De nuptiis Philologiae et Mercurii, Book IV (De arte dialectica), part 2 of 3 (about §§ 367-388)
QUALITY, we said, is that according to which we are called of a certain sort. Of qualities there is one form in which a certain disposition and habit of mind is understood, as in all arts that have been mastered, wisdom, grammar, rhetoric and the rest, which so cling to the mind that they can hardly be lost. But among these some are perfect, some imperfect. For instance, if someone has given his labor to the art of grammar but is still mistaken in most things, it cannot yet be called a HABIT but is only called a DISPOSITION. So not every disposition is a habit, but every habit is understood to be a disposition. The second kind is of those qualities which we may rightly call passible, as sweet and bitter, hot and cold, not because the substances themselves suffer anything from these, but because they compel our senses to suffer something. For heat compels one who touches, and sweetness one who tastes, to suffer something. Likewise those which have become ingrained in us from some affection of nature, according to which one is called pale or red, yet not in such a way that someone grows pale or red from some sudden cause. For the affections themselves are more rightly so called, not qualities, since according to these we are not called of a certain sort. For it does not follow that one who grows pale is pallid, or one who loves a lover, or one who is drunk a drunkard. Those, then, are affections, these qualities. The third kind is of those qualities which are understood not from what one already is but from what he can be, as we say brittle wood, not because it is already broken but because it can be broken. For we call a body wrestling-like in two ways, both that which is formed by the wrestling-school and that which by nature is so formed as to be suited to this art, although it has not been steeped in it. Yet that is rightly called palaestric from the palaestra which has the effect of the art itself, but the name of the quality itself from which that palaestric which is not yet but can be is named and derived is not found. Wherefore it must be recognized that certain substances are named from qualities whose names are not found. For as we say good from goodness, we do not so say best from bestness. So, then, palaestric, which we understand from the fact that it can take on the palaestra, has no certain name of quality from which it seems to be named, yet it is agreed that it is named from a quality. The fourth kind is of those qualities according to which we understand forms and figures, as square, round, beautiful, ugly and the like. Quality receives more and less, yet not every quality. For nothing square is more square than another square. But something can be called more white than a white thing. And there is a question in many cases whether one can be called more just than another. Many, however, seem to have observed subtly who say that the qualities themselves do not receive more and less but the things named from them, so that justice is itself one perfect notion, so that it cannot be said, “this justice is more than that,” yet it can be said, “this man is more just than that one”; likewise it cannot be said, “this health is more than that,” yet it can be said, “this man is healthier than that one.” Hence it comes about that substance does not receive more and less, but qualities can do so through the substances themselves. Likewise quality has a contrary, yet not every quality. For while weakness is contrary to health, nothing is contrary to the square or the round. It must be seen, however, that whatever is contrary to a quality must be a quality. Sweetness is a quality; therefore bitterness is a quality, and the like.
QUANTITY is twofold, in that one is discrete, another continuous. Discrete, as numbers and speech; CONTINUOUS, as lines and time. Again there is another division of quantity, in that one has a certain position of its parts, another does not. For a line is understood by a certain position of its parts, since it can be said which part of it is in which place, and it seems to have right and left. But number or speech or time has none of these, although they may have order, so that in them there is something first and second and last and middle, yet nothing that is understood in place. All quantity lacks a contrary. For what is contrary to two feet long or three feet long? And if someone says that greater and less are contraries, which seem to be words of quantity, let him know that the quantity is not defined. And so if someone says something is greater, there seems to be contrary to it what is less. If I ask for a certain thing, “greater than what?”, and he answers, it is manifest that what are called greater and less are said relatively. For anything compared to a lesser is greater, and the same compared to a greater is less. If, then, greater and less are contraries, we are forced to confess, which is quite absurd, that contraries can happen to a thing at one and the same time. Again, we are forced to understand another absurdity, that one and the same thing is contrary to itself, since one thing compared with different quantities can at the same time be greater and less. Quantity does not receive greater and less. For five are not more five than two are two, nor are two more two than other two, nor will they be more two tomorrow than they are today. It is a property of quantity that according to it we say equal and unequal, as it is a property of quality that according to it we say like and unlike, although in different things either may be used by abuse. THE RELATIVE is that which, in what it is said to be, is of something or can in any manner be referred to something, as a son cannot be understood without a father or mother, nor a slave without a master, nor they in turn without these. Relatives are spoken of in three ways: either of something, as son; or to something, as neighbor; or toward something, as double, since double is toward something single. All relatives correspond in turn to those to which they are referred. For as the son is the son of the father, so the father is the father of some son. And they correspond so that some answer in the same cases, some change cases. For what I said of the son, we can say likewise of the slave, since the slave is the slave of a master, the master the master of a slave. These correspond to each other so as to keep the same cases in conversion. So too the double is double of some single and the single single of some double; so the greater is greater than some lesser and the lesser lesser than some greater. It is manifest, then, that these keep cases in conversion. But knowledge, though relative, for it is the knowledge of some knowable thing, in conversion changes the case of that to which it is referred. For as we say that knowledge is of a knowable thing, we cannot say that the knowable thing is of knowledge, but that the knowable thing is knowable by knowledge. Likewise sense is the sense of some sensible thing; conversely a sensible thing is sensible by sense. These therefore are converted not, like those spoken of above, with the same cases kept, but with them changed. Certain relatives agree with those to which they refer also in time, and begin to be and cease to be together, as a slave cannot be unless a master has begun to be, and when the master has ceased to be the slave ceases to be, and likewise a master cannot be called a master if he has had no slave. But the knowable thing is prior by nature to knowledge. For if you take away the knowable things there will be no knowledge, but if you take away knowledge, something can be knowable, though he who knows is lacking. Relatives can have a contrary, but not all. For knowledge is contrary to ignorance, enmity to friendship, but to the double there is nothing contrary, nor to the greater or lesser; whoever thinks these [things] contrary is forced to confess that one and the same thing can be contrary to itself at one and the same time. Since the greater, compared with the lesser, is greater, and the same compared with the greater is lesser at one and the same time, which can by no means happen to contraries. For at the time when a man is foolish, he cannot at the same time be wise, nor at the time when he is white can he at the same time be black; and since we have shown that this cannot happen in the greater and the lesser, we must admit that greater and less are not contraries. Likewise the double is not contrary to the single, since this same double can be toward something single. Not all relatives, therefore, can have a contrary. Again, some receive more and less, some do not. For this man is more a friend than that one, but this cannot be more double than that double, because if it is double, it is double in such a way that if it is more or less it is not double. It is asked whether any substance can be called relatively. But there is no question that the first substance cannot be called relatively. For Cicero cannot be called of something or referred to something. Likewise a horse: for a horse such as Rhoebus is not of something by the very fact that he is Rhoebus, but because he is a beast of burden he is a beast of burden of someone. The first substance, then, cannot be called relatively, nor any part of it, which without doubt is itself also a first substance. For as Cicero is a first substance, so is his hand. But a hand is not his but specifically a hand, so that the second substance cannot be called relatively. For they do not correspond by their own conversion, as if we say “the hand of Cicero,” Cicero is not Cicero by a hand, nor is the hand itself a hand because it is Cicero’s, but because it is so affected it is called a hand, not because it is someone’s. As we said, therefore, neither the first substance nor its parts can be called relatively. The question, then, is about the parts of the second substance. For about the substance itself there is no question. For man is not man of something, but a hand is specifically the hand of some man, and so that it may answer by mutual conversion, it is the hand of some handed creature, so that we can convert thus, because a handed thing is also handed by a hand. Likewise a hoof is not the hoof of a first substance but of some hoofed creature, because the hoofed thing is hoofed by a hoof, so that it may have mutual conversion, which we said is proper to relatives. If, then, that definition of relatives remains, that a relative is whatever can be said to be of something, we can hardly resist calling the parts of second substances relative. But if that definition is changed, so that relatives are those which are referred to something, except for the fact that they are in something, no substance falls under this definition. As servitude, apart from being in the same slave, that is, in some man, is referred to the master. But a feather is the feather of some feathered creature in such a way that, apart from being in some feathered creature, it can be referred to nothing. We should certainly be admonished not to be ashamed to make new words by necessity of conversion. For if mutual conversion does not answer, we do not express relatively. In this way: when I say feather, wishing to show it relative, I should not be ashamed to say “something feathered” for the sake of conversion. For the word is so familiar that it does not offend the ears. If the matter is of the foot, let us not be ashamed to fashion by like derivation a word known to conversion. Likewise one must know that he who is ignorant to what a relative is referred cannot know at all whether what he says can be referred to something. In this way: when we say “this is a double,” you know its single, that is, that to which it is double, or if you do not know that, you cannot know at all whether it is double.
TO DO and TO SUFFER can have a contrary, as to heat and to cool, and to be heated and to be cooled. They also have more and less, as to burn more and less and to be burned more and less. POSITION is all spoken of by derivation, as sedere from sessio, stare from statio. And although sometimes nouns from which positions are named are lacking, the reason does not fail. As to those three that remain, the examples given above suffice. For WHEN, as we say yesterday, tomorrow; WHERE, as at Rome, at Athens; HABIT, as shod, armed. Which of these receives more and less appears easily when it occurs in speech. These are the ten predications, of which we necessarily utter something singly. For whatever we have said that signifies anything at all, and yet cannot be understood to be true or false, is one of these ten, excepting only those, in a manner, joints of words. For there are many things enumerated by the grammarians among the parts of speech which by themselves have no force at all nor signify anything full, unless they are joined to verbs, such as conjunctions, prepositions and whatever such they teach.
It remains to speak of opposites. OPPOSITES are those which seem as it were to stand against each other from opposite sides, as CONTRARIES. Yet not all things that are opposed to each other are contraries, but all contraries are opposed. They are opposed to each other either relatively, as great to small and half to double; or as contraries, as folly to wisdom; or habit to privation, as seeing to blindness; or affirmation to negation, as “Cicero disputes,” “Cicero does not dispute.” These differ somewhat among themselves. For a RELATIVE is opposed to a RELATIVE in such a way that this very thing which is opposed is of that to which it is opposed, or is referred to it in any manner. The half is opposed to the double and is the half of the same double. So it is opposed to it in such a way as to be its own, to which it is opposed. And the small is opposed to the great, in such a way as to be so its own that the small itself is small in relation to the great to which it is opposed. CONTRARIES, however, are opposed to each other so that they are not of those to which they are opposed, yet are referred to them in some manner, since folly is contrary to wisdom in such a way that it is not the folly of that same wisdom but is folly in relation to it. It must be known, however, that some contraries have a middle, some not. For there are such that in that thing in which they can be, one or other is necessarily present by turns and they lack a middle, as health and weakness. These two contraries are naturally in the bodies of animals and are necessarily present by turns, as we said, so that in whatever body of an animal health is not, weakness necessarily is, and in which weakness is not, health necessarily is. But white and black, though contraries and naturally found in bodies, do not lack a middle, because it is not necessary that a body be white or black. For white may be absent without black being present, and in this way on the other side. A middle color, then, can be found, as yellow or green. HABIT and PRIVATION are opposed to each other in such a way that in that thing to which they can happen, one of them is necessarily present, from that time at least at which nature permits it to be. As we call that creature toothed which has teeth, but we do not call toothless one that has no teeth, but one to whom it belongs by nature to have them from that time at which nature permits it to have them. For we do not rightly call a stone toothless, which never has teeth, nor an infant. For although it may sometime have them, yet at that time nature does not yet permit it to have them. This third kind of opposites differs from the first, of relatives, in that seeing is opposed to blindness in such a way that it is not of that blindness nor referred to it in any way. From the second kind, that is, of contraries, it differs from those contraries which have a middle, in that seeing and blindness are understood with regard to eyes, so that one of them is necessarily present. In this, then, they differ from those contraries which have a middle, that one of those is not necessarily present in a substance, but of these [the middle] is necessary. From those contraries which lack a middle, these very opposites differ in that those must befall by turns, at every time, the thing to whose nature they belong, as health and weakness the body of an animal. For one or other of them is always in the body of an animal; but these can both sometimes be absent from the thing to which they can belong by nature, as an infant, while it is not yet the time at which it can have teeth, is called neither toothed nor toothless, and the eyes of some animal, the time not yet having come at which they can see, are called neither blind nor seeing, and yet have no middle. Therefore of contraries which lack a middle there are two kinds: those which befall by turns the thing in which they can be, with no middle intervening, as health and weakness; and those which can be absent together from a substance in which they cannot be present together, and yet when they are absent together no middle intervenes, as seeing and blindness, or the habit and loss of teeth. The fourth kind of opposites is AFFIRMATION and NEGATION, as “Cicero disputes,” “Cicero does not dispute.” These differ from the above in that those can be said singly, these only when connected. From relatives they differ in that those are also said relatively, these not relatively. For one who disputes is not referred to one who does not dispute. From contraries they differ in that, if those are said connected, they are true or false only as long as that exists in which they can be present, but when this has ceased to be they are neither true nor false: as “that man is foolish” or “that man is wise,” as long as he lives one of these is true; when he has ceased to be, both are false, because he who is not can be neither foolish nor wise. But “Cicero disputes” and “Cicero does not dispute” are so opposed that while Cicero lives one of them is necessarily true, and when he is dead, what is said, that he disputes, is false, but that he does not dispute is true. In this way these are distinguished also from habit and privation. For he who is not is neither blind nor seeing. Nor should you be troubled that we seem already to have said something of propositions, of which we must speak later. For this was done on the occasion of the opposites.
A noun is that which signifies some thing and can be inflected through cases. A verb is that which signifies something and can be inflected through tenses. As Cicero is a noun, disputes a verb. These, separated from each other, signify something indeed, yet cannot be called true or false. But when they have been joined, they can then be affirmed and denied; as “Cicero disputes” can now be followed by “Cicero does not dispute.” [The nominative case of the noun and the third person of the verb ought to be present.] The first person signifies something which can now be affirmed and denied and falls only upon a man. In it the noun is understood even if it is not said, so that disputo is [wholly] complete, even if you do not say ego. Likewise the second person is itself already subject to truth or falsity but falls also upon a man, and we do not rightly say disputas to one who cannot hear or understand what is said. Therefore this too, when said without a noun, yet has the noun understood there. Otherwise we use the first or second person figuratively, as when you bring in as speaking one who cannot speak, or turn the speech to one who can neither hear nor understand.