Aristotle · a new plain-English translation from the original language
1| Sagacity is a kind of good aim at the middle term, in a time too short for reflection — for example, if someone, seeing that the moon always has its bright side turned toward the sun, quickly grasped why this is so, namely because it shines by light from the sun; or, seeing someone conversing with a rich man, recognized why he was borrowing money; or grasped that two people were friends because they were enemies of the same man. For by seeing all the middle terms, which are the causes, he recognized the extremes. Let 'having its bright side toward the sun' be A, 'shining by light from the sun' be B, and 'moon' be C. Then B, shining by light from the sun, belongs to C, the moon; and A, having its bright side toward that from which it shines, belongs to B; so that A too belongs to C, through B. B.
2| The things we seek are equal in number to the things we know. We seek four things: the fact, the reason why, whether a thing is, and what a thing is. For when we seek whether this or that is the case, casting it as a choice between alternatives — for instance, whether the sun is eclipsed or not — we are seeking the fact. Here is a sign of this: once we have found that it is eclipsed, we stop; and if from the start we know that it is eclipsed, we do not go on to ask whether it is. But when we know the fact, we seek the reason why — for instance, knowing that it is eclipsed and that the earth moves, we seek the reason it is eclipsed, or the reason the earth moves. These, then, we seek in this way; but some things we seek in another way, for instance whether or not a centaur or a god exists. And by 'whether it is or not' I mean without qualification, not whether it is white or not. But once we have learned that it is, we seek what it is — for instance, what then is a god, or what is a man. The things we seek, then, and the things we know once we have found them, are these, and this many. We seek: when we seek the fact, or whether a thing is without qualification, whether there is a middle term for it or not; and when, having come to know
3| either the fact or whether it is — whether in a particular case or without qualification — we seek again the reason why, or what the thing is, then we are seeking what the middle term is. By 'that it is,' taken in a particular case and without qualification, I mean this: in a particular case, is the moon eclipsed, or is it waxing? For where something is or is not the case of a thing, it is in cases like these that we seek it; without qualification, whether or not the moon exists, or night exists. It follows, then, that in every inquiry we seek either whether there is a middle term, or what the middle term is. For the cause is the middle term, and in every case it is this that is sought. Is it eclipsed? Is there some cause or not? After this, having learned that there is some cause, we then seek what this is. For the cause of a thing's being — not being this or that, but being a substance without qualification — or of its having some attribute not without qualification, but one belonging to it in its own right or accidentally, is the middle term. By 'without qualification' I mean the subject, for instance moon or earth or sun or triangle; by 'some attribute' I mean eclipse, equality, inequality, whether it stands in the middle or not. For in all these cases it is plain that what a thing is and why it is are the same thing.
4| What is an eclipse? A privation of light from the moon, caused by the earth's blocking it. Why is there an eclipse — or why is the moon eclipsed? Because the light fails as the earth blocks it. What is a concord? A ratio of numbers between the high note and the low. Why does the high note concord with the low? Because the high and the low stand in a ratio of numbers. Can the high and the low concord at all? Is their ratio expressible in numbers? Once we have grasped that it is, we then ask what the ratio is. That the inquiry is always for the middle term is shown by all the cases in which the middle term is perceptible. For when we have not perceived it, we seek whether the eclipse, say, is occurring or not. But if we were on the moon, we would not seek either whether it happens or why, but it would be plain at once. For from perceiving it, knowledge of the universal would also have come to be for us. For perception would tell us that the earth is now blocking the light (since it would then be plain that an eclipse is now occurring); and from this the universal would have come to be. So, as we say, to know what a thing is is the same as to know why it is — and this either without qualification, and not with respect to some attribute, or with respect to one of its attributes, as that it has two right angles, or that it is greater or less.
5| That all the things sought, then, are a seeking for a middle term, is clear. But how what a thing is is exhibited, and what the manner of the reduction to it is, and what a definition is and of what things there is one, let us now state, having first worked through the puzzles about them. Let the starting point of what follows be the one most proper to the argument now before us. For one might raise the puzzle whether it is possible to know the same thing, in the same respect, both by definition and by demonstration, or whether this is impossible. For a definition seems to be of what a thing is, and what a thing is is in every case universal and affirmative; but of syllogisms some are negative and some are not universal — for instance, all those in the second figure are negative, and those in the third figure are not universal. Further, not even of all the affirmative conclusions in the first figure is there a definition — for instance, that every triangle has angles equal to two right angles. The reason for this is that to know a demonstrable thing is to have its demonstration; so that, since there is a demonstration of such things, it is clear that there could not also be a definition of them; for then one would know the thing by the definition too, without having the demonstration — for nothing prevents one's not having both at once.
6| A sufficient proof of this comes also from induction: we have never come to know anything by defining it, neither among the things that belong to a thing in its own right nor among its accidents. Further, if a definition is a way of coming to know some substance, then it is clear that things of this sort, at least, are not substances. That there is not a definition of everything of which there is also a demonstration, then, is clear. But what of the converse: is there a demonstration of everything of which there is a definition, or not? Here too there is one and the same account. For of one thing, qua one, there is one science. So that, if to know a demonstrable thing is to have its demonstration, something impossible will follow: for someone who has the definition will have knowledge without having the demonstration. Further, the principles of demonstrations are definitions, and it has been shown earlier that there cannot be demonstrations of these — or else the principles will be demonstrable
7| and principles of principles, and this will go on to infinity, or else the first things will be undemonstrated definitions. But is it perhaps the case that, if not of every same thing, still of some one and the same thing there is both a definition and a demonstration? Or is this impossible? For there is no demonstration of that of which there is a definition. For definition is of the what-it-is and of substance; but all demonstrations evidently posit and assume the what-it-is, as the mathematical ones assume what a unit is and what the odd is, and the others likewise. Further, every demonstration shows something of something, namely that it is or that it is not; but in a definition nothing is predicated of anything else — for instance, animal is not predicated of two-footed, nor this of animal, nor indeed is figure predicated of plane, since the plane is not a figure, nor the figure a plane. Further, to show what a thing is and to show that it is are different things. So the definition makes clear what a thing is, while the demonstration shows that this holds of that, or does not hold. And of one thing there is one demonstration and of another a different one, unless one stands to the other as part to whole. By this I mean, for example, that it has been shown of the isosceles that it has angles equal to two right angles, if this has been shown of every triangle; for the isosceles is a part, the triangle the whole. But the fact that a thing is and what it is do not stand to each other in this way, for neither is a part of the other. It is clear, then, that of everything of which there is a definition there is not also a demonstration, nor of everything of which there is a demonstration is there also a definition, nor in general can the same thing have both. So it is plain that definition and demonstration could be neither the same thing nor one contained in the other; for otherwise their subjects too would stand in the same relation.
8| Let these difficulties be raised up to this point. But as to whether there is a syllogism and a demonstration of the what-it-is or not, as our argument has just now assumed — a syllogism shows something of something through a middle term; but the what-it-is is both proper to the thing and is predicated within the category of what-it-is, and these must convert with one another. For if A is proper to C, clearly it is proper to B too, and B to C, so that all convert with one another. Moreover, if A belongs to every B within the category of what-it-is, and B is said universally of every C within the category of what-it-is, then A too must be said of C within the category of what-it-is. But if one does not take it doubled in this way, it will not be necessary for A to be predicated of C within the category of what-it-is, even if A belongs to B within the category of what-it-is, unless B is so predicated of everything it holds of.
9| But the what-it-is will have both these features; so B too will be the what-it-is with respect to C. If, then, both the what-it-is and the essence hold, the essence will already belong to the middle term. And in general, if it is possible to show what man is, let C be man, and let B be the what-it-is, whether animal biped or something else. If, then, there is to be a syllogism, B must be predicated of every C; but this will require another middle term, so that this too will turn out to be what man is. So it assumes what it needs to show; for B too will be what man is. One must examine this in the case of the two premises, and among the first and immediate ones, since that is where what is being said becomes most evident. Now those who show what soul is, or what man is, or anything else that is, by means of conversion, are begging the original question — as, for example, if someone should claim that soul is that which is the cause of its own life, and that this is a number moving itself; for it is necessary to have already assumed that soul is precisely a number moving itself, treating this as being the very same thing as soul.
10| For it is not the case that, if A follows on B and B on C, A will therefore be the essence of C; it will only be true to say it of C. Nor is it the essence even if A is a 'just what' something and is predicated of every B. For being an animal is predicated of being a man (since it is true that everything a man's being is, an animal's being is too, just as every man is an animal), but not in such a way that the two are one and the same. If, then, one does not take it in this stronger sense, one will not have proved by syllogism that A is the essence and substance of C; and if one does take it in this sense, one will already have assumed in advance what the essence of C is. So nothing has been demonstrated; the very thing at issue has been assumed from the start. But neither, again, does the method proceeding through divisions amount to a syllogism, as has been said in the analysis concerning the figures. For nowhere does it become necessary that, these things being so, that thing should be so; rather it is as with one who argues by induction — he does not demonstrate either. For the conclusion should not be a matter of being asked, nor should it depend on the answerer's granting it, but
11| it must be necessary given that those other things are so, even if the one answering will not say so. Is man an animal or something inanimate? Then one takes 'animal' — but nothing has thereby been proved by syllogism. Again: every animal is either land-dwelling or water-dwelling; one takes 'land-dwelling.' And that man's whole being is 'land-dwelling animal' does not follow necessarily from what has been said; this too is simply assumed besides. And it makes no difference whether one proceeds this way over many steps or few, for it is the same thing. (So the procedure turns out to be without syllogism even for those who apply it to matters that could in fact be proved by syllogism.) For what is to prevent all of this being true of man, and yet not making clear the what-it-is or the essence? Further, what is to prevent something being added, or something taken away, or some part of the substance being passed over? Now these difficulties are indeed left unaddressed by such reasoners, but it is possible to resolve them by taking everything within the category of what-it-is, proceeding through the division in due order, positing the first term, and leaving nothing out. And this is possible, if everything falls within the division and nothing is missing; for by then the term reached must already be indivisible. But all the same it is not a syllogism; rather, if it accomplishes anything, it produces knowledge in a different way. And there is nothing strange in this, since presumably one who argues by induction does not demonstrate either, but nonetheless makes something clear. But one who states a definition arrived at by division is not thereby stating a syllogism. For just as, in conclusions given without the middle terms, if someone says that, these things being so, this must be so, one may still ask why, so it is also with definitions reached by division. What is man? A mortal animal, footed, two-footed, wingless. Why, at each addition? For he will answer, and will show by the division, as he supposes, that everything is either mortal or immortal. But an account of this whole kind is not a definition at all; so that even if it were in fact being demonstrated by the division, the definition would still not turn out to be a syllogism.
12| But is it perhaps possible after all to demonstrate the what-it-is according to substance, though only from a hypothesis — taking the essence to be that which is proper among the things within the category of what-it-is, taking these alone to belong within the category of what-it-is, and taking the whole of them together to be proper to the thing? For this is what it is for that thing to be what it is. Or has one, once again, simply assumed the essence in this too? For it is necessary to show it through the middle term.
13| Further, just as in a syllogism it is not assumed what "having reasoned syllogistically" is (for the premise from which the syllogism proceeds is always the whole or a part), so too the essence need not be present within the syllogism, but should stand apart from what is laid down; and to someone who disputes whether a conclusion has been reached or not, one should answer, "yes, for this was the syllogism"; and to someone who says the essence has not been established by syllogism, one should say, "yes it has, for this was laid down by us as the essence." So it is necessary that a syllogism, or a proof of the essence, be established of something even without the "what." And even if one demonstrates from a hypothesis — for instance: if being bad is being divisible, and being the contrary of something is being the contrary of the contrary, for all things that have some contrary; and the good is the contrary of the bad, and the indivisible is the contrary of the divisible; then it follows that being good is being indivisible — even here, in demonstrating, one takes the essence as an assumption; but one assumes it in order to demonstrate the essence of something else. Still, that is a different thing — granted; for in demonstrations too one shows that this holds of that, not that they are the same thing, nor things of which there is the same account, and it converts. But against both — against the one who demonstrates by division and against the one who reasons in this way — the same difficulty arises: why will man be a footed, two-footed animal, rather than an animal and footed and two-footed? For from what is assumed there is no necessity at all that the predicate become one thing, any more than that the same man be both musical and literate.
14| How, then, will the one who defines something show its substance, or what it is? He will not make it clear, as one demonstrating from agreed premises, that given those things something else must necessarily be so — for that is demonstration. Nor will he do it as one who reaches a conclusion by induction, through the particulars being clear, on the ground that everything is thus because nothing is otherwise; for that does not show what a thing is, but that it is or is not. What other way, then, remains? For surely he will not show it by perception, or by pointing a finger.
15| Again, how will he show what a thing is? For anyone who knows what man is, or anything else whatever, must also know that it is — for no one knows what a non-being is, but only what an account or a name signifies; when I say "goat-stag," I can know what the word signifies, but it is impossible to know what a goat-stag is. But then, if he is to show both what a thing is and that it is, how will he show this by the same account? For a definition makes clear one thing, and so does a demonstration; but what man is, and that man exists, are different. Further, we say it is necessary for everything that is to be shown by demonstration, unless it is a substance. But being is not a substance for anything, since being is not a genus. So there will have to be a demonstration that a thing is — which is in fact what the sciences do now. What "triangle" signifies, the geometer assumes; that it exists, he demonstrates. What, then, will the one defining show, other than what a triangle is? So someone who knows by a definition what a thing is will not know whether it exists. But that is impossible. And it is also clear, from the ways definitions are currently framed, that those who define do not show that the thing exists.
16| For even if there is something equal derived from the midpoint, still, why does the thing defined exist? And why is this a circle? One might just as well say it is made of orichalc. Definitions neither make clear that the thing spoken of is possible, nor that it is the very thing of which they claim to be definitions; it is always possible to ask "why." If, then, the one who defines shows either what a thing is or what the name signifies, and if it is in no way what the thing is, the definition would be an account signifying the same as a name. But that is absurd. For in the first place, there would then be definitions even of non-substances and of things that do not exist — since it is possible to signify even things that do not exist. Further, every account would then be a definition; for it would be possible to attach a name to any account whatever, so that we would all be conversing in definitions, and even the Iliad would be a definition. Again, no demonstration could ever demonstrate that this name signifies this thing; so definitions do not make that clear either. From these considerations, then, it appears that a definition and a syllogism are not the same thing, nor is a syllogism of the same thing as a definition; and further, that a definition neither demonstrates anything nor shows anything, and that what a thing is cannot be known either by definition or by demonstration.
17| We must consider again what in this is said rightly and what not rightly, and what a definition is, and whether there is in some way a demonstration and a definition of what a thing is, or none at all. Since, as we said, knowing what a thing is and knowing the cause of its existing are the same thing (the reason being that there is some cause, and this is either the same as the thing or different from it, and if different, either demonstrable or non-demonstrable) — if, then, it is different and admits of demonstration, the cause must be a middle term and must be shown in the first figure, since what is shown is universal and affirmative. One way, then, would be the one just examined: showing what a thing is through something else; for of essences the middle term must be an essence, and of proper attributes, a proper attribute. So it will show one of the two essences belonging to the same thing, but not the other. Now it has already been said that this way could not be a demonstration; but it is a dialectical syllogism of what a thing is. Let us state the way in which it is possible, speaking again from the beginning. Just as we seek the reason why when we already have the fact — and sometimes both become clear at once, though the reason why can never be known before the fact — so it is clear that likewise the essence cannot be known apart from the fact that the thing exists;
18| for it is impossible to know what a thing is while not knowing whether it exists. Now we grasp that a thing exists sometimes only accidentally, and sometimes by grasping something of the thing itself — for instance, of thunder, that it is a certain noise in the clouds; of eclipse, that it is a certain deprivation of light; of man, that he is a certain animal; of soul, that it is something that moves itself. Now in all cases where we know that a thing exists only accidentally, we are necessarily in no position at all with respect to what it is — for we do not even really know that it exists; and to seek what a thing is without grasping that it exists is to seek nothing at all. But where we grasp something of the thing, it is easier. So, as we stand with respect to whether it exists, so we stand with respect to what it is. Of the cases, then, where we grasp something of what a thing is, let the first be
19| as follows. Let eclipse be A, moon be C, and screening by the earth be B. Now to ask whether the moon is eclipsed or not is to ask whether B exists or not. And this is no different from asking whether there is an account of it; and if there is, we say that the eclipse exists too. Or again, of a pair of contradictories, to ask which one the account belongs to — whether to having two right angles or to not having them. When we find the answer, we know the fact and the reason why at the same time, if it is through immediate terms; if not, we know the fact, but not the reason why. Let moon be C, eclipse be A, and being unable, at full moon, to cast a shadow when nothing perceptible stands between us and it, be B. If, then, B — being unable to cast a shadow when nothing is between us — belongs to C, and A — having been eclipsed — belongs to B, it is clear that the moon is eclipsed, but not yet why; and we know that an eclipse exists, but not what it is. And once it is clear that A belongs to C, to ask why it belongs is to ask what B is — whether it is screening, or a turning of the moon, or an extinguishing.
20| This is the account of the other extreme term — in this case, of A. For an eclipse is a blocking of light by the earth. What is thunder? An extinguishing of fire in a cloud. Why does it thunder? Because the fire is extinguished in the cloud. Let cloud be C, thunder A, extinguishing of fire B. Then B belongs to C, the cloud (for the fire is extinguished in it), and A, noise, belongs to this; and B is indeed the account of the first extreme term. And if again there is some other middle term for this, it will come from the remaining accounts. How, then, the what-it-is is grasped and becomes known has been stated: so that there is no syllogism of the what-it-is, nor demonstration of it, yet it is made evident through syllogism and through demonstration. So that the what-it-is cannot be known without demonstration where there is some other cause of it, nor is there demonstration of it itself — as we also said in stating the difficulties. Now of some things there is some other cause, and of others there is not. So it is clear that, among the things that are a what-it-is, some are immediate and principles, which one must posit both as being and as being what they are, or else make evident in some other way
21| (which is what the arithmetician does: he posits both what the unit is, and that it is). But of those that have a middle term, and of which there is some other cause of their substance, it is possible to make this evident through demonstration, as we said, without demonstrating the what-it-is itself. Since a definition is said to be an account of the what-it-is, it is clear that one kind of definition will be an account of what a name signifies, or another, name-like account — for instance, what "triangle" signifies. Once we have this — that it is — we then look for why it is; but it is hard to grasp things in this way when we do not know that they are. The cause of this difficulty has been stated before: that we do not even know whether a thing is or not, except accidentally. (An account is one in two ways: one by conjunction, as the Iliad is one, the other by signifying one thing of one thing, not accidentally.) One kind of definition of a term, then, is the one just described; another kind of definition is an account that makes clear why a thing is. So the former signifies but does not prove, while the latter will clearly be, as it were, a demonstration of the what-it-is, differing from a demonstration in its arrangement. For it makes a difference whether one says why it thunders or what thunder is: in the one case one will say, because the fire is extinguished in the clouds; but what is thunder? A noise of fire being extinguished in the clouds. So the same account is stated in a different way — in the one way a continuous demonstration, in the other a definition.
22| (Further, a definition of thunder is: noise in the clouds; and this is the conclusion of the demonstration of the what-it-is.) The definition of immediate things is a positing of the what-it-is, undemonstrated. Definition, then, is in one sense an undemonstrated account of the what-it-is; in another, a syllogism of the what-it-is, differing from a demonstration in grammatical case; and in a third sense, the conclusion of the demonstration of the what-it-is. It is clear, then, from what has been said, both how there is demonstration of the what-it-is and how there is not, and of what things there is and of what things there is not; further, in how many ways definition is spoken of, and how it shows the what-it-is and how it does not, and of what things it holds and of what it does not; further, how it stands in relation to demonstration, and how it is and how it is not possible for the same thing to be both.
23| Since we think we have knowledge when we know the cause, and there are four causes — one, the essence; one, what things being the case make it necessary that this be; another, what first set the thing in motion; and a fourth, that for the sake of which — all of these are shown through the middle term. For that, given which something else must be, is not shown when a single premise is taken, but when two are; and this occurs when they have one middle term. So once this one thing is taken, the conclusion is necessarily so. This is clear also in the following way. Why is the angle in a semicircle right? Given what is it right? Let A be right, B half of two right angles, C the angle in a semicircle. Then the cause of the right angle belonging to C, the angle in the semicircle, is B: for this angle is equal to A, and C is equal to B, since it is half of two right angles. So, given that B is half of two right angles, it belongs to C — and this was just what it is for the angle in a semicircle to be right. And this is the same as the essence, in that this is what the account signifies. But indeed it has also been shown that the essence, that is, the middle term, is a cause.
24| Why did the Persian war come about for the Athenians? What is the cause of the Athenians being made war on? Because they invaded Sardis together with the Eretrians: for this is what first set it in motion. Let war be A, being the first to invade B, the Athenians C. Then B belongs to C: being the first to invade belongs to the Athenians. And A belongs to B: for men make war on those who first do them wrong. So A belongs to B — being made war on belongs to those who were first to begin — and this, B, belongs to the Athenians, for they were first to begin. So here too the middle term is the cause, the thing that first set the war in motion. Now of things whose cause is that for the sake of which — for instance, why does he walk about? So that he may be healthy. Why is there a house?
25| So that the furnishings may be preserved — the one is for the sake of being healthy, the other for the sake of preservation. And it makes no difference whether one asks why one must walk about after dinner, or for the sake of what one must. Let walking about after dinner be C, the food's not floating up be B, being healthy be A. Let it be posited that walking about after dinner has the effect of making the food not float up near the mouth of the stomach, and that this is healthy. For it seems that B, the not floating up of the food, belongs to C, walking about, and that A, being healthy, belongs to this. What, then, is the cause for C of A's belonging to it — the that-for-the-sake-of-which? It is B, the not floating up. And this is, as it were, an account of A: for A will be rendered in these terms. Why does B belong to C? Because this is what being in such a condition is. But one must translate the accounts into one another, and in this way each point will be more apparent. Here the comings-to-be are reversed compared to those among causes involving motion: there the middle term must come about first, but here C, the last term, comes first, and last of all the that-for-the-sake-of-which. And it is possible for the same thing to be both for the sake of something and of necessity — for instance, light through a lantern:
26| for it is also of necessity that what has smaller parts passes through the larger pores, if indeed light comes about by passing through them, and also for the sake of something, namely so that we may not stumble. Is it, then, the case that if it is possible for a thing to be, it is also possible for it to come to be — as, for instance, if it thunders because, when the fire is extinguished, it is necessary that it hiss and make noise; and also, if the Pythagoreans say so, for the sake of threatening those in Tartarus, so that they may be afraid? There are very many such cases, and especially among things constituted and composed by nature: for nature does some things for the sake of something, and others of necessity. And necessity is twofold: one kind in accordance with nature and its impulse, the other by force, contrary to impulse — as, for instance, a stone is of necessity carried both upward and downward, but not by the same necessity. But among things that come from thought, some never come about by chance — for instance a house or a statue — nor of necessity, but for the sake of something; while others also come about by luck, for instance health and safety. And it is especially in cases where a thing can turn out this way or otherwise, when the coming-to-be, not being by chance, is such that the end is good, that it comes about for the sake of something, either by nature or by craft. But nothing that comes about by luck comes about for the sake of something.
27| The same cause applies to things coming to be, things that have come to be, and things that will be, as applies to things that are (for the middle term is the cause), except that for things that are, it is a cause that is; for things coming to be, one that is coming to be; for things that have come to be, one that has come to be; and for things that will be, one that will be. For example: why has an eclipse occurred? Because the earth has come to be in the middle; it is occurring because it is occurring; it will be because it will be; and it is because it is. What is ice? Let it be taken that it is water that has solidified. Let water be C, solidified be A, and let the cause, the middle term, be B: complete failure of heat. Then B belongs to C, and to this belongs the being-solidified, which is A. Ice comes to be when B is coming to be, has come to be when B has come to be, and will be when B will be. So a cause of this sort, and that of which it is a cause, come to be together, when it comes to be, and are together, when it is; and likewise for having come to be and being about to be. But in the case of things not simultaneous, is it as we suppose, that within continuous time different things are causes of different things - one thing having come to be being the cause of this thing's coming to be, one thing about to be being the cause of that thing's being about to be, and one thing coming to be being the cause of another's coming to be, if something earlier came to be?
28| The syllogism proceeds from what came to be later (the starting-point even for these being the things that have come to be); hence it is the same with things coming to be. But it does not proceed from what is earlier - as, since this came to be, that came to be later; and likewise for what will be. For neither if the time is indefinite nor if it is determinate will it be true, from the fact that it is true to say this has come to be, to say that the later thing has come to be. For in the interval it will be false to say this, once the other has already come to be. The same account holds for what will be too: it is not the case that, since this has come to be, that will be. For the middle term must be of the same kind as its extremes - of things that have come to be, one that has come to be; of things that will be, one that will be; of things coming to be, one that is coming to be; of things that are, one that is. But between having-come-to-be and being-about-to-be there cannot be a term of the same kind.
29| Further, the intervening time can be neither indefinite nor determinate; for it will be false to make any statement within the interval. We must examine what it is that holds things together, so that after having-come-to-be, coming-to-be belongs in the facts. Or is it clear that what is coming to be is not next to what has come to be? For neither is one thing that has come to be next to another thing that has come to be; for these are limits and indivisible - just as points are not next to one another, neither are things that have come to be, for both are indivisible. Nor, for the same reason, is what is coming to be next to what has come to be; for what is coming to be is divisible, while what has come to be is indivisible. So as a line stands to a point, so does what is coming to be stand to what has come to be; for infinitely many things that have come to be are present within what is coming to be. But this must be stated more clearly in the general discussion of motion. So much, then, let this account, taken this far, say about how the middle term as cause would hold if the coming-to-be proceeds in succession. For in these cases too the middle term and the first term must be immediate. For example: A has come to be, since C has come to be (C came to be later, A earlier; C is the starting-point because it is nearer to the now, which is the starting-point of time).
30| And C has come to be, if D has come to be. So if D has come to be, A must have come to be. And the cause is this: if D has come to be, C must have come to be, and if C has come to be, A must have come to be earlier. Taking the middle term in this way, will it at some point come to rest at an immediate term, or will another always be interposed, because of infinity? For, as was said, a thing that has come to be is not next to another thing that has come to be. But nonetheless it is necessary to start from an immediate term, and from the first now. The same holds for what will be. For if it is true to say that D will be, it must be true earlier to say that A will be. And the cause of this is C; for if D will be, C will be earlier, and if C will be, A will be earlier. And likewise the division is infinite in these cases too; for things that will be are not next to one another. Here too an immediate starting-point must be taken. This is how it stands with works: if a house has come to be, stones must have been cut
31| and have come to be. Why is this? Because a foundation must have come to be, if indeed a house has come to be; and if a foundation, then stones must have come to be earlier. Again, if a house will be, likewise stones will be earlier, and this is shown through the middle term in the same way; for a foundation will be earlier. Now since we see that among things coming to be there is a kind of circular coming-to-be, this can happen, provided the middle term and the extremes follow one another; for in these cases there is conversion. It has been shown in the earlier discussions that the conclusions convert; and this is what circular means. It appears in the case of works as follows: when the earth has been wetted, vapor must come to be; when this has come to be, cloud; when this has come to be, water; and when this has come to be, the earth must have been wetted - but this was the starting-point, so it has come round in a circle; for when any one of these is present, another is present, and from that another, and from this the first. Now some things come to be universally (for they always and in every case either are so or come to be so in this way), while others do not always so come to be but for the most part - for example, not every male human grows a beard, but this happens for the most part. Of such things, the middle term too must hold for the most part. For if A is predicated universally of B, and B universally of C, then A must be predicated of C always and in every case; for this is what universal means - holding in every case and always. But it was assumed to hold for the most part; therefore the middle term too, the one for which B stands, must hold for the most part. There will, then, be immediate starting-points even among things that hold for the most part - as many as are or come to be in this way, for the most part.
32| How the what-it-is is rendered into terms, and in what way there is or is not demonstration or definition of it, has been stated earlier. Let us now say how one ought to hunt for the things predicated in the what-it-is. Among the attributes that always belong to each thing, some extend more widely, yet not outside the genus. By belonging more widely I mean whatever belongs universally to each thing, and yet also to
33| something else. For example, there is something that belongs to every triad, but also to what is not a triad - as being belongs to the triad, but also to what is not a number; while the odd belongs to every triad, and belongs more widely too (for it belongs to the pentad as well), but not outside the genus; for the pentad is a number, and nothing outside number is odd. Such attributes must be taken up to the point where just so many are taken, being first, as each belong more widely, but not all of them together belong more widely; for this combination must be the substance of the thing. For example, to every triad belong: number, the odd, being prime in both senses - both as not being measured by a number, and as not being composed of numbers. This, then, is already the triad: a number, odd, prime, and prime in this latter way. For of these, some belong to all odd numbers as well, while the last also belongs to the dyad, but all together belong to none other. Since it has been shown by us above that the things predicated in the what-it-is are universal (and universal things are necessary), and since these are what are taken as belonging to the triad - and to anything else to which they are taken in this same way, as belonging in the what-it-is - it follows that the triad would be these things of necessity.
34| That it is a substance is clear from the following. For necessarily, if this were not what it is to be a triad, this would be some genus, either named or nameless. It will then belong to more things than the triad. For let the genus be assumed to be such that, in virtue of its potentiality, it holds of more things. If then it belongs to nothing else but the atomic triads, this would be what it is to be a triad (for let this too be assumed: that the substance of each thing is the ultimate such predication that holds of the atomic individuals); so that likewise, for anything else shown in this way, what it is to be that thing will hold too. Now when one is working through some whole, one must divide the genus into the individuals that are first in form—for instance number into triad and dyad—and then try to grasp definitions of those, for instance of the straight line and the circle and the right angle; and after that, having grasped what the genus is, for instance whether it is one of the quantities or one of the qualities, study the attributes proper to it by means of the first common items.
35| For in the case of things composed out of the individuals, what follows from them will be evident from the definitions, because the definition is the starting point of everything, and the simple; and it is only to the simple things that the attributes belong in their own right, while to the others they belong on account of those. Divisions made according to the differentiae are useful for proceeding in this way; how they demonstrate has been stated earlier. They would be useful only in this way, for syllogizing what a thing is. And yet it might seem that they show nothing, but assume everything straightaway, as if one were assuming it from the start without the division. But it makes some difference which of the predicated items is predicated first and which later—for instance, to say "tame biped animal" rather than "biped tame animal." For if the whole is made of two things, and "tame animal" is some one thing, and again man, or whatever the one thing so named happens to be, is made out of this and the differentia, then in dividing one must proceed by demand accordingly. Further, it is only in this way that nothing can be left out in stating what a thing is. For when the first genus has been taken, if one then takes one of the divisions from further down, not everything will fall under it—for instance, not every animal is either whole-winged or split-winged, but every winged animal is one or the other;
36| for this is the differentia of that group. The first differentia of animal is the one into which every animal falls. And likewise for each of the others too, both the genera outside it and those under it—for instance of bird, the differentia into which every bird falls, and of fish, into which every fish falls. Proceeding in this way, then, one can know that nothing has been left out; proceeding otherwise, one is bound to leave something out, and not know it—for there is no reason why the person defining and dividing should know everything there is. And yet some say it is impossible to know the differentiae that belong to each thing without knowing each thing; and without the differentiae, they say, it is impossible to know each thing—for a thing is the same as that from which it does not differ, and other than that from which it differs. Now, in the first place, this is false: for a thing is not "other" in virtue of every differentia; many differentiae belong to things that are the same in species, but not with respect to substance nor in their own right.
37| Again, when one has grasped the opposed pair and the differentia, and that everything falls into the one or the other, and has grasped that the thing sought is in one of them, and knows this, it makes no difference whether one knows or does not know the further things of which the differentiae are also predicated. For it is clear that if one proceeds in this way and arrives at things that no longer admit of a differentia, one will have the account of the substance. And that everything falls within the division, provided the opposed terms are such that there is nothing between them, is not something one needs to postulate; for necessarily everything is in one or the other of them, if it is indeed the differentia of that genus. As for what one should aim at in constructing a definition by means of divisions, there are three things: to grasp the items predicated in what a thing is; to arrange these as to which is first and which second; and to establish that these are all of them. The first of these is possible through being able to syllogize, as with an accident, that it belongs, and to establish it by means of the genus. The proper ordering will be achieved if one grasps what is first. This will be achieved if one takes what follows on all the items while not everything follows on it; for there must be some such thing. Once this has been taken, the same method applies again to the items below: for the first of the others will be second, and third will be the first of the remaining ones;
38| for once what stands above has been removed, what remains will be first among the others. And likewise for the rest as well. That these are all of them is clear from taking the first item by division—that every animal is either this or that, and this belongs to it—and again taking the differentia of this whole, and that of the last item there is no longer a differentia, or rather that, immediately with the last differentia, the compound no longer differs in species at all. For it is clear that nothing more is added, since everything has been taken up in what the thing is, and nothing is left out; for whatever was left out would have to be either a genus or a differentia. Now the genus is the first item, together with this taken along with the differentiae; and all the differentiae are included, for there is no later one—since otherwise the last item would differ in species, but it has been stated that it does not differ. One should inquire by looking at things that are alike and undifferentiated,
39| first, what all of them have that is the same; then again in the case of others, which are in the same genus as those, but are themselves the same as one another in species, though different from the former. When it has been grasped what all of these have that is the same, and likewise for the others, one should look again at the items so grasped, to see whether they are the same, until one arrives at a single account—for this will be the definition of the thing. But if it does not converge on one thing but on two or more, it is clear that what is sought would not be some one thing, but several. For example, I mean this: if we were inquiring what greatness of soul is, we should examine some great-souled people whom we know, to see what one thing all of them have in virtue of being such. For instance, if Alcibiades was great-souled, or Achilles and Ajax, what do they all have in common? Not putting up with being insulted—for one made war, another raged, another killed himself. Again, in the case of others, Lysander say, or Socrates. If then what they have in common is being unaffected alike by good fortune and bad, I take these two traits and examine what is the same in them—both the indifference toward fortune and the refusal to endure dishonor. But if there is nothing common, there would be two species of greatness of soul.
40| Every definition is always universal; for the doctor does not prescribe what is healthy for some particular eye, but marks it off either for every eye or for a given kind. It is easier to define the particular case than the universal, which is why one should pass from particulars to universals; for equivocations too go unnoticed more in universals than in things undifferentiated from one another. And just as in demonstrations there must be a valid syllogism, so too in definitions there must be clarity. This will come about if, through what has been grasped in particular cases, one defines separately what belongs in each genus—for instance not "the similar" as a whole, but the similar in colors and in shapes, and "sharp" separately in sound—and so proceeds toward what is common, being careful not to run into an equivocation. And if one must not argue by means of metaphors, it is clear that one must not define by means of metaphors either, nor define things that are spoken of metaphorically; for otherwise one would necessarily be arguing by means of metaphors. To have the problems available, one must select the
41| ...the dissections and the divisions, and one must select in this way: positing the genus common to all the things examined — for instance, if the things examined were animals — determine what belongs to every animal; and once these are grasped, again, of what remains, determine what follows every member of the first subordinate group — for instance, if this group is bird, what follows every bird — and so on always down to the nearest group. For it is clear that we shall then be able to state the reason why the following attributes belong to the things falling under the common genus — for instance, why they belong to man or to horse. Let animal be A, let B be the attributes following every animal, and let C, D be certain animals. It is then clear why B belongs to D: because of A. And likewise for the others; and always the same account holds as we move down through the lower groups. Now, we have so far been speaking in terms of the traditionally handed-down common names, but one must not confine one's inquiry to these alone; if some other common attribute is seen to hold, one must take it up as well, and then ask to which things it attaches and what follows upon it — for instance, to the horned animals belongs having a multi-chambered stomach, and not having teeth in both jaws; and again, to which animals does having horns itself belong? For then it will be clear why the stated attribute belongs to those animals — since it belongs to them because they have horns. There is, further, another way of selecting, proceeding by analogy. For it is not possible to grasp one and the same thing to call, indifferently, the cuttlebone, the fish-spine, and the bone; yet there will be attributes following upon these too, as though there were some single nature common to them of this kind.
42| Some problems are the same because they have the same middle term — for instance, that all such cases are cases of mutual displacement. Others are the same in genus, namely those which have differences by belonging to different things, or by belonging in different ways — for instance, why there is an echo, why there is a reflected image, and why there is a rainbow; for all of these are the same problem in genus, since all are cases of reflection, but they differ in species. Others differ as problems by having their middle term fall under a further, different middle term — for instance, why does the Nile flow more heavily as the month wanes? Because the waning month is more wintry. And why is the waning month more wintry? Because the moon is failing. For these facts stand in this relation to one another.
43| Concerning the cause and that of which it is the cause, one might raise the puzzle: whenever the effect is present, is the cause also present? (Just as, if a plant sheds its leaves, or the moon is eclipsed, the cause of the eclipse or of the leaf-shedding will also be present — for instance, if the effect in question is having broad leaves, and the cause of the eclipse is the earth's being in the middle; for if the cause is not present, something else will be the cause of these effects.) And, conversely, if the cause is present, is the effect present at the same time? (For instance, if the earth is in the middle, the moon is eclipsed; or if a plant is broad-leaved, it sheds its leaves.) And if this is so, would cause and effect exist together and be demonstrated through each other? Let leaf-shedding be A, being broad-leaved be B, and vine be C. If, then, A belongs to B (for every broad-leaved plant sheds its leaves), and B belongs to C (for every vine is broad-leaved), then A belongs to C, and every vine sheds its leaves. And the cause is B, the middle term. But it is also possible to demonstrate, through leaf-shedding, that the vine is broad-leaved. Let D be broad-leaved, E be leaf-shedding, and vine be F.
44| To F, then, E belongs (for every vine sheds its leaves), and to E, D belongs (for everything that sheds its leaves is broad-leaved); therefore every vine is broad-leaved. And the cause here is leaf-shedding. But if it is not possible for two things to be causes of each other — for the cause is prior to that of which it is the cause, and the cause of the eclipse is the earth's being in the middle, whereas the earth's being in the middle is not the cause of the eclipse — then, since demonstration through the cause gives the reason why, while demonstration not through the cause gives only the fact that, in the second case one knows that the earth is in the middle, but not why. And it is evident that leaf-shedding is not the cause of the earth's being in the middle, but rather this is the cause of leaf-shedding; for in the account of eclipse, the earth's being in the middle is contained, so that it is clear that it is through this that the other is known, and not this through that. But is it possible for one thing to have several causes? Indeed it is, if the same attribute can be predicated primitively of several subjects. Let A belong primitively to B, and also, as another primitive case, to C, and let B and C belong to D and E respectively. Then A will belong to D and E. And the cause is B for D, and C for E.
45| So that when the cause is present, the effect is of necessity present; but when the effect is present, it is not necessary that every possible cause be present — some cause is present, but not every one. Or is it rather this: since the problem is always universal, the cause too is some whole, and that of which it is the cause is likewise universal? For instance, leaf-shedding is marked off as belonging to some whole kind, even if there are species of it, and is universal with respect to these — either to plants in general, or to plants of a certain kind; so that the middle term must be equal in extension both to these subjects and to that of which it is the cause, and must be convertible with it. For instance, why do trees shed their leaves? If it is because of the congealing of the sap, then, if a tree sheds its leaves, congealing must be present in it, and if congealing is present — not in just anything, but in a tree — then leaf-shedding must follow.
46| Is it possible for the same effect not to have the same cause in every instance, but a different one, or is this not possible? If the conclusion has been demonstrated in its own right, and not by way of a sign or an accident, this is not possible; for the middle term is the account of the extreme term. But if it has not been demonstrated in this way, it is possible. It is also possible to examine that of which something is the cause with respect to accident, though such connections are not thought to be genuine problems. But where the demonstration is not in its own right, the middle term will behave correspondingly: if the extreme terms are equivocal, the middle term is equivocal; if they belong as falling under one genus, the middle term will behave in the same fashion. For instance, why does proportion hold by alternation as well as by simple ratio? The cause is different in the case of lines and of numbers, and yet the same too — different insofar as the subject is a line, but the same insofar as it has an increase of a certain kind. And so it is in every such case. But of things being alike in color and alike in shape, the cause is different for the one and for the other. For 'alike' is equivocal in these cases: in the one case it means, perhaps, having proportional sides and equal angles, while in the case of colors it means that the perception of them is one, or something else of that kind. But things that are the same by analogy will also have their middle term by analogy. And the cause, that of which it is the cause, and that to which it belongs, accompany one another in the following way. Taking each singly, that of which something is the cause extends more widely than the cause itself — for instance, having exterior angles equal to four right angles extends more widely than triangle or square — but taken all together, it is equal in extension to it, since it holds of all and only the things that have exterior angles equal to four right angles. And the middle term behaves in the same way. The middle term is an account —
47| ...of the first extreme term. That is why all the sciences come about through definition. For instance, shedding of leaves goes together with the vine, and applies more widely than the vine; it goes together with the fig tree too, and again applies more widely — but it does not exceed them all — with the whole class it is coextensive. If, then, you take the first middle term, it is the account of shedding leaves. For there will first be a middle term on one side, namely that all such plants have such-and-such a feature; and then a middle term for this, namely that the sap congeals, or something else of that kind. And what is shedding of leaves? The congealing of the sap at the point where the seed is attached. In the case of figures, this is how one should set the matter out for those inquiring into the coextension of the cause and that of which it is the cause. Let A hold of all B, and let B hold of each of the Ds, but of more things besides. Then B would be universal to the Ds — for I call universal that which does not convert, but the primary universal is that of which, while no single term converts with it, all the terms together do convert with it and extend equally. So for the Ds, B is the cause of A. A must therefore extend more widely than B; otherwise, why would this be the cause of that rather than the reverse? If, then, A holds of all the things wider than the Ds, there will be some single thing, other than B, that is the cause for those. For if not, ...that A holds of everything of which E holds, but E does not hold of everything of which A holds? For why will there not be some cause why A holds of all of them, just as there was for the Ds? But will those wider things also form some single thing? This must be examined; let it be called C. It is possible, then, for there to be several causes of one and the same thing, but not for things that are the same in species — for instance, of being long-lived: in four-footed animals the cause is not having bile, in winged animals it is being dry, or something else of that kind. But if the inquirers do not arrive at once at the indivisible term, and
48| the middle term is not one but several, then the causes too are several. But which of the middle terms is the cause — the one nearer to the primary universal, or the one nearer to the particular, for the particulars? Clearly it is the one nearest to each thing that is its cause. For this is the cause of the primary universal's holding beneath it — for instance, C is the cause of B's holding of D. So for D, C is the cause of A; for C, it is B; and for B, it is B itself.
49| Concerning syllogism and demonstration, then — what each of them is and how it comes about — this is now clear, and at the same time also concerning demonstrative knowledge, since it is the same thing. But concerning the principles — how they become known, and what the knowing state of mind is — this will become clear once we have first worked through some preliminary difficulties. We have said before that it is not possible to have knowledge through demonstration without knowing the primary, immediate principles. But as for the knowledge of immediates, one might raise the difficulty whether it is the same kind of knowledge as demonstrative knowledge or not the same; and whether there is knowledge of each of the two, or knowledge of the one and some other kind of thing for the other; and whether the states are not present in us and come to be, or are present in us without our noticing. Now if we already possess them, it is absurd — for it follows that we possess pieces of knowledge more exact than demonstration without our having noticed it. But if we acquire them without having had them before, how could we come to know and learn them except from pre-existing knowledge? For that is impossible, as we said also concerning demonstration. It is clear, then, that it is not possible either to possess them, or for them to come to be in people who are ignorant and possess no state of mind at all. We must therefore possess some capacity, but not one so constituted as to outrank these principles in exactness. And this evidently belongs to all animals. For they possess an innate discriminating capacity, which is called perception. And when perception is present, in some animals a retention of what was perceived comes about, and in others it does not. Now for those in which it does not come about, there is no knowledge outside of perceiving — either at all, or with respect to the things for which it does not come about; but for those in which, once they have perceived, the perceived object still remains present in the soul, knowledge does come about. And when many such retentions come about, a further difference then arises, so that for some a rational account comes about from the persistence of such things, while for others it does not.
50| From perception, then, memory comes about, as we say; and from memory, when it occurs often of the same thing, experience — for memories that are many in number amount to a single experience. And from experience, or from the whole universal that has come to rest in the soul — the one over and above the many, whatever is one and the same in all of those particulars — comes the starting point of craft and of knowledge: of craft, if it concerns coming-to-be; of knowledge, if it concerns what is. So these states are neither present in us already determinate, nor do they come about from other states that are more knowing than they are; rather they come from perception — as in a battle, when a rout occurs, if one man makes a stand, another stands too, and then another, until it reaches the starting point. And the soul is of such a nature as to be capable of undergoing this. What was said just now, though not clearly, let us say again. When one of the undifferentiated items has made a stand, there is a first universal present in the soul — for although what one perceives is the particular, perception is of the universal, for instance of man, not of Callias the man. Again a stand is made among these, until the partless items — the universals — make their stand; for instance, such-and-such a species of animal, until one reaches animal, and so likewise for this.
51| It is clear, then, that we must come to know the primary things by induction; for this is in fact how perception instills the universal as well. Now among the states of mind by which we grasp the truth, some are always true, while others admit falsehood — for instance opinion and calculation — but knowledge and intellect are always true, and no other kind of thing is more exact than knowledge except intellect. And the principles of demonstrations are more familiar than what follows from them, while all knowledge involves an account. There could not, then, be knowledge of the principles; but since nothing can be truer than knowledge except intellect, there would be intellect of the principles — this follows both from these considerations, and from the fact that the principle of a demonstration is not itself a demonstration, so that the principle of knowledge is not itself knowledge. If, then, we possess no other kind of thing that is true besides knowledge, intellect would be the principle of knowledge. And it would be the principle of the starting point, while knowledge as a whole stands in a similar relation to its whole subject matter.