THE PYTHAGOREAN SOURCEBOOK AND LIBRARY
THE FRAGMENTS OF ARCHYTAS
ARCHYTAS OF TARENTUM (first half of the fourth century B.C.E.) was a student of Philolaus and a personal friend of Plato, who came to visit him in 388 B.C.E. He made a major contribution to harmonic theory, was engaged in mathematical studies, and was the first to solve the geometrical problem of doubling the volume of the cube.
Like Pythagoras himself, Archytas was also involved in political affairs; he was quite well liked in this capacity, being elected chief magistrate of Tarentum for seven terms though the law, which was waived in his favor, allowed for a maximum of one term. Archytas also seems to have had a knack for practical inventions: he is said to have created a mechanical pigeon, made of wood, which flew, and Aristotle refers to another well-known invention, Archytas' rattle, "which they give to children so that by using it they may refrain from breaking things about the house; for young things cannot keep still."
With the exception of the mathematical fragments and a few others, the fragments of Archytas are not considered genuine. For example, "The Ten Categories of Archytas" are obviously indebted to Aristotelian thought rather than vice versa. Nonetheless, even though not written by Archytas himself, some of the other fragments are quite valuable, especially the ethical ones. The correspondence between Plato and Archytas, reproduced below in the biography from Diogenes Laertius, is thought to be spurious.
For more on Archytas see Freeman's Companion to the Pre-Socratic Philosophers, section 47, and Guthrie's History of Greek Philosophy, vol. 1, 333 ff.
THE LIFE OF ARCHYTAS
ARCHYTAS OF TARENTUM, son of Mnesagoras, or of Hestius, according to Aristoxenus, also was a Pythagorean. It was he who, by a letter, saved Plato from the death threatened by Dionysius. He possessed all the virtues, so that, being the admiration of the crowd, he was seven times named general, in spite of the law which prohibited reelection after one year. Plato wrote him two letters, in response to this one of Archytas:
"Greetings. It is fortunate for you that you have recovered from your illness, for I have heard of it not only from you, but also from Lamiscus. I have busied myself about those notes, and took a trip into Lucania, where I met descendants of Ocellus. I have in my possession the treatises On Law and On Kingship, On Sanctity, and On the Origin of All Things, and I am sending them to you. The others could not be discovered. Should they be found, they will be sent to you."
"Greetings. I am delighted to have received the works which you have sent me, and I acknowledge a great admiration for him who wrote them. He seems to be worthy of his ancient and glorious ancestors, who are said to be from Myra, and among the number of those Trojans who emigrated under the leadership of Laomedon, all worthy people, as the legend proves. Those works of mine about which you wrote me are not in a sufficient state of perfection, but I send them such as they are. Both of us are in perfect agreement on the subject of protecting them. No use to renew the request. May your health improve!"
Such are these two letters.
There were four Archytases: the first, of whom we have just spoken; the second, from Mytilene, was a musician; the third wrote On Agriculture; the fourth is an author of epigrams. Some mention a fifth, an architect, who left a treatise On Mechanics, beginning as follows: "This book contains what I have been taught by Teucer of Carthage. " The musician is said to have made this joke: on being reproached for not advertising himself more, he said "It is my instrument which speaks for me."
Aristoxenus claims that the philosopher Archytas was never defeated during his command. Once, overcome by envy, he had been obliged to resign his command, and his fellow-citizens were immediately conquered. He was the first who methodically applied the principles of mathematics to mechanics; who imparted an organic motion to a geometric figure, by the section of the semi-cylinder seeking two means that would be proportional, in order to double the cube.  He also first, by geometry, discovered the properties of the cube, as Plato records in the Republic (528 B).
THE FRAGMENTS OF ARCHYTAS
1. Metaphysical Fragments
1. There are necessarily two principles of beings: the one contains the series of beings organized, and finished; the other, contains unordered and unfinished beings. That one which is susceptible of being expressed, by speech, and which can be explained, embraces both beings, and determines and organizes the nonbeing.
For every time that it approaches the things of becoming, it orders them, and measures them, and makes them participate in the essence and form of the universal. On the contrary, the series of beings which escapes speech and reason, injures ordered things, and destroys those which aspire to essence and being; whenever it approaches them, it assimilates them to its own nature.
But since there are two principles of things of an opposite character, the one the principle of good, and the other the principle of evil, there are therefore also two reasons, the one of beneficent nature, the other of maleficent nature.
That is why the things that owe their existence to art, and also those which owe it to nature, must above all participate in these two principles: form and substance.
The form is the cause of essence; substance is the substrate which receives the form. Neither can substance alone participate in form, by itself; nor can form by itself apply itself to substance; there must therefore exist another cause which moves the substance of things, and forms them. This cause is primary, as regards substance, and the most excellent of all. Its most suitable name is God.
There are therefore three principles: God, the substance of things, and form. God is the artist, the mover; the substance is the matter, the moved; the essence is what you might call the art, and that to which the substance is brought by the mover. But since the mover contains forces which are self- contrary, those of simple bodies, and as the contraries are in need of a principle harmonizing and unifying them, it must necessarily receive its efficacious virtues and proportions from numbers, and all that is manifested in numbers and geometric forms, virtues and proportions capable of binding and uniting into form the contraries that exist in the substance of things. For, by itself, substance is formless; only after having been moved towards form does it become formed and receive the rational relations of order. Likewise, if movement exists, besides the thing moved, there must exist a prime mover; there must therefore be three principles: the substance of things, the form, and the principle that moves itself, and which by its power is the first; not only must this principle be an intelligence, it must be above intelligence, and we call it God.
Evidently the relation of equality applies to the being which can be defined by language and reason. The relation of inequality applies to the irrational being, and cannot be fixed by language; it is substance, and that is why all begetting and destruction take place in substance and do not occur without it.
2. In short, the philosophers began only by so to speak contrary principles; but above these elements they knew another superior one, as is testified to by Philolaus, who says that God has produced, and realized the Limited and Unlimited, and shown that at the Limit is attached the whole series which has a greater affinity with the One, and to the Unlimited, the series that is below. Thus, above these two principles they have posited a unifying cause, superior to everything; which, according to Archenetus, is the cause before the cause, and, according to Philolaus, the universal principle.
3. A. Which One are you referring to? The supreme One, or the infinitely small One that you can find in the parts? The Pythagoreans distinguish between the One and the Monad, as says Archytas: the One and the Monad have a natural affinity, yet they differ.
B. Archytas and Philolaus indiscriminately call the One a Monad, and Monad a One. The majority, however, add to the name Monad, the distinction of first Monad, for there is a Monad which is not the first, and which is posterior to the Monad in itself, and to the One.
C. Pythagoras said that the human soul was a tetragon with right angles. Archytas, on the contrary, instead of defining the soul by the tetragon, did so by a circle, because the soul is a self-mover, and consequently, the prime mover, and this is a circle or a sphere.
D. Plato and Archytas and the other Pythagoreans claim that there are three parts in the soul: reason, courage and desire.
4. The beginning of knowledge of beings is in the things that produce themselves. Of these some are intelligible, and others sensible; the former are immovable, the latter are moved. The criterion of intelligible things is the world; that of sensible things is sensation.
Of the things that do not manifest in things themselves, some are science, the others, opinion; science is immovable, opinion is movable.
We must, besides, admit these three things: the subject that judges, the object that is judged, and the rule by which that object is judged. What judges is the mind, or sensation; what is judged is the logos, or rational essence; the rule of judgement is the act itself which occurs in the being, whether intelligible or sensible. The mind is the judge of essence, whether it tends towards an intelligible being or a sensible one. When reason seeks intelligible things, it tends towards an intelligible element; when it seeks things of sense, it tends towards their element. Hence come those false graphic representations in figures and numbers seen in geometry, those researches in causes and probable ends, whose object are beings subject to becoming, and moral acts, in physiology or politics. It is while tending toward the intelligible element that reason recognizes that harmony is in the double relation [the octave] but sensation alone attests that this double relation is concordant. In mechanics, the object of science is figures, numbers, proportions -- namely, rational proportions; the effects are perceived by sensation, for you can neither study nor know them outside of the matter or movement. In short, it is impossible to know the reason of an individual thing, unless you have preliminarily by the mind grasped the essence of the individual thing; the knowledge of the existence, and of quality, belongs to reason and sensation: to reason, whenever we effect a thing's demonstration by a syllogism whose conclusion is inevitable; to sensation, when the latter is the criterion of a thing's essence.
5. Sensation occurs in the body, reason in the soul. The former is the principle of sensible things, the latter, of intelligible ones. Popular measures are number, length, the foot, weight, equilibrium, and the scales, while the rule and the measure of straightness in both vertical and longitudinal directions is the right angle.
Thus sensation is the principle and measure of the bodies; reason is the principle and measure of intelligible things. The latter is the principle of beings that are intelligible and naturally primary; the former is the principle of sense-objects, and is naturally secondary. Reason is the principle of our soul; sensation is the principle of our body. The mind is the judge of the noblest things; sensation is the judge of the most useful. Sensation was created in view of our bodies, and to serve them; reason was created in view of the soul, and to initiate wisdom therein. Reason is the principle of science; sensation is that of opinion. The latter derives its activity from sensible things; the former, from intelligible forms. Sensible objects participate in movement and change; intelligible objects participate in immutability and eternity. There is analogy between sensation and reason; for sensation's object is the sensible, which moves, changes, and never remains self-identical; therefore, as you can see, it improves or deteriorates. Reason's object is the intelligible, whose essence is immobility; wherefore in the intelligible we cannot conceive of either more or less, better or worse; and just as reason sees the primary being, and the [cosmic] model, so sensation sees the image, and the copied. Reason sees man in himself; sensation sees in them the circle of the sun, and the forms of artificial objects. Reason is perfectly simple and indivisible, as unity, and the point; it is the same with intelligible beings.
The idea is neither the limit nor the frontier of the body; it is only the figure of being, that by which the being exists, while sensation has parts, and is divisible.
Some beings are perceived by sensation, others by opinion, others by science, and others by reason.
The bodies that offer resistance are sensible; opinion knows those that participate in the ideas, and are its images, so to speak. Thus some particular man participates in the idea of man, and this triangle, in the triangle-idea. The objects of science are the necessary accidents of ideas; thus the object of geometry is the properties of the figures; reason knows the ideas themselves, and the principles of the sciences and of their objects, for example, the circle, the triangle, and the pure sphere in itself. Likewise, in us, in our souls, there are four kinds of knowledge: pure thought, science, opinion and sensation; two are principles of knowledge [thought and sensation], two are its purpose, science and opinion.
It is always the similar which is capable of knowing the similar: reason knows intelligible things; science understands knowable things; opinion knows conjecturable things; sensation knows sensible things.
That is why thought must rise from things that are sensible, to the conjecturable, and from these to the knowable, and on to the intelligible; and he who wishes to know the truth about these objects, must in a harmonious grouping combine all these means and objects of knowledge. This being established, you might represent them under the image of a line divided into two equal parts, each of which would be similarly divided; if we separate the sensible, dividing it into two parts, in the same proportion, the one will be clearer, the other obscurer. One of the sections of the sensible contains images of things, such as you see reflected in water, or mirrors; the second represents the plants and animals of which the former are images. Similarly dividing the intelligible, the different kinds of sciences will represent the images; for the students of geometry begin by establishing by hypothesis the odd and the even, figures, three kinds of angles, and from these hypotheses deduce their science. As to the things themselves, they leave them aside, as if they knew them, though they cannot account for them to themselves or to others; they employ sensible things as images, but these things are neither the object nor the end proposed in their researches and reasonings, which pursue only things in themselves, such as the diameter, or square. The second section is that of the intelligible, the object of dialectics. It really makes no hypotheses, positing principles whence it rises to arrive at the unconditioned, universal principle; then, by an inverse movement, grasping that principle, it descends to the end of the reasoning, without employing any sensible object, exclusively using pure ideas. By these four divisions, you can also analyze the soul-states, and give the highest the name of thought, reasoning to the second, faith to the third, and imagination to the fourth.
6. Archytas, at the beginning of his book On Wisdom gives this advice: in all human things, wisdom is as superior as sight is to all the other senses of the body, as mind is superior to soul, as the sun is superior to the stars. Of all the senses, sight is the one that extends furthest in its sphere of action, and gives us the most ideas. Mind, being supreme, accomplishes its legitimate operation by reason and reasoning; it is like sight, and is the power of the noblest objects. The sun is the eye and soul of natural things, for it is through it that they are all seen, begotten, and thought; through it the plants produced by root or seed are fed, developed, and endowed with sensation.
Of all beings, man is the wisest by far. For he is able to contemplate beings, and to acquire knowledge and understanding of all. That is why divinity has engraved in him, and has revealed to him the system of speech, which extends to everything, a system in which are classified all the beings, kinds of beings, and the meanings of nouns and verbs. For the specialized seats of the voice are the pharynx, the mouth and the nose. As man is naturally organized to produced sounds, through which nouns and verbs are expressed and formed, likewise he is naturally destined to contemplate the notions contained in visible objects. Such, in my view, is the purpose for which man has been created, and was born, and for which he received from God his organs and faculties.
Man is born and was created to know the essence of universal nature; and precisely the function of wisdom is to possess and contemplate the intelligence manifested in [all] beings.
The object of wisdom is no particular being, but all the beings, absolutely; and it should not begin to seek the principles of an individual being, but the principles common to all. The object of wisdom is all the beings, as the object of sight is all visible things. The function of wisdom is to see all the beings in their totality, and to know their universal attributes, and that is how wisdom discovers the principles of all beings.
He who is capable of analyzing all the species, and tracing and grouping them, by an inverse operation, into one single principle, seems to me the wisest, and the closest to the truth; he seems to have found that sublime observatory from the peak of which he may observe God, and all the things that belong to the series and order of divine things. Being master of this royal road, his mind will be able to rush forwards, and arrive at the end of the career, uniting principles to the purposes of things, and knowing that God is the principle, the middle and the end of all things made according to the rules of justice and right reason.
2. Physical and Mathematical Fragments
7. As Eudemus reports, Archytas used to ask this question: "If I was situated at the extreme and immovable limit of the world, could I, or could I not, extend a wand outside of it?" To say I could not, is absurd; but if I can, there must be something outside of the world, be it body or space; and in whatever manner we reason, by the same reasoning we will ever return to this limit. I will still place myself there, and ask, "Is there anything else on which I may place my wand?" Therefore, the Unlimited exists; if it is a body, our proposition is demonstrated; if it is space, place is that in which a body could be; and if it exists potentially, we will have to place it and classify it among the eternal things, and the Unlimited will then be a body and a place.
8. The essence of place is that all other things are in it, while itself is not in anything. For if it was in a place, there would be a place in a place, and that would continue to infinity. All other beings must therefore be in place, and place in nothing. Its relation to things is the same as Limit to limited things; for the place of the entire world is the Limit of all things.
9 A. Some say that time is the sphere of the world; such was the sentiment of the Pythagoreans, according to those who had heard Archytas give this general definition of time: "Time is the interval of the nature of all."
B. The divine Iamblichus, in the first book of his Commentaries on the Categories, said that Archytas thus defined time: "It is the number of movement, or in general the interval of the nature of all."
C. We must combine these two definitions, and recognize time as both continuous and discrete, though it is properly continuous. Iamblichus claims that Archytas taught the distinction of physical time, and psychic time. So at least Iamblichus interpreted Archytas, but we must recognize that there, and often elsewhere, he adds his own commentaries to explain matters.
10. The general proper essence of "when-ness" and time is to be indivisible and unsubstantial. For, being indivisible, the present time has passed, while expressing it and thinking of it; nothing remains of it, and so becoming continuously the same it never subsists numerically, but only specifically. In fact. the actually present time and the future are not identical with former time. For the one has past, and is no more; the other one passes while being produced and thought. Thus the present is never but a bond; it perpetually becomes, changes, and perishes, but nevertheless it remains identical in its own kind.
In fact, every present is without parts, and indivisible; it is the term of past time, the beginning of time to come; just as in a broken line, the point where the break occurs becomes the beginning of a line, and the end of the other. Time is continuous, and not discrete as are number, speech and harmony.
In speech, the syllables are parts, and distinct parts; in harmony, they are the sounds; in number, the unities. The line, place and space are continuous; if they are divided, their parts form common sections. For the line divides into points, the surface into lines, the solid into surfaces. Therefore time is continuous. In fact there was no time when time was not; and there was no moment when the present was not. But the present has always been, it will always be, and will never fail; it changes perpetually, and becomes another according to the number, but remains the same according to kind. The line differs from the other continua, in that if you divide the line, place, and space, its parts will subsist; but in time, the past has perished, and the future will. That is why either time does absolutely not exist, or it hardly exists, and has but an insensible existence. For of its parts one, the past, is no more, and the future is not yet; how then could the present, without parts and indivisible, possess true reality?
11. Plato says that the movement is the great and small, the non-being, the unusual, and all that reduces to these; like Archytas, we had better say that it is a cause.
12. Why do all natural bodies take the spherical form? Is it, as said Archytas, because in the natural movement is the proportion of equality? For everything moves in proportion; and this proportion of equality is the only one which, when it occurs, produces circles and spheres, because it returns on itself.
13. He who knows must have learned from another, or have found his knowledge by himself. The science that you learn from another, is as you might say, exterior; what you find by yourself, belongs to ourselves individually. To find without seeking is something difficult and rare; to find what one is seeking is commodious and easy; to ignore, and seek what you ignore, is impossible (DK 3).
14. The Pythagorean opinion about sciences to me seems correct, and they seem to show an exact judgment about each of them. Having known how to form a just idea of the nature of a ball, they should have likewise seen the essential nature of the parts. They have left us certain and evident theories about arithmetic, geometry and spherics, also about music, for all these sciences seem to be kindred. In fact, the first two kinds of being are indistinguishable.
15. A. First they have seen that it was not possible that noise should exist unless there was a shock of one body against another; they said there is a shock when moving bodies meet and strike each other. The bodies moved in the air in an opposite direction and those that are moved with an unequal swiftness-in the same direction-the first, when overtaken, makes a noise, because struck. Many of these noises are not susceptible of being perceived by our organs; some because of the slightness of the shock, the others because of their too great distance from us, some even because of the very excess of their intensity, for noises too great do not enter into our ears, as we cannot introduce anything into jars with too narrow an opening when one pours in too much at a time.
Of the sounds that fall within the range of our senses, some -- those that come quickly from the bodies struck -- seem shrill; those that arrive slowly and feebly, seem of low pitch. In fact, when one agitates some object slowly and feebly, the shock produces a low pitch; if the waving is done quickly, and with energy, the sound is shrill. This is not the only proof of the fact, which we can prove when we speak or sing; when we wish to speak loud and high, we use a great force of breath. So also with something thrown; if you throw them hard, they go far; if you throw them without energy, they fall near, for the air yields more to bodies moved with much force, than to those thrown with little. This phenomenon is also reproduced in the sound of the voice, for the sounds produced by an energetic breath are shrill, while those produced by a feeble breath are weak and low in pitch. This same observation can be seen in the force of a signal given from any place: if you pronounce it loud, it can be heard far; if you pronounce the same signal low, we do not hear it even when near. So also in flutes, the breath emitted by the mouth and which presents itself to the holes nearest the mouthpiece, produces a shriller sound, because the impulsive force is greater; farther [down], they are of lower pitch. It is therefore evident that the swiftness of the movement produces shrillness, and slowness, lower pitch. The same thing is seen in the bull roarers which are spun in the Mysteries; those that move slowly produce a low pitch, while those that move quickly with force make a shrill noise. Let us yet adduce the reed: if you close the lower opening, and blow into it, it will produce a certain sound; and if you stop it in the center, or in the front, the sound will be shrill. For the same breath traversing a long space weakens, while traversing a shorter, it remains of the same power. After having developed this opinion that the movement of the voice is measured by intervals, he resumes his discussion, saying, that the shrill sounds are the result of a swifter movement, the lower sounds, of a slower movement. This is a fact which numerous experiments demonstrate clearly.
B. Eudoxus and Archytas believed that the reasons of the agreement of the sounds was in the numbers; they agree in thinking that these reasons consist in the movements, the shrill movement being quick, because the agitation of the air is continuous, and the vibration more rapid; the low pitch movement being slow, because it is calmer.
16. Explaining himself about the means; Archytas writes: In music there are three means: the first is the arithmetical mean, the second is the geometrical, the third is the subcontrary mean, which is called harmonic. The mean is arithmetical, when the three terms are in a relation of analogical excess, that is to say, when the difference between the first and second is the same as between second and third; in this proportion, the relation of the greater terms is smaller, and the relation of the smaller is greater. The geometric mean exists when the first term is to the second as the second is to the third; here the relation of the greater is identical with the relation of the smaller terms. The subcontrary mean, which we call harmonic, exists when the first term exceeds the second by a fraction of itself, identically with the fraction [of the third] by which the second exceeds the third; in this proportion the relation of the greater terms is greater, and that of the smaller, smaller.
3. Ethical Fragments
17. A. We must first know that the good man is not thereby necessarily happy, but that the happy man is necessarily good; for the happy man is he who deserves praise and congratulations; the good man deserves only praise.
We praise a man because of his virtue, we congratulate him because of his success. The good man is such because of the goods that proceed from virtue; the happy man is such because of the goods that come from fortune. From the good man you cannot take his virtue; sometimes the happy man loses his good fortune. The power of virtue depends on nobody; that of happiness, on the contrary, is dependent. Long diseases, the loss of our senses, cause to fade the flower of our happiness.
B. God differs from the good man in that God not only possesses a perfect virtue, purified from all mortal affection, but enjoys a virtue whose power is faultless and independent, as suits the majesty and magnificence of his works.
Man, on the contrary, not only possesses an inferior virtue, because of the mortal constitution of his nature, but even sometimes by the very abundance of his goods, now by the force of habit, by the vice of nature, or from other causes, he is incapable of attaining the perfection of the good.
C. The good man, in my opinion, is he who knows how to act properly in serious circumstances and occasions. He will therefore know how to support good and bad fortune; in a brilliant and glorious condition, he will show himself worthy of it, and if fortune happens to change, he will know how to accept properly his actual fate. In short, the good man is he who, in every occasion, and according to the circumstances, well plays his part, and knows how to fit to it not only himself, but also those who have confidence in him, and are associated with his fortunes.
D. Since amidst the goods, some are desirable for themselves, and not for anything else, and others are desirable for something else, and not for themselves, there must necessarily exist a third kind of goods, which are desirable both for themselves and for other things. Which are the goods naturally desirable for themselves, and not for anything else? Evidently they include happiness, for it is the end on account of which we seek everything else, while we seek it only for itself, and not in view of anything else. Secondly, which are the goods chosen for something else, and not for themselves? Evidently those that are useful, and which are the means of procuring the real goods, which thus become the causes of the goods desirable for themselves; for instance: the bodily fatigues, the exercises, the tests which procure health; reading, meditation, the studies which procure virtues, and the quality of honesty. Finally, which are those goods which are both desirable for themselves, and for something else? The virtues, and the habitual possession of virtues, the resolutions of the soul, the actions, and in short anything pertaining to the possession of the beautiful. That which is to be considered for itself, and not for anything else, that is the only good.
Now what we seek for itself and for something else is divided into three classes: the one whose object is the soul, the body, and external goods. The first contains the virtues of the soul; the second contains the advantages of the body; the third consists in friends, glory, honor and wealth. Likewise with the goods that are desirable only for something else: one part of them procures goods for the soul, the other which regards the body, procures goods for it; the external goods furnish wealth, glory, honor and friendship.
We can prove that it is the characteristic of virtue to be desirable for itself, as follows: in fact, if the naturally inferior goods, I mean those of the body, are by us sought for themselves, and if the soul is better than the body, it is evident that we like the goods of the soul for themselves, and not for the result that they might produce.
E. In human life there are three circumstances: prosperity, adversity, and intermediary comfort. Since the good man who possesses virtue and practices it, practices it in these three circumstances -- either in adversity, or prosperity, or comfort, since besides in adversity he is unhappy, in prosperity he is happy, and in comfort he is not happy -- it is evident that happiness is nothing else than the use of virtue in prosperity. I speak here of human happiness. Man is not only a soul, he is also a body. The living being is a composite of both, and man also; for if the body is an instrument of the soul, it is as much a part of the man as the soul. That is why, among the goods, some belong to the man, and others belong to his component parts. The good of man is happiness amidst its integral parts. The soul's goods are prudence, courage, justice, and temperance; the body's are beauty, health, good disposition of its members, and the perfect condition of its senses. The external goods -- wealth, glory, honor, nobility -- are naturally superfluous advantages of man, and are naturally subordinate to the superior goods.
The inferior goods serve as satellites to the superior goods. Friendship, glory, and wealth are the satellites of the body and soul. Health, strength and sense-perfection are satellites of the body. Prudence, courage, justice and temperance are the satellites of the reason of the soul. Reason is the satellite of God; he is omnipotent, the supreme master. It is for these goods that the others must exist; for the army obeys the general, the sailors heed the pilot, the world obeys God, the soul heeds reason, the happy life is contingent on prudence. For prudence is nothing more than the science of the happy life, or the science of the goods which belong to human nature.
F. To God belongs happiness and the happy life; man cannot possess but a grouping of science, virtue and prosperity forming a single body. I call wisdom the science of the Gods and geniuses, and term prudence the science of human things, the science of life. For science should be the name of virtues which rest upon reasons and demonstrations, and moral virtue, the excellent habit of the irrational part of the soul, which makes you give the name of certain qualities corresponding to our habits, namely the names of liberal, just and temperate people. And I call prosperity this affluence of goods which we receive without reason being their cause. Then since virtue and science depend on us, and prosperity does not depend thereon, since happiness consists in the contemplation and practice of good things, and since contemplation and action when they meet obstacles, lend us a necessary support, when they go by an easy road, they bring us distraction and happiness. Since after all it is prosperity that gives us these benefits, it is evident that happiness is nothing else than the use of virtue in prosperity.
G. Man's relations with prosperity resemble a healthy and vigorous human body; he also can stand heat and cold, can raise a great burden, and can easily bear many other miseries.
H. Since happiness is the use of virtue in prosperity, let us speak of virtue and prosperity, the former first. Some goods, such as virtue, are not subject to excess; for excess is impossible in virtue, for one can never be too decent a man. Indeed, virtue's measure is duty, and is the habit of duty in practical life. But prosperity is subject to excess and lack, which excesses produce certain evils, disturbing man from his usual mood, so as to oppose him to virtue; this is not only the case with prosperity, but other more numerous causes also produce this effect. You need not be surprised at seeing in the hall certain impudent artists, who neglect true art, misleading the ignorant by a false picture; but do you suppose that this race does not exist as regards virtue? On the contrary, the greater and more beautiful virtue is, the more do people feign to adorn themselves with it. There are indeed many things which dishonor the appearance of virtue: first are the deceivers who simulate it, others are the natural passions which accompany it, and sometimes twist the dispositions of the soul into a contrary direction. Others are the bad habits which the body has rooted in us, or which have been ingrained in us by youth, age, prosperity, adversity, or by a thousand other circumstances. Wherefore we must not at all be surprised at entirely wrong judgments, because the true nature of our soul has been falsified within us. Just as we see an artist who is excellent make errors in works we are examining -- or the general, the pilot or the painter and like may make errors without our detracting from their talent -- so we must not call unworthy him who has had a moment of weakness, nor among the worthy a man who has done no more than a single action; but in respect to the evil, we must consider chance, and for the good, error, and to make an equitable and just judgment, and not regard a single circumstance, or a single period of time, but the whole life.
Just as the body suffers from both excess and lack, but as nevertheless the excess and so-called superfluities naturally produce the greatest diseases, so the soul suffers from both prosperity and adversity when they arrive at wrong times, and yet the greatest evils come from so-called absolute prosperity -- which is absolute because like wine it intoxicates the reason of the worthy.
I. That is why it is not adversity but prosperity which is the hardest to stand properly. All men, when they are in adversity, at least the greater part of them, seem moderate and modest; but in good fortune, ambitious, vain and proud. For adversity is apt to moderate the soul, and concentrate it, while on the contrary prosperity excites it and puffs it up. That is why wretches are docile to advice, and prudent in conduct, while the happy are bold and venturesome.
J. Thus there is a measure and limit of prosperity that the worthy man should desire to have as auxiliary in the accomplishment of his actions, just as there is a measure in the size of the ship, and in the length of the tiller, which permits the experienced pilot to traverse an immense extent of sea, and to carry through a great voyage.
The result of excess of prosperity, even among worthy people, is that the soul loses leadership to prosperity; just as too bright a light dazzles the eyes so too great a prosperity dazzles the reason of the soul. Enough about prosperity.
18. I insist that virtue is sufficient to preclude unhappiness, that badness precludes happiness, if we know how properly to judge of the genuine condition of the soul in these two conditions. For the evil reason is necessarily always unhappy, whether in abundance -- which he does not know how properly to judge or use -- or in poverty, just as a blind man is always wondering whether he is in brilliant light, or in darkness. But the worthy man is not always happy, for happiness does not consist in the possession of virtue, but in its use, just as a man who sees does not see all the time will not see without light.
Life is as it were divided into two roads: the rougher one, followed by patient Ulysses, and the more agreeable one followed by Nestor. I mean that virtue desires the one, but can also follow the other. But nature cries aloud that happiness is life desirable in itself, whose state is assured, because one can realize one's purposes in it, so that if life is traversed by things one has not desired, one is not happy, without however being absolutely unhappy. Therefore be not so bold as to insist that the worthy man is exempt from sickness, and suffering; dare not to say that he does not know pain, for if the body is allow some causes of pain, the soul should also be allowed some. The griefs of the insane lack reason and measure, while those of the wise are contained within the measure which reason gives to everything. But this so advertised insensitivity to sorrow enervates the character of generosity of virtue, when it stands trials, great sorrows, when it is exposed to death, suffering, and poverty, for it is easy to support small sorrows. You must therefore practice metriopathy or sorrow -- standardization so as to avoid the insensitivity just as much as the over-sensibility of pain, and not in words to boast about our strength above the measure of our human nature.
19. We might define philosophy as the desire of knowing and understanding things in themselves, joined with practical virtue, inspired and realized by the love of science. The beginning of philosophy is the science of nature, the middle, practical life, and the end, science itself. It is fortunate to have been well born, to have received a good education, to have been accustomed to obey a just rule, and to have habits conformable to nature. One must also have been exercised in virtue, and have been educated by wise parents, governors and masters. It is fine to impose the rule of duty on oneself, to have no need of constraint, to be docile to those who give us good advice about life and science. For a fortunate disposition of nature, and a good education are often more powerful than lessons to bring us to the good; its only lack would be the efficacious light of reason, which science gives us. Two rival directions of life contend for mastery, these being practical and philosophical life. By far the most perfect life unites them both, and in each different path adapts itself to circumstances. We are born for rational activity, which we call practical. Practical reason leads us to politics; the theoretical reason, to the contemplation of the universality of things. Mind itself, which is universal, embraces these two powers necessary to happiness, which we define as the activity of virtue in prosperity; it is not exclusively either a practical life which would exclude science, nor a speculative life which would exclude the practical. Perfect reason inclines towards these two omnipotent principles for which man is born, the principles of society and science. For if these opposite principles seem mutually to interfere in their development, the political principles turning us away from speculation, and the speculative principles turning us from politics, to persuade us to live at rest, nevertheless nature, uniting the ends of these two movements, shows them fused; for virtues are not contradictory and mutually antipathetic. Indeed, no harmony is more constant than the harmony of virtues. If from his youth man has subjected himself to the principles of virtues, and to the divine law of the world harmony, he will lead an easy life; and if, by his own inclination, he inclines towards evil and has the luck of meeting better guides, he will, by rectifying his course, arrive at happiness, like passengers favored by chance, finishing a fortunate sea-passage -- thanks to the pilot -- and the fortunate passage of life is happiness. But if by himself he cannot know his real interests, and if he does not have the luck of meeting prudent directors, what benefit would it be if he did have immense treasures? For the fool, even if he had for himself all the other elements of luck, is eternally unhappy. And since, in everything, you must first consider the end -- for that is what is done by the pilots ever meditating over the harbor whither they are to land the ship, by the drivers who keep their eye on the goal of their trip, and by the archers and slingers who consider their objective, for it is the objective towards which all their efforts must tend-virtue must necessarily undertake an objective, which should become the art of living, and that is the name I give it in both directions it can take. For practical life this objective is improvement; for the philosophical life, the perfect good, which, in their human affairs the sages call happiness. Those who are in misery are not capable of judging of happiness according to exact ideas, and those who do not see it clearly would not know how to choose it. Those who consider that pleasure is the sovereign good are punished therefore by foolishness; those who above all seek the absence of pain, also receive their punishment. In summary: to define life-happiness as the enjoyment of the body, in an unreflective state of soul, is to expose oneself to all the whirlwinds of the tempest. Those who suppress moral beauty, by avoiding all discussion, all reflection about the matter, and seeking pleasure, absence of pain, simple and primitive physical enjoyments, and the irreflective inclinations of body and soul, are not more fortunate, for they commit a double fault by reducing the good of the soul and its superior functions to the level of that of the body, and in raising the good of the body to the high level due to the good of the soul. For an exact discernment of these goods, we should outline its proper part for the divine element, and for nature; yet some do not observe this relation of dignity from the better to the worse. But we do so when we say that if the body is the organ of the soul, then reason is the guide of the entire soul, the mistress of the body, this tent of the soul, and that all the other physical advantages should serve only as instruments to the intellectual activity, if you wish it to be perfect in power, duration and wealth.
20. These are the most important conditions to become a sage: first, you must have received from fate a mind endowed with facility to understand, memory, and industry. You must then from youth on exercise your intelligence by the practice of argumentation, by mathematical studies, and by the exact sciences. Then you must study healthful philosophy, after which you may undertake the knowledge of the Gods, of laws, and of human life. For there are two means of arriving at this state known as wisdom. The first is to acquire the habit of work that is intellectual, and the taste for knowledge; the other is to seek to see many things, to undertake business frequently, and to know them, either directly at first hand, or indirectly. For he who from youth on has exercised reason by dialectic reasonings, mathematical studies, and exact sciences, is not yet ready for wisdom, any more than he who has neglected these labors, and has only listened to others, and has immersed himself in business. The one has become blind, when the business is to judge particular facts; the other, when he is to judge of general deductions. Just as in calculations you obtain the total by combining the parts, so also, in business practice, reason can vaguely sketch the general formula, but experience alone can enable us to grasp the details and individual facts.
21. Age is in the same relation to youth. Youth makes men energetic, age makes them prudent. Never by imprudence does it let a thought escape. It reflects on what it has done, it considers maturely what it ought to do, in order that this comparison of the future with the present, and of the present with the future lead it to good conduct. To the past it applies memory, to the present, sensation, and to the future, foresight; for our memory has always as object the past, foresight the future, and sensation the present. He who therefore wishes to lead an honest and beautiful life must not only have senses and memory, but foresight.
4. Political Fragments
22 A. The laws of the wicked and atheists are opposed by the unwritten laws of the Gods, who inflict evils and terrible punishments on the disobedient. It is these divine laws which have developed and directed the laws and written maxims given to men.
B. The relation of law to the soul and human life is identical to that of harmony to the sense of hearing, and the voice; for the law instructs the soul, and thereby, the life, as harmony regulates the voice through education of the ear. In my opinion, every society is composed of the commander, the commanded, and the laws. Among the latter, one is living, namely the king, and the other is inanimate, this being the written letter. The law is therefore the most essential; only through it is the king legitimate, the magistrate regularly instituted, the commanded free, and the whole community happy. When it is violated, the king is no more than a tyrant, the magistrate is illegitimate, the commanded becomes a slave, and the whole community becomes unhappy. Human acts are like a mingled tissue, formed of command, duty, obedience, and force sufficient to overcome resistance. Essentially, the command belongs to the better, being commanded to the inferior, and force belongs to both. For the reasonable part of the soul commands, and the irrational part is commanded. Both have the force to conquer the passions. Virtue is born from the harmonious cooperation of both and leads the soul to rest and indifference by turning it away from pleasures and sorrows.
C. Law must conform to nature, and exercise an efficient power over things, and be useful to the social community; for if it lacks one, two, or all of these characteristics, it is no longer a law, or at least it is no longer a perfect law. It conforms to nature if it is the image of natural right, which fits itself, and distributes to each according to his deserts. It prevails if it harmonizes with the men who are to be subject thereto; for there are many people who are not apt to receive what by nature is the first of goods, and who are fitted to practice only the good which is in relation with them, and possible for them, for that is how the sick and the suffering have to be nursed. Law is useful to the political society if it is not monarchical, if it does not constitute privileged classes, if it is made in the interest of all, and is equally imposed on all. Law must also regard the country and the lands, for not all soils can yield the same returns, neither all human souls the same virtues. That is why some establish the aristocratic constitution, While others prefer the democratic or oligarchic. The aristocratic constitution is founded on the subcontrary proportion,  and is the most just, for this proportion attributes the greatest results to the greatest terms, and the smallest to the smallest. The democratic constitution is founded on the geometrical proportion, in which the results of the great and small are equal [in ratio]. The oligarchic and tyrannic constitutions are founded on the arithmetical proportion, which, being the opposite of the subcontrary, attributes to the smallest terms the greatest results, and vice versa.
Such are the kinds of proportions, and you can observe their image in families and political constitutions; for either the honors, punishments and virtues are equally attributed to the great and small, or they are so attributed unequally, according to superiority, in virtue, wealth or power. Equal distribution is the characteristic of democracy; and the unequal, that of aristocracy and oligarchy.
D. The best law and constitution must be a composite of all other constitutions, and contain something democratic, oligarchic, monarchic and aristocratic, as in Lacedaemon; for in it the kings formed the monarchic element, the elders the aristocracy, the magistrates the oligarchy, while the cavalry generals and the youths formed the democracy. Law must therefore not only be beautiful and good, but its different parts must mutually compensate. This will give it power and durability, and by this mutual opposition I mean that the same magistracy command and be commanded, as in the wise laws of Lacedaemon. For the power of its kings is balanced by the magistrates, this by the elders, and between these two powers are the cavalry generals and the youths, who, as soon as they see anyone party acquire the preponderance, throw themselves on the other side.
The law's first duty is to decide about the Gods, the geniuses, the parents -- in short, on all that is estimable and worthy -- and later decide about utility. It is proper that the secondary regulations should follow the best, and that the laws be inscribed, not on the houses and doors, but in the depths of the souls of the citizens. Even in Lacedaemon, which has excellent laws, the State is not administered by manifold written ordinances. Law is useful to the political community, if it is not monarchical, and does not serve private interests, if it is useful to all, if it extends its obligation to all, and if it aims its punishments to shame the guilty, and to brand him with infamy, rather than to deprive him of his wealth. If, indeed, you are seeking to punish the guilty by ignominy, the citizens will try to lead a wiser and more honest life, so as to avoid the law's punishment; if it is only by money fines, they will rate above everything wealth, understanding that it is their best means to repair their faults. The best would be that the State should be organized in a manner such that it would need nothing from strangers, neither for virtue, power, or anything else. In the same way the right constitution of a body, a house, or an army is to contain, and not to depend on outside sources for the principle of its safety; for in that way the body is more vigorous, the house better ordered, and the anny will be neither mercenary nor badly drilled.
Beings that are thus organized are superior to others; they are free and liberated from servitude unless, for their conservation, they need many things, but have only few needs easily satisfied. In that way the vigorous man becomes able to bear heavy burdens, and the athlete, to resist cold, for men are exercised by events and misfortunes. The temperate man, who has tested his body and soul, finds any food, drink, even a bed of leaves, delectable. He who has preferred to live like a Sybarite among delights, would finally scorn and reject the magnificence of the great [Persian] king. Law must therefore deeply penetrate into the souls and habits of the citizens; it will make them satisfied with their fate, and distribute to each his deserts. Thus the sun, in traversing the zodiac, distributes to everything on the earth growth, food, life, in the proper measure, and institutes this wise legislation which regulates the succession of the seasons. That is why we call Zeus nomios, law-giver, from Nomeios, and we call nomeus he who distributes their food to the sheep; that is why we call the verses sung by the lyre players nomoi,  for these verses impart order to the soul because they are sung according to the laws of harmony, rhythm, and measure.
23. The true chief must not only possess the science and power of commanding well, but he must also love men; for it is absurd that a shepherd should hate his flock, and feel hostile towards those he is educating. Besides, he must be legitimate; only thus can he sustain a chiefs dignity. His science will permit him to discern well, his power to punish, his kindness to be beneficent, and the law to do everything according to reason. The best chief would be he who would closest approach the law, for he would never act in his own interest, and always in that of others, since the law does not exist for itself, but for its subjects.
24. See 21 A.
25. When the art of reflection was discovered, dissension diminished and concord increased; those who possess it feel the pride of predominance yielding to the sentiment of equality. It is by reflection that we succeed in adjusting our affairs in a friendly fashion; through it the poor receive riches, and the rich give to the poor, each possessing the confidence that he possesses the equality of rights.
26. Reflection is like a rule which hinders and turns aside the people who know how to reflect from committing injustices, for it convinces them that they cannot remain hidden if they carry out their purposes, and the punishment which has overtaken those who have not known how to abstain makes them reflect and not become back-sliders.
5. Logical Fragments
27. Logic, compared with the other sciences, is by far the most successful and succeeds in demonstrating its objectives even better than geometry. Where geometric demonstration fails, logic succeeds; and logic deals not only with general classes, but also with their exceptions.
28. In my opinion it is a complete error to insist that about every subject there are two contrary opinions which are equally true. To begin with, I consider it impossible that, if both opinions are true, they should contradict each other, and that beauty should contradict beauty, and whiteness whiteness. It cannot be so, for beauty and ugliness, whiteness and blackness are contraries. Likewise, the true is contrary to the false, and you cannot produce two contrary opinions either true or false; the one must be true, at the expense of the falseness of the other. For instance, he who praises the soul of man and accuses his body is not speaking of the same object, unless you claim that speaking exclusively of the heaven you are speaking exclusively of the earth. Why no -- they are not one, but two propositions. What am I trying to demonstrate? That he who says that the Athenians are skillful and witty and he who says they are not grateful, are not supporting contradictory propositions, for contradictories are opposed to each other on the same points, and here the two points are different.
29. Archytas' Ten Universal Categories. First, all kinds of arts deal with five things: the matter, the instrument, the part, the definition, the end. The first notion, the substance, is something self-existent and self-subsistent. It needs nothing else for its essence, though it is subject to growth if it happens to be something that is born, for only the divine is uncreated, and veritably self-subsistent. The other notions are considered in relation to substance when the latter by opposition to them is termed self- subsisting, but such is not the case in relation to the divine. The nine notions appear and disappear without implying the ruin of the subject, the substrate, and that is what is called the universal accident. For the same subject does not lose its identity by being increased or diminished in quantity. Thus, excessive feeding creates excessive size and stoutness; sobriety and abstinence make men lean, but it is always the same body, the same substrate. Thus also human beings passing from childhood to youth remain the same substance, differing only in quantity. Without changing essence, the identical object may become white or black, changing only as regards quality. Again, without changing essence, the identical man may change disposition and relation, as he is friend or enemy, but being today in Thebes, and tomorrow in Athens changes nothing in his substantial nature. Without changing essence, we remain the same today that we were yesterday; the change affected only time. The man standing is the same as the man sitting; he has changed only in situation. Being armed or unarmed is a difference only of possession; the striker and the cutter are the same man in essence, though not in action. He who is cut or struck -- which belongs to the category of suffering -- still retains his essence.
The differences of the other categories are clearer. Those of quality, possession, and suffering present some difficulties in the differences, for we hesitate about the question of knowing if having fever, shivering or rejoicing belong to the category of quality, possession or suffering. We must distinguish: if we say it is fever, it is shivering, it is joy, it is quality; if we say he has fever, he shivers, he rejoices, it is possession. Possession again differs from suffering, in that the latter can be conceived without the agent. Suffering is a relation to the agent, and is understood only by him who produces it. If we say he is cut, he is beaten, we express the patient; if we say he suffers, we express possession.
We say that Archytas has ten, and no more universal notions, of which we may convince ourselves by the following division: the being is in a subject [a substance], or is not in a subject. That which is not in a subject, forms the substance. That which is in a subject is conceived by itself, or is not conceived by itself. That which is not conceived by itself constitutes relation, for relative beings, which are not conceived by themselves, but which forcibly import the idea of another being, are what is called scheseis, conditions; thus the term son is associated with the term father, that of slave, master. Thus all relative beings are conceived in a necessary bond together with something else, and not by themselves. The self-conceivable being is either divisible -- when it is quantity -- or indivisible, when it constitutes quality. The six other notions are produced by combination of the former. Substance mingled with quantity, if seen in space, constitutes the category of where; if seen in time, constitutes that of when. Mingled with quality, substance is either active, and forms the category of action, or when passive, forms that of suffering or passivity. Combined with relation, it is either posited in another, and that is what is called situation, or it is attributed to somebody else, and then it is possession.
As to the order of the categories, quantity follows substance and precedes quality because, by a natural law, everything that receives quality also receives mass, and that it is only by means of something so determinate that quality can be so affirmed and expressed. Again, quality precedes relation, because the former is self-sufficient, and the latter [subsists] through a relation; we first have to conceive and express something by itself before in a relation.
After these universal categories follow the others. Action precedes passivity, because its force is greater; the category of situation precedes that of possession, because being situated is something simpler than being possessed, and you cannot conceive something attributed to another, without conceiving the former as situated somewhere. That which is situated is also in a position, such as standing, seated, or lying. The characteristic of substance is more-or-lessness; for we say that a man is no more of an animal than a horse, by substance, and do not admit the contraries. The characteristic of quality is to admit more or less; for we say, more or less white, or black. The characteristic of quantity is to admit equality or inequality; for a square foot is not equal to an acre, and 144 square inches equals a square foot; five is not equal to ten, and twice five is equal to ten. The characteristic of relation is to join contraries; for if there is a father, there is a son, and if there is a master, there is a slave. The characteristic of whereness is to include, and of whenness not to remain, of situation to be located, and of possession to be attributed. The composite of substance and quantity is anterior to the composite of quality; the composite of substance and quality in its turn precedes that of substance and relation. Whereness precedes whenness because whereness presupposes the place that is fixed and permanent; whenness relates to time, and time, ever in movement, has no fixity, and rest is anterior to movement. Action is anterior to passivity, and situation to possession.
A. Category of Substance. Substance is divided into corporeal and incorporeal; the corporeal may be divided into bodies animate and inanimate. Animated bodies are divisible into those endowed with sensation, and without sensation. Sense-bodies can be divided into animals and zoophytes, which do not further divide into opposite distinctions. The animal is divided into rational and irrational; the rational is divisible into mortal and immortal; the mortal can be divided into differences of genus, such as man, ox, horse, and the rest. The species are divided into individuals who have no abiding value. Each of the sections that we obtained above by opposite divisions is susceptible of being in turn divided equally, until we arrive at the indivisible individuals who are of no value.
B. Category of Quantity. This is divided into seven parts: the line, surface, the body, the place, the time, the number, and language. Quantity is either continuous or discrete: of continuous quantities there are five; of the discrete, number and language. In quantity, you may distinguish that which is composed of parts having position relative to each other, such as line, surface, body, and space; and of those whose parts have no position, such as number, language, and time. For although time is a continuous quantity, nevertheless its parts have no position because it is not permanent, and that which has no permanence could not have any position. Quantity has produced four sciences: immovable continuous quantity, geometry; movable continuous quantity, astronomy; immovable discrete quantity, arithmetic; and the movable discrete, music.
C. Category of Quality. This is divided into hexis, or habit, and diathesis, or affection, passive quality and passivity, power and impotence, figure and form. Habit is affection in a state of energetic tension. It is the permanence and fixity derived from continuity and the energy of affection; it is affection become [second] nature, a second enriched nature. Another explanation of habit is the qualities given us by nature, and which are derived neither from affection, nor from the natural progress of the being; as sight and the other senses; both passive quality and passivity are increase, intensity, and weakening. To both of these are attributed anger, hate, intemperance, the other vicious passions, the affections of sickness, heat and cold; but these are classified at will under habit and affection, or under passive quality and passivity. You might say that so far as affection is communicable it might be called habit; so far as it causes a passion, it might be called a passive quality, which refers both to its permanence and fixity. For a modification contained in the measure is called passion. Thus from the one to whom it is communicated, heat may be called a habit. From the cause which produces the modification, we may say that it is either the passive quality, or the power of the passion; as when we say of a child that he is potentially a runner or a philosopher, and, in short, when at a given moment the being does not have the power to act, but it is possible that after the lapse of a certain period of time this power may belong to him. Impotence is when nature refuses itself to the possibility of accomplishing certain actions, as when the man is impotent to fly, the horse to speak, the eagle to live in water, and all the natural impossibilities.
Figure is a conformation of a determined character. Form is the quality showing itself exteriorly by color, or beauty or ugliness showing itself on the surface by color, and in short any form that is apparent, determinate, and striking. Some limit figure to inanimate things reserving form to living beings. Some say that the word figure gives the idea of the dimension of depth, and that the word form is applied only to the superficial appearance; but you have been taught all of that.
D. Category of Relation. Generally the relatives are divided into four classes: nature, art, chance and will. The relation of father to son is natural; that of master to disciple, that of art; that of master to slave, that of chance; and that of friend to friend, and enemy to enemy, that of will, although you might say that these are all natural relations.
E. Category of Whereness. The simplest division is into six: up, down, forwards, backwards, right and left. Each of these subdivisions contains varieties. There are many differences in upness: in the air, in the stars, to the pole, or beyond the pole, and such differences are repeated below. The infinitely divided spaces themselves are further subject to an infinity of differences, but this very ambiguous point will be explained later.
F. Category of Whenness. This is divided into present, past and future. The present is indivisible, the past is divided into nine subdivisions, the future into five. We have already spoken of them.
G. Category of Action. This is divided into action, discourse and thought. Action is in work of the hands, with tools, and with the feet, and each of these divisions is subdivided into technical divisions which also have their parts. Language is divided into Greek or barbarian, and each of these divisions has its varieties, namely, its dialects. Thought is divided into an infinite world of thoughts, whose objects are the world, other people, and the hypercosmic. Language and thought really belong to action, for they are acts of the reasonable nature; in fact, if we are asked, "What is Mr. X doing?" we answer that he is chatting, conversing, thinking, reflecting, and so on.
H. Category of Passivity. Passivity is divided into suffering of the soul and of the body. Each of these is subdivided into passions which result from actions of somebody else, as for instance, when somebody is struck, and passions which arise without the active intervention of someone else which occur in a thousand different forms.
I. Category of Situation. This is divided into three: standing, sitting, and lying, and each of these is subdivided by differences of location. We may stand on our feet, or on the tips of our fingers, with the leg unflexed, or the knee bent. Further differences are equal or unequal steps or walking on one or two feet. Being seated has the same differences: one may be straight, bent, reversed; the knees may form an acute or obtuse angle; the feet may be placed over each other, or in some other way. Likewise with lying down prone or head forwards, or to the side, the body extended, in a circle, or angularly. Far from uniform are these divisions; they are quite various. Position is also subject to other divisions: for instance, an object may be spread out like corn, sand, oil, and like all the other solids that are susceptible to position, and like all the liquids that we know. Nevertheless, being extended belongs to position, as with cloth and nets.
J. Category of Possession. "Having" signifies things that we put on, such as shoes, arms, coverings; things which are put on others, such as a basket, a bottle, and other vases, for we say that the basket has oats, that the bottle has wine. The same is true also of wealth and estates; we say, he has a fortune, fields, cattle, and other similar things.
30. The order of the categories is the following: in the first rank is substance, because it alone serves as substrate to all the others. We can conceive it alone, and by itself, but the others cannot be conceived without it, for all attributes' subjects reside therein, or are affirmed thereof. The second is quality, for it is impossible for a thing to have a quality without an essence.
31. Every naturally physical and sensible substance must, to be conceived by man, be either classified within the categories, or be determined by them, and cannot be conceived without them.
32. Substance has three differences: the one consists in matter, the other in form, and the third in the mixture of both.
33. These notions, these categories, have characteristics that are common and individual. I say that they are characteristics common to substance, not to receive more-or-lessness; for it is not possible to be more or less man, God, or plant. The characteristics have no contraries, for man is not the contrary of man, neither God of a God; neither is it contrary to other substances, to exist by oneself, and not to be in another, as green or blue color is the characteristic of the eye, since all substance depends on itself. All the things that belong to it intimately, or the accidents in it, cannot exist without it; quality is suited by several characteristics of substance, for example, not to be subject to more-or-lessness.
34. It is the property to remain self-identical, one in number, and to be susceptible of the contraries. Waking is the contrary of sleep; slowness is contrary to swiftness, sickness to health, and the same man is susceptible of all these differences. For he awakes, sleeps, moves slowly or quickly, is well or sick, and in short is able to receive all similar contraries, so long as they be not simultaneous.
35. Quantity has three differences: one consists in weight, like bullion; the other in size, as the yard; the other in multitude, as ten.
36. Including its accidents, substance is necessarily primary; that is how they [the categories] are in relation to something else. After the substance come the relations of accidental qualities.
37. A common property which must be added to quality is to admit certain contraries and privation. The relation is subject to more-or-lessness. For though a being remains ever the same, to be greater or smaller than anything else is moreness. But all the relations are not susceptible thereto, for you cannot be more or less father, brother, or son. I do not mean to express the sentiments of both parents, nor the degree of tenderness held mutually by beings of the same blood, and the sons of the same parents; I only mean the tenderness which is in the nature of these relations.
38. Quality has certain common characteristics: for example, of receiving the contraries and privation, which more or less affect the passions. That is why the passions are marked by the characteristics of indetermination, because they are in a greater or less indeterminate measure.
39. Relation is susceptible to conversion, and this conversion is founded either on resemblance, as the equal, and the brother, or on lack of resemblance, the large and the small. There are relatives which are not converted, for instance, science and sensation; for we may speak of the science of the intelligible, and of the sensation of the sensible, and the reason is that the intelligible and the sensible can exist independently of science and sensation while science and sensation cannot exist without the intelligible and the sensible [...] The characteristic of relatives is to exist simultaneously in each other, for if we grant the existence of doubleness, the half must necessarily exist; and if the half exists necessarily must the double exist, as it is the cause of the half, as the half is the cause of the double.
40. Since every moved thing moves in a place, since action and passivity are actualized movements, it is clear that there must be a primary space in which exist the acting and the passive objects.
41. The characteristic of the agent is to contain the cause of the motion, while the characteristic of the thing done, which is passive, is to have it in some other. For the sculptor contains the cause of the making of the statue, the bronze possesses the cause of the modification it undergoes, both in itself and in the sculptor. So also with the passions of the soul, for it is in the nature of anger to be aroused as the result of something else -- that it be excited by some other external thing, as for example by scorn, dishonor, and outrage -- and he who acts thus towards another, contains the cause of his action.
42. The highest degree of the action is the act which contains three differences: it may be accomplished in the contemplation of the stars, or in doing, such as healing or constructing, or in action, as in commanding an army, or administering the affairs of state. An act may occur even without reasoning, as in irrational animals. Those are the most general contraries.
43. Passion differs from the passive state, for passion is accompanied by sensation, like anger, pleasure and fear, while one can undergo something without sensation, such as the wax that melts, or the mud that dries. Then also the deed done differs also from the passive state, for the deed done has undergone a certain action, while everything that has undergone a certain action is not a deed done; for a thing may be in a passive state as a result of lack or privation.
44. On one side there is the agent, on the other the patient; for example, in nature, God is the being who acts, matter the being which undergoes, and the elements are neither the one nor the other.
45. The characteristic of possession is to be something adventitious, something corporeal, separated from essence. Thus a veil or shoes are distinct from the possessor; they are not natural characteristics, nor essential accidents, like the blue color of the eyes, and rarefaction. The latter are two incorporeal characteristics while possession relates to something corporeal and adventitious.
46. Since the signs and the things signified have a purpose, and because man uses these signs and signified things is to fulfill the perfect function of speech, let us finish what we have said by proving that the harmonious grouping of all these categories does not belong to man in general, but to a certain definite individual. Necessarily it must be a definite man existing somewhere who possesses quality, quantity, relation, action, passivity, location and possession, who is in a place and time. The man in himself receives only the first of these expressions, I mean essence and form. But he has no quality, no age, he is not old, neither does he suffer anything, he has no location, he possesses nothing, he exists neither in place nor time. All those are only accidents of the physical and corporeal being, but not of the intelligible, immovable, and indivisible being.
47. Among contraries, some are said to be mutually opposed by convention and nature, as good to evil, the sick to the well man, truth to error; the others, as possession is opposed to privation, such as life and death, sight and blindness, science and ignorance; others as relatives, as the double and the half, the commander and the commanded, the master and the slave; others, like affirmation and negation, as being man and not a man, being honest and not.
48. The relatives arise and disappear necessarily simultaneously; the existence of the double is impossible without implying that of the half and vice versa. If something becomes double, the half must arise, and if the double is destroyed, the half passes away with it.
49. Of the relatives, some respond to each other in two senses, as the greater, the smaller, the brother, the relative. Others again respond, but not in the two senses, for we say equally, the science of the intelligible, and the science of the sensible, but we do not say the reciprocal, the intelligible of science, and the sensible of sensation. The reason is that the object of judgment can exist independently of him who judges, for instance, the sensible can exist without sensation, and the intelligible without science, while it is not possible that the subject which bears a judgment exists without the object which he judges. For example, there can be no sensation without sensible object, nor science without intelligible object. Relatives which respond reciprocally are of two kinds: these are those that respond indifferently, as the relative, the brother, the equal, for they are mutually similar and equal. Some respond reciprocally, but not indifferently, for this one is greater than that one, and that one is smaller than this one, and this one is the father of that one, and that one the son of this one.
50. These opposites divide into kinds which band together; for of the contraries some are without a middle term and the others have one. There is no middle term between sickness and health, rest and movement, waking and sleep, straightness and curvedness, and other such contraries. But between the much and the little, there is a just medium; between the shrill and the low, there is the unison; between the rapid and slow, there is the equality of movement; between the greatest and the smallest, the equality of measure. Of universal contraries there must be one that belongs to what receives them, for they do not admit any medium term. Thus there is no medium term between health and sickness, for every living being is necessarily sick or well; neither between waking and sleeping, for every living being is either awake or asleep; nor between rest and movement, for every human being is either at rest or moving. [Concerning the opposites of which neither belong to the subject which may receive them,] between black and white there is the fawn, and it is not necessary that an animal be black or white. Between the great and the small there is the equal, and it is not necessary that a living being be either great or small; between the rough and soft there is the gentle, and it is not necessary that a living being be either rough or soft. In the opposites there are three differences: some are opposed, as the good is to evil, for instance, or health to sickness; the others, like evil to evil, as for instance, avarice to lechery; the others, as being neither the one or the other, for instance, as white is opposed to black, and the heavy to the light. Of the opposites, some occur in genus or genera, for the good is opposed to evil, and the good is the genus of virtues, and evil that of the evils. Other occur in the genera of species; virtue is the opposite of vice, and virtue is the genus of prudence and temperance, and vice is the genus of foolishness and debauch. Others occur in the species: courage is opposed to cowardliness, justice to injustice, and justice and excellence are species of virtue, injustice and debauch species of vice. The primary genera, which we call genera of genera, can be divided; the last species, which are the immediate nearest to the object, that is sensible, could no longer be genera, and are only species. For the triangle is the genus of the rectangle, of the equilateral and of the scalene [...] the species of good [...]
51. The opposites differ from each other in that for some -- the contraries -- it is not necessary that they arise at the same time, and disappear simultaneously. For health is the contrary of sickness, and rest that of movement; nevertheless neither of them arises or perishes at the same time as its opposite. Possession and privation of production differ in this, that it is in the nature of contraries that one passes from one to the other, for instance, from sickness to health and vice versa. It is not so with possession and privation; you do indeed pass from possession to privation, but the privation does not return to possession: the living die, but the dead never return to life. In short, possession is the persistence of what is according to nature, while privation is its lack and decay. Relatives necessarily arise and disappear simultaneously; for it is impossible for the double to exist without half, or vice versa. If some double happens to arise, it is impossible that the half should not arise, or if some double be destroyed, that the half be not destroyed. Affirmation and negation are forms of proposition, and they eminently express the true and the false. Being a man is a true proposition, if the thing exists, and false if it does not exist. You could say as much of negation: it is true or false according to the thing expressed.
Moreover, between good and evil there is a medium which is neither good nor evil; between much and little, the just measure; between the slow and the fast, the equality of speed; between possession and privation there is no medium. For there is nothing between life and death, and sight and blindness, unless indeed you say that the living who is not yet born, but who is being born, is between life and death, and that the puppy who does not yet see is between blindness and sight. In such an expression we are using an accidental medium and not one according to the true and proper definition of contraries.
Relatives have middle terms, for between the master and the slave there is the free man, and between the greatest and the smallest there is equality; between the wide and the narrow there is the proper width. One might likewise find between the other contraries a medium, whether or not it has a name.
Between affirmation [and negation] there are no contraries, for instance, between being a man and not being a man, being a musician and not being a musician. In short, we have to affirm or deny. Affirming is showing of something that it is a man, for instance, or a horse, or an attribute of these beings, as of the man that he is a musician, and of the horse that he is warlike. We call it denying when we show of something that it is not something, not man, not horse, or that it lacks an attribute of these beings, for instance, that the man is not a musician and that the horse is not warlike; and between this affirmation and this negation there is nothing.
52. Privation and being deprived is taken in three senses: one does not at all have the thing, as the blind man does not have sight, the mute does not have voice, and the ignorant does not have science; or that one does not have it but partially, as the man hard of hearing has hearing, and that the man with sore eyes has sight; or one can say that partially he does not have it, as one says that a man whose legs are [so] crooked that he has no legs, and of a man who has [such] a bad voice that he has no voice.
1. See Heath, A History of Greek Mathematics, vol. 1. 246-49.
2. I.e., the harmonic mean.
2. Nomoi, in addition to meaning "laws," is also the term used for the various modes of Greek music. Each Greek mode or "scale" was associated with a distinctive style of playing and affect.