finite things to be prior to infinite ones, such as equal to unequal, virtue to vices, certain to uncertain, stable and fixed to changeable. But all things that are put forward either by a defined part of speech or by affirmation are more finite than either a name with a negative particle or total negation, therefore division should be made more to the finite than to the infinite.

But if through these things some anxiety is prepared for someone or perhaps things are more obscure than he desires, it has nothing to do with me promising easy knowledge, for we do not propose these things of the whole art to beginners but to those who are well versed and have almost progressed further for reading and learning.

As for the order of this work, I have carefully explained it when I was to speak about ‘On the order of the Peripatetic discipline’.

These things have indeed been said about the opposition which affirmation and negation constitute, but that which is made according to habit and privation seems also to be similar to the one above. For privation in some way denies habit, but it differs in that negation can always exist, but privation not always, but only when it is possible to have habit (this we have already been taught by the Categories).

Therefore, some form is understood to be privation, for it not only deprives but also disposes each deprived thing around itself. For not only does blindness deprive the eye of light but it also disposes the deprived thing itself according to light, for a blind person is said to be in some way disposed and affected towards privation (this also Aristotle testifies, in the Physics). Hence it happens that we often use the difference of privation for the division of the genus.

But here also in the same way as in contradiction it must be done, for the habit, which is similar to affirmation, must be set first, after privation, which is to negation. Sometimes, however, some privations are put forward with the name of habit, such as “orphan”, “blind”, “widow”, sometimes with the particle of privation, as when we say “finite” and “infinite”, “equal” and “unequal”, but in these “equal” and “finite” must be set first in the division, privations second.

And let these things that have been said about the opposition of privation and habit suffice.

The opposition of contraries, however, is perhaps doubted whether it seems to be according to privation and habit, such as white and black, whether indeed white is the privation of black, and black of white - but this is for another time, now, however, it must be treated as if it is another kind of opposition, as it is arranged in the Categories by Aristotle himself.

In contraries, however, there is much division of genera, for we almost lead all differences into contraries, but since contraries are some lacking a middle, others mediated, the division must also be made in this way, such as “Some colors are white, others black, others neither”.

Every definition and every division would be made with two predicate terms unless, as has already been said above, the lack (which often exists) in the name prevented it. How both would be made with two terms will be made clear in this way. For when I say “Some animals are rational, others irrational” a rational animal strives for the definition of a man, but since rational animal is not one name, let’s put a name to it from the letter: “again from the letter”, which is a rational animal, “some are mortal, others immortal”. Therefore, wanting to give the definition of a man, we will say: “A man is a mortal letter” for if the definition of a man is a mortal rational animal, and a rational animal is signified by the letter, “a mortal” feels the same as if it were said “a mortal rational animal”, for ‘a’, as was said, signifies a rational animal.

So then, the definition is made with two terms, ‘a letter’ and ‘mortal’; if names were found in all, the whole definition would always be made with two terms. But the division, with names put, since it always splits into two terms, is clear if someone imposes a name on the genus and difference when it is missing, as when we say: “Of figures which are three-sided, some are equilateral, some have two equal sides, some are wholly unequal”.

Therefore, this three-part division, if presented this way, would become a double: “Of figures which are three-sided, some are equal, others unequal; of the unequal, some have only two equal sides, others have three unequal”, that is, all; and when we say “Of all things, some are good, others bad, others indifferent”, which are neither good nor bad, if it were said this way, a twin division would emerge: “Of all things, some are different, others indifferent; of the different, some are good, others bad”. Thus, every division would be cut into twins if names were not lacking for species and differences.

But we said the fourth opposition is according to something else, like father to son, master to servant, double to middle, sensible to sense. These therefore have no substantial difference by which they differ from each other, rather they have a kinship of this kind by which they refer to each other and cannot exist without each other. Therefore, no division of genus should be made into relative parts, but the whole section of this kind should be separated from the genus, for neither servant nor master is a species of man, nor is middle or double a species of number.

Therefore, since there are four differences, of affirmation and negation, if it is not always necessary, yet the division of relation is to be rejected, of privation and habit and of contraries to be taken. However, contrariety should be put most in differences and also privation, therefore, since it seems to put something contrary against habit, as is finite and infinite; although it is privation, yet the infinite is formed by the imagination of the contrary, for it is, as has been said, a form.

It is indeed worthy of inquiry whether genera are rightly divided into species or differences, for the definition of division is the distribution of genus into the nearest species. Therefore, according to the nature of division and according to definition, the disintegration of the genus should always be made into its own species (but this cannot sometimes be done for the reason we have given above, for many species have no names) and therefore, since some are primary genera, some last, some middle: first as substance, last as animal, middle as body, for body is a genus of animal, substance of body, but neither can anything be found above substance that can be placed in the place of genus nor under animal, for man is a species, not a genus.

Therefore, the division into species will seem older if there is no lack of names, but if we do not abound in all these, it is appropriate to separate the first genera up to the last into differences. This is done in this way, as we disaggregate the first genus into its differences, not into later ones, and again the later one into its own, but not into later ones. For the differences of body are not the same as those of an animal, for if anyone says “Of substances, some are corporeal, others incorporeal” he has rightly made a division, for these differences are proper to substance; but if anyone thus, “Of substances, some are animate, others inanimate”, he has not rightly divided the differences of substance, for they are differences of body, not of substance, that is, of the second genus not the first.

Therefore, it is clear that the division of the previous genera should be made according to their own differences, not according to the genus that comes after.

However, as often as the genus is resolved either into differences or species, after the division has been made, definitions or examples should be immediately added, but if anyone does not abound in definitions, it is enough to add examples, as when we say “Of bodies, some are animate” we should add “like humans or beasts; others inanimate, like stones”.

But the division also, like the term, should not be diminished or superfluous, for neither should more species be added than are under the genus, nor fewer, so that the division itself, like the term, may be converted. For the term is converted thus: “Virtue is the best habit of the mind”, again “The best habit of the mind is virtue”. So also the division: “Every genus will be something of those that are species”, again “Any species is its own genus”.

The division of the same genus is made in multiple ways, as of all bodies and whatever is of a certain size. For just as we distribute the circle into semicircles and into those which the Greeks call “tomeas” (we could say divisions), and the tetragon we separate in different ways, sometimes by drawing a diameter through the angle into triangles, sometimes into parallelograms, sometimes into tetragons, so too the genus, as when we say “Numbers are either even or odd” and again “either prime or non-prime”, and “Triangles are either equilateral, or have only two equal sides, or are totally unequal on all sides” and again “Triangles are either right-angled, or have three acute angles, or have an obtuse angle”. Thus, a multiple division is made of one genus.

However, it is very useful to know that, since a genus is in a way a likeness of many species which shows their substantial agreement, and therefore the genus is a collection of many species, while the species of one genus are disjunctive. Since they are informed by differences, as has been said, therefore there cannot be fewer than two species under one genus, for every difference consists in the plurality of discrepant things. But much has been said about the division of genus and species.

Definition.

Therefore, for those who insist, a more ready ability is opened through the division of the genus to the definition of species, but it is necessary not only to learn the differences we take for the definition, but also to embrace the art of the definition itself with the most diligent knowledge. And indeed, whether any definition can be demonstrated and how it can be found by demonstration, and whatever subtler things about it have been treated in the last Analytics by Aristotle, I will omit, I will only follow the single rule of defining.

For things are either superior, inferior, or middle. No definition encompasses the superior because their superior genera cannot be found; moreover, the inferiors, which are individuals, lack specific differences, which is why they too are excluded from the definition; therefore, the middle things which both have genera and are predicated of others or of genera or of species or individuals can fall under definition.

Given therefore a species of this kind which both has a genus and is predicated of a posterior, first I take its genus and divide the differences of that genus; and I add the difference to the genus, and I see whether that difference joined with the genus could be equal with that species which I have undertaken to circumscribe by definition. But if the species is smaller, we again place that difference which we had just placed with the genus as if it were a genus and we separate it into its other differences, and again we join these two differences to the superior genus, and, if it has equated the species, it will be said to be the definition of the species, if not, we again separate the second difference into others. We join all of these with the genus and again we consider whether all the differences with the genus are equal to the species that is being defined. And finally, we distribute the differences to differences as many times as necessary until all of them joined to the genus describe the species with an equal definition.

However, examples will make clearer the knowledge of this matter in this way. Let it be proposed to us that we wish to define “name”. Therefore, the term of name is predicated of many names and is in a way a species containing individuals under it. Therefore, I define the name in this way. I take its genus which is sound and I divide: “Sounds are either significant or not at all.” But a sound that is not significant has nothing to do with the name, for the name signifies; therefore, I take the difference which is significant and I join it with the genus, that is, with the sound, and I make “significant sound” and then I look whether this genus and difference are equal to the name.

But they are not yet equal, for a sound can be significant and yet not be a name, for there are certain sounds which designate pain, others which naturally express emotions which are not names, such as interjections. Again, I divide the significance of sounds into other differences: “Significant sounds are either according to position or naturally”, and indeed a sound signifying naturally has nothing to do with the name, but a sound signifying according to the position of people suits the name. Therefore, I join these two differences, significant and according to position, with the sound, that is, with the genus, and I say: “A name is a sound signifying according to agreement.”

But again it does not equate to the name for me, for there are also words which are significant sounds and according to position; therefore, it is not the definition of the name alone. I distribute again the difference which is according to position and I say “According to the position of significant sounds, some are with time, some without time”, and indeed the difference with time is not joined to the name because it is the job of verbs to signify times, not of names; therefore, the difference which is without time remains suitable. Therefore, I join these three differences to the genus and I say: “A name is a sound signifying according to agreement without time.”

But again, the full conclusion of the definition does not occur to me, for a sound can be significant and according to position and without time and not be a single name but joined names, which is a sentence, such as: “Socrates with Plato and his disciples,” but although this is an imperfect sentence, it is still a sentence. Therefore, the ultimate difference, which is without time, must be divided into other differences as well, and we will say: “Among significant sounds according to position and without time, some are those whose part signifies something extra,” this pertains to a sentence, “others are those whose part signifies nothing extra,” this pertains to a name, for no part of a name designates anything extra. Therefore, the definition is made in this way: “A name is a significant sound according to agreement and without time, none of whose parts is significant separately.”

Do you see therefore how straight the definition has been constituted? For by saying “sound,” I distinguished a name from other noises, by adding “significant,” I separated a name from non-significant sounds, by “according to agreement” and “without time,” the property of names was distributed from sounds signifying naturally and from verbs, by proposing that its parts signify nothing extra, I distinguished it from a sentence, whose parts signify something separately. Hence, it happens that whatever name there will be, it is enclosed by that definition, and wherever this method of definition will be suitable, I will not doubt that it is a name.

It should also be said that the genus in division is the whole, in definition it is part, and so the definition is as if certain parts join the whole, so the division is as if the whole is dissolved into parts, and the division of the whole genus is similar to division, the definition of the whole to composition. For in the division of the genus, animal is the whole of man, for it contains man within itself, but in the definition it is part, for the genus joined with other differences makes up the species, as when I say “Some animals are rational, others are irrational” and again “Some rational beings are mortal, others are immortal”, rational animal is the whole and again rational mortal, and these three are man. But if in the definition I say: “Man is a rational mortal animal” these three join into one man, therefore part of it and genus and difference are found.

So, therefore, in division, the genus is the whole, the species is part, in the same way, the differences are the whole, the parts into which they are divided. But in the definition, both the genus and the differences are parts, the defined species is the whole. But this so far.

Division of the Whole.

Now we will speak about that division which is of the whole into parts, for this was the second division after the division of the genus. For what we call whole, we signify in multiple ways: the whole is what is continuous, as a body or a line or something of this kind; we also call whole what is not continuous, as the whole flock or the whole people or the whole army; we also call whole what is universal, as man or horse, for these are wholes of their parts, that is, of men or horses, hence we also call each individual man; it is also called whole what consists of certain virtues, as one power of the soul is for understanding, another for sensing, another for vegetating.

Therefore, since the whole is spoken of in so many ways, a division of the whole is to be made - first indeed, if it is continuous, into those parts from which the whole itself is seen to consist, otherwise, division is not made. For you would divide the body of a man into its parts, into head, hands, chest, feet, and if in any other way according to its own parts the right division is made.

For those whose composition is multiple, the division is also multiple, as an animal is indeed separated into parts which have similar parts, into flesh, and bones, again into those which do not have similar parts, into hands, into feet, in the same way also a ship and a house.

We also break a book down into verses and these into sentences, these however into syllables, syllables into letters, thus it happens that letters and syllables and names and verses seem to be certain parts of the whole book, yet received in another way, they are not parts of the whole but parts of parts.

However, it is necessary not to look at everything as if it is actually divided but as if it is divided by the mind and reason, as we divide wine mixed with water into mixed wines of water, this actually, we also divide into wine and water from which it is mixed, this by reason, for these once mixed cannot be separated.

But the division of the whole is also made into matter and form, otherwise a statue consists from its parts, otherwise from matter and form, that is, from bronze and shape.

Likewise, also those wholes are to be divided which are not continuous in the same way also those which are universal, as “Some men are in Europe, others in Asia, others in Africa”.

The division of that whole which consists of virtues should also be done in this way: “One part of the soul is in plants, another in animals” and again “of that which is in animals, some is rational, some is sensitive” and again, these are dispersed under further sub-divisions. But the soul is not a genus of these but a whole, for these parts are parts of the soul, but not as in quantity, but as in some power and virtue, for from these powers the substance of the soul is united. Hence it happens that this kind of division has something similar to both the division of the genus and the division of the whole, for whatever part of it will be, the predicate of the soul follows it, it refers to the division of the genus, wherever the species of it will be, the genus immediately follows; however, not every soul is joined to all parts but different parts to different ones, this necessarily refers to the nature of the whole.

Division of Speech.

Therefore, what remains is that we deal with the division of speech into significances. The division of speech, however, is made in three ways. It is divided into significances as equivocal or ambiguous, for one name signifies several things, as “dog”, and one speech again signifies several things, as when I say the Greeks conquered the Trojans. In another way, however, according to the mode, these indeed do not signify several things but in many ways, as when we say “infinite” it indeed signifies one thing whose limit cannot be found, but we say this either according to measure or according to multitude or according to species: according to measure, as the world is infinite, for we say it is infinite in magnitude; according to multitude, as the division of bodies is infinite, for we signify an infinite multitude of divisions; again according to species, as we say figures are infinite, for there are infinite species of figures.

We also say something is infinite according to time, as we say the world is infinite, whose limit according to time cannot be found, in the same way also we say God is infinite, whose limit of divine life according to time cannot be found. Therefore, this word does not signify several things according to itself but is predicated in many ways about each thing, while it itself signifies one thing.

Another way, however, is according to determination. For as often as any word is spoken without determination, it causes doubt in understanding, as is “man”, for this word signifies many things, for without a concluded definition it carries away the understanding of the listener with many waves and leads to errors. For what does any listener understand where that which the speaker is saying is not concluded with any determination? Unless someone thus defines it saying: “Every man walks” or certainly: “Some man walks” and designates this by name, if it so happens, the understanding of the listener does not have what it may rationally understand.

There are also other determinations, such as if someone says: “Give it to me!” no one understands when or what they should give unless understanding and a certain reason for determination are added, or if someone says: “Come to me!” where or when they should come is not known unless by determination. However, every ambiguous thing is indeed doubtful, but not every doubtful thing is ambiguous, for these things which have been said are indeed doubtful, but not ambiguous. In ambiguous things, each listener reasonably thinks they have understood themselves, as when someone says: “I hear the Greeks conquered the Trojans” one can understand that the Greeks have defeated the Trojans, another that the Trojans defeated the Greeks, and both reasonably understand this from the speaker’s words themselves. But when I say: “Give me!” what they should give, no listener reasonably understands from these words themselves, for what I did not say, they would rather suspect than clearly see by any reason what is not brought forth from me.

So, in these many ways, when the division of speech is made, either through significances or through the mode of significations or through determination, in those things which are divided according to significance, not only should the significances be divided but it should also be shown by definition that there are diverse things which are signified. For Aristotle in his Topics carefully instructed this, that in those things which are said to be good, some are good, as those which retain the quality of good, others which are indeed said to have no quality but because they do a good thing are therefore said to be good.

However, we should especially practice this art, as Aristotle himself says, against sophistical importunities, for if there is no subject thing which the voice signifies, it is not said to be designative, but if there is one thing which the voice signifies, it is said to be simple, but if there are many, it is multiplex and signifies many things. Therefore, these things must be divided so that we are not caught in any syllogism.

But if the speech is amphibolous, it happens that often both the things which are signified are possible, as what I said above; for it could have happened that the Greeks conquered the Trojans and the Trojans overcame the Greeks. However, there are other things which are impossible, as when I say a man is eating bread, it indeed signifies that a man is eating bread, again that bread is eating a man, but this is impossible. Therefore, as often as it comes to contention, both the possible and impossible things should be divided, as often as to truth, only the possible things should be said, the impossible things should be left.

Therefore, since there are many species of words signifying many things, it must be said that some have a multiplicity of signification in the particle, others in the whole speech, and of those which have it in the particle, the part itself is said to be equivocal, the whole speech itself, however, is multiplex according to equivocation, but that which retains a multiplicity of signification in the whole speech (as has already been said above) is called ambiguous.

However, the significations of equivocal terms are divided according to the equivocation of a single particle of speeches by definition, such as when I say: “Man lives” both the real and the depicted are understood; but it is divided in this way: “A rational mortal animal lives” (which is true), “A simulation of a rational mortal animal lives” (which is false). It is divided by any addition that limits, either of gender or case or any article;

for example, when I say: “Canna was stained with Roman blood” it denotes both a reed and a river, but we divide it like this: with the article, as we say: “This Canna was stained with Roman blood” or by gender, as: “Canna was full of Roman blood” or by case or number, for in one it is only singular, in the other it is plural, and the same way with others.

There are others according to accent, others according to orthography, and according to accent indeed like “pone” and “pone”, according to orthography like “quaeror” and “queror” from inquiry and complaint; and these again are divided either according to the orthography itself or according to action and passion, because “quaeror” from inquiry is passive, but “queror” from complaint is active.

However, a division of ambiguous sentences must be made, either by addition or by diminution or by division or by some transposition, as when it is said: “I hear the Trojans conquered the Greeks” we should say: “I hear that the Greeks conquered the Trojans” for this ambiguity is solved by any of these methods.

However, not every signification of words should be divided as if it were a genus: in a genus, all species are enumerated, but in ambiguity, as many are sufficient as can be useful to that speech which one or the other sentence connects.

And about the signification of voice indeed sufficient has been said, but also about the division of genus and whole has been proposed and explained. Therefore, everything has been very diligently discussed according to their divisions.

Division by Accident.

Now we will speak about those divisions which are made by accident. The common precept of these, however, is that whatever of them is divided into opposites is disaggregated, so if we divide the subject into accidents, we do not say “Some bodies are white, some are sweet”, which are not opposites, but “Some bodies are white, some are black, some are neither”, in the same way also in other divisions according to accident it must be divided.

And it must be clearly seen, that nothing more or less is said, as it happens in the division of genus. For it is not necessary to leave any accident from the same opposition that is inherent in that subject which is not said in the division, nor indeed to add anything that cannot be inherent in the subject.

Indeed, the later Peripatetic school with the most careful reasoning observed the differences of divisions and separated and distributed the division by itself from that which is according to accident and these from each other, but the older ones indifferently used the accident for the genus and accidents for species or differences, hence it seemed very opportune to us both to reveal the commonalities of these divisions and to separate them by their own differences.

And indeed about every division, as much as the brevity of the introduction allows, we have carefully expressed.

Thiago’s Translations Blog

Tuesday, May 9, 2023

On Division, by Anicius Manlius Severinus Boethius