SECTION V

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, the logical succeeds; and logic treats not only with general classes, but 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 of 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 exclusive 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'S TEN UNIVERSAL NOTIONS. 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 subject to growth, if it happens to be something that is born; for only the divine is uncreated, and veritably self-subsistent; for the other notions are considered in relation to substance when the latter by opposition to them is termed self-subsisting: but it is not such, 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 always the same body, the same substrate. Thus also human beings passing from childhood to youth remain the same in 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; and 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 aimed 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 Ñ which belongs to the category of suffering, Ñ 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; while 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 or 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 an other being, are what is called scheseis, conditions. Thus the term son is associated with the term farther, 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 Ñ 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 place, 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 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 by 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 less-ness; for we say that a man is no more of an animal than a horse, by substance, and not to 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 sq. inches equal 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 it to remain; of situation, to be located; 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.

1. CATEGORY OF SUBSTANCE. Substance is divided into corporeal and incorporeal; the corporeal into bodies animate and inanimate. Animated bodies, into those endowed with sensation, and without sensation. Senses-bodies into animals and zoophytes, which do not farther divide into opposite distinctions. The animal is divided into rational and irrational; the rational into mortal and immortal; the mortal 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 to the indivisible individuals who are of no value.

2. 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 qualities 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 place; and 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 quantity, geometry; movable continuous quantity, astronomy; immovable discrete quantity, arithmetic; and the movable, music.

3. 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 cause 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 that 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, 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 form is applied only to the superficial appearance; but you have been taught all of that.

4. CATEGORIES 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.

5. 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 up-ness, in the air, in the stars, to the pole, beyond the pole; and such differences are repeated below; the infinitely divided places themselves are further subject to an infinity of differences, but this very ambiguous point will be explained later.

6. CATEGORY OF WHENNESS. This is divided in 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.

7. CATEGORY OF ACTION. This is divided into action, discourse and thought; action in work of the hands, with tools, and with feet; and each of' these divisions is subdivided into technical divisions which also have their parts. Language is divided into Greek, barbarian, and each of these divisions have their parts, namely, its dialects. Thought is divided into and infinite world of thoughts, whose objects are the worlds, other people, and the hypercosmic. Language and thought really belong to action, for they are the acts of the reasonable nature; in fact, if we are asked: What is Mr. X doing? we answer, he is chatting, conversing, thinking, reflecting, and so on.

8. CATEGORY OF PASSIVITY. Passivity is divided in suffering of the soul, and of the body; and 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.

9. 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 very various. Position is also subject to other divisions, for an instance, an object may be spread out like corn, sand, oil, and all the other solids; that are susceptible of position, and all the liquids that we know. Nevertheless being extended belongs to position, as cloth and nets.

10. CATEGORY OF POSSESIONS. "Having" signifies things that we put on, as shoes, arms, coverings; things which are put on others, such as a peck, a bottle, and other vases; for we say that the peck has oats, that the bottle has wine; 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, that we can conceive it alone, and by itself, and that the others cannot be conceived without it; for all attributes' subject 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 ant; to 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 are in it; or cannot exit 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 to swiftness, sickness to health; and the same man, identically one, 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 are in relation to some thing 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 remain 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; whereby I do not mean to express the sentiments of both parents, nor the degree of tenderness is 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 characters, for example, of receiving the contraries, and privation; more and 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 of 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 thy 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 place 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 obtains 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, 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 in administering the affairs of state. An act may occur even without reasoning, as in irrational animal. These are the most general contraries.

43. Passion differs from the passive state; [as] 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, when the deed done has undergone a certain action, [whi]le 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 of privation.

44. On the one side there is the agent, on the other, the patient; for example, in nature, God is the being who acts; matter is 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; those are not natural characteristics, nor essential accidents, like the blue color of the eyes, and rarefaction; these are two incorporeal characteristics, while possession relates to something corporeal and adventitious.

46. Since the signs and the things signified have a purpose, and since the man who 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 finite 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, he neither does, nor suffers anything, he has no location, he possesses nothing, he is 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 [and] 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; those that respond indifferently, as the relative, the brother, the equal; for they are mutually similar, and equal. Some respond reciprocally, but not in-differently; 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 hang together; for of the contraries, some are without 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 such other 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; 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 at movement. The opposites of which neither of any or both necessarily belong to the subject that may receive them; have any middle terms; between black and white, there is the [----]; 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 the 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, 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 the genus of genera; for the good is opposed to evil, and the good is the genus of virtues, and evil that of the evils. Others 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 of injustice, and justice and virtue 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 pesistance 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 implying the half ; or vice versa. If some double happens to arise, it, is impossibly that the half should not arise, or if some double be destroyed, that the half be not destroyed. Affirmation and negation are forms of preposition, 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.

Besides, between good and evil there is 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; between 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 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 be between the other contraries a medium, whether or no it has a name.

Between affimation (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 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; or one does not at all have at all have the thing, as that the blind man does not have sight, the mute does not have voice, and the ignorant, no science; or that one does not have it but partially, as that 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 crooked that he has no legs, and of a man who has a bad voice, that he has no voice.