[5] Or, first, is the other argument any better fitted to the universal than to the particular case? For if two right angles belong not as isosceles but as triangle, one who knows that the isosceles has two right angles will know it less well as such than one who knows that a triangle has two right angles.

And in general, if it does not hold as triangle and yet someone proves it, this will not be a demonstration; and if it does, it is the man who knows a thing as it [10] belongs who knows it better. Thus if triangle extends further, and there is the same account and triangles are not so called in virtue of a homonymy, and two right angles belong to every triangle, it will not be that the triangle has two right angles as isosceles but that the isosceles has such angles as triangle. Hence one who knows universally knows it better as it belongs than one who knows it particularly. [15] Therefore the universal demonstration is better than the particular.

Again, if there is some single account and the universal is not a homonymy, it will be some thing no less than some of the particulars, but actually more so, inasmuch as what is imperishable is among the former and it is rather the particulars that are perishable. And again, there is no necessity to believe that this is [20] a thing apart from the particulars on the grounds that it makes one thing clear, any more than in the case of the other things which do not signify an individual but either quality or quantity or relation or doing. If, therefore, this is believed, it is not the demonstration but the audience which is responsible.

Again, if demonstration is a probative deduction of an explanation and the reason why, and the universal is more explanatory (for that to which something [25] belongs in itself, is itself explanatory for itself; and the universal is primitive: therefore the universal is explanatory); hence the universal demonstration is better; for it is more a demonstration of the explanation and the reason why it is the case.

Again, we seek the reason why up to this point, and it is then we think we know, when it is not the case that this either comes about or is because something else does; [30] for the last term is in this way an end and a limit. E.g. with what aim did he come? So as to get the money—and that so as to give back what he owed; and that so as not to be dishonest. And going on in this way, when it is no longer because of something else or with some other aim, we say it is because of this as an end that he came (and that it is and that it came about) and that then we best know why he came. Thus if [35] the same goes for all explanations and reasons why, and in the case of explanations in terms of aim we know best in this way—in the other cases too, therefore, we then know best when this no longer belongs to it because it is something else. So when we are aware that the external angles are equal to four right angles because it is isosceles, it still remains to ask why the isosceles is so because it is a triangle, and [86a1] that because it is a rectilineal figure. And if this is no longer the case because it is something else, it is then we know best. And it is then too that it is universal; therefore the universal demonstration is better.

Again, the more particular a demonstration is, the more it falls into what is [5] indefinite, while the universal tends to the simple and the limit. And as indefinite, things are not understandable; but as finite they are understandable. Therefore they are more understandable as universal than as particular. Therefore universals are more demonstrable. And of more demonstrable things there is more of a demonstration; for correlatives vary in degree together. Therefore the universal demonstration is better, since it is more of a demonstration. [10]

Again, if a demonstration in virtue of which one knows this and something else is preferable to one in virtue of which one knows this alone; and one who has the universal demonstration knows the particular fact too, but the latter does not know the universal fact31—hence in this way too it will be preferable.

Again, as follows: to prove more universally is to prove through a middle term that is nearer to the principle. The immediate is nearest, and this is a principle. So if [15] a demonstration depending on a principle is more precise than one not depending on a principle, a demonstration more dependent on a principle is more precise than one less so; and the more universal demonstration is of such a type; therefore the universal will be superior. E.g. if you had to demonstrate A of D; the middle terms are B, C: well, B is higher, so that the demonstration through it is more [20] universal.

But some of the things we have said are general. It is most clear that universal demonstration is more important from the fact that grasping the prior of the propositions we have in a sense the posterior one too and we grasp it potentially. E.g. if someone knows that every triangle has two right angles, he knows in a sense of the [25] isosceles too that it has two right angles—potentially—even if he does not know of the isosceles that it is a triangle. But one who grasps the latter proposition does not know the universal in any sense, neither potentially nor actually.

And the universal proposition is comprehensible, while the particular terminates in perceptions. [30]

25 · So much, then, for the view that universal demonstration is better than particular; that probative is better than negative is clear from what follows.

Let that demonstration be better which, other things being equal, depends on fewer postulates or suppositions or propositions. For if they are equally familiar, [35] knowing will come about more quickly in this way; and that is preferable.

The argument for the proposition that the one depending on fewer things is better is, put universally, this: if it is the case that the middle terms are equally familiar, and the prior terms are more familiar, let the one demonstration show that A belongs to E through middle terms B, C, D, and the other that A belongs to E through F, G. Thus that A belongs to D and that A belongs to E are similar. But that [86b1] A belongs to D is prior to and more familiar than the proposition that A belongs to E; for the latter is demonstrated through the former, and that through which a thing [5] is demonstrated is more convincing. Therefore the demonstration through the fewer items is better, other things being equal.

Now both are proved through three terms and two propositions, but the one assumes that something is the case and the other both that something is and that something is not the case; therefore it is through more items, so that it is worse.

[10] Again, since it has been proved that it is impossible for a deduction to come about when both propositions are negative, but that one must be so and the other to the effect that something belongs, in addition to that one must assume this: the affirmative propositions, as the demonstration increases, necessarily become more numerous, whereas it is impossible for the negatives to be more than one in any [15] deduction.

For let A belong to none of the B’s and B belong to every C. Well, if we must again increase both propositions, a middle term must be interpolated. Let it be D for A B, and E for B C. Well, it is evident that E is affirmative, and that D is affirmative [20] of B but lies as negative towards A. For D holds of every B, and A must belong to none of the D’s. So a single negative proposition, A D, comes about.

The same holds of the other deductions too. For the middle for the affirmative [25] terms is always affirmative both ways; but for the negative it is necessarily negative in one way, so that this comes to be the single such proposition and the others are affirmative.

Thus if that through which something is proved is more familiar and more convincing, and the negative demonstration is proved through the affirmative while the latter is not proved through the former, then, being prior and more familiar and more convincing, the affirmative will be better.

[30] Again, if the universal immediate proposition is a principle of deduction, and the universal proposition is affirmative in the probative demonstration and negative in the negative, and the affirmative is prior to and more familiar than the negative [35] (for the negation is familiar because of the affirmation, and the affirmation is prior, just as being the case is prior to not being the case)—hence the principle of the probative is better than that of the negative; and the one which uses better principles is better.

Again, it is more principle-like; for without the probative there is no negative.

[87a1] 26 · Since affirmative demonstration is better than negative, it is clear that it is also better than demonstration leading to the impossible. But we must know what is the difference between them.

Well, let A belong to no B and B to every C; thus it is necessary for A to belong [5] to no C. Now if things are assumed in this way, the negative demonstration that A does not belong to C will be probative. The demonstration leading to the impossible goes thus: if we should have to prove that A does not belong to B, we must assume that it does belong and that B belongs to C, so that it results that A belongs to C. Let [10] it be familiar and agreed that this is impossible. Therefore it is not impossible for A to belong to B. So if B is agreed to belong to C, it is impossible for A to belong to B.

So the terms are similarly arranged, and the difference is a matter of which negative proposition is the more familiar—that A does not belong to B or that A [15] does not belong to C. Now when the conclusion (that it is not the case) is more familiar, demonstration to the impossible comes about; but when the proposition in the deduction is more familiar, we have demonstrative demonstration. By nature the proposition A B is prior to A C. For that on which the conclusion depends is prior to the conclusion; and that A does not belong to C is a conclusion, whereas that A does not belong to B is something on which the conclusion depends. For it is not the [20] case that if it happens that something is disproved, then this is a conclusion and those are what it depends on; but what a deduction depends on is whatever is so related as to be related as whole to part or part to whole—and the propositions B C and A B32 are not so related to one another.

So if the demonstration depending on what is more familiar and prior is [25] superior, and in both cases conviction depends on something’s not being the case, but in the one on something prior and in the other on something posterior, then the negative demonstration will be better simpliciter than the one to the impossible; hence the affirmative, which is better than this, is clearly also better than the one to the impossible. [30]

27 · One science is more precise than another and prior to it both if it is at the same time of the fact and of the reason why and not of the fact separately from the science of the reason why; and if it is not said of an underlying subject and the other is said of an underlying subject (e.g. arithmetic and harmonics); and if it depends on fewer items and the other on an additional posit (e.g. arithmetic and geometry). (I mean by on an additional posit, e.g. a unit is a positionless [35] substance, and a point a substance having position—the latter depends on an additional posit.)

28 · A science is one if it is of one genus—of whatever things are composed from the primitives and are parts or attributes of these in themselves. One science is different from another if their principles depend neither on the same thing nor the ones on the others. There is evidence for this when one comes to the non-demonstrables; [87b1] for these must be in the same genus as the things demonstrated. And there is evidence for this when the things that are proved through them are in the same genus and of a kind.

29 · It is possible for there to be several demonstrations of the same thing [5] not only if one takes a non-continuous middle term from the same chain—e.g. C and D and F for A B—but also if one takes a middle term from a different chain. E.g. let A be altering, D changing, B enjoying, and again G coming to rest. Now it is true to predicate both D of B and A of D; for the man who is enjoying himself is changing, [10] and what is changing is altering. Again, it is true to predicate A of G and G of B; for everyone who is enjoying himself is coming to rest, and one who is coming to rest is altering. Hence the deduction is through middle terms that are different and not from the same chain—yet not in such a way that neither of the middle terms is said of the other; for it is necessary for them both to belong to some one thing. Inquire [15] in how many ways it is possible for a deduction of the same thing to come about through the other figures.

30 · There is no understanding through demonstration of what holds by [20] chance. For what holds by chance is neither necessary nor for the most part, but what comes about apart from these; and demonstration is of one or other of these. For every deduction is either through necessary or through for the most part propositions; and if the propositions are necessary, the conclusion is necessary too; [25] and if for the most part, the conclusion too is such. Hence if what happens by chance is neither for the most part nor necessary, there will not be demonstration of it.

31 · Nor can one understand through perception. For even if perception is of [30] what is such and such, and not of individuals, still one necessarily perceives an individual and at a place and at a time, and it is impossible to perceive what is universal and holds in every case; for that is not an individual not at a time; for then it would not be universal—for it is what is always and everywhere that we call universal.

So, since demonstrations are universal, and it is not possible to perceive these, [35] it is evident that it is not possible to understand through perception either; but it is clear that even if one could perceive of the triangle that it has its angles equal to two right angles, we would seek a demonstration and would not, as some say, understand it; for one necessarily perceives particulars, whereas understanding comes by becoming familiar with the universal.

That is also why if we were on the moon and saw the earth screening it we [88a1] would not know the explanation of the eclipse. For we would perceive that it is eclipsed and not why at all; for there turned out to be no perception of the universal. Nevertheless, if, from considering this often happening, we hunted the universal, we would have a demonstration; for from several particulars the universal is clear.

[5] The universal is valuable because it makes clear the explanation; hence universal demonstration is more valuable than perception and comprehension33—with regard to those things whose explanation is something different; but for the primitives there is a different account.

So it is evident that it is impossible by perceiving to understand anything [10] demonstrable—unless someone calls this perceiving: having understanding through demonstration.

Yet some of our problems are referred to want of perception; for in some cases if we saw we should not seek—not on the grounds that we knew by seeing, but that we grasped the universal from seeing. E.g. if we saw the glass to be perforated and [15] the light coming through it, it would also be clear why it does, even if seeing34 occurs separately for each piece of glass while comprehending grasps at one time that it is thus in every case.

32 · It is impossible for all deductions to have the same principles. First, let us consider it in general terms.

Some deductions are true and some false. For even if it is possible to reduce a [20] truth from falsehoods, yet this only comes about once. E.g. if A is true of C, and the middle, B, is false (for A does not belong to B nor B to C); but if middle terms are assumed for these propositions they will be false, because every false conclusion [25] depends on falsehoods, while true conclusions depend on truths, and the truths and the falsehoods are different.

Next, not even falsehoods depend on the same things as one another; for there are falsehoods which are actually contrary to one another and cannot be the case together—e.g. that justice is injustice or cowardice, and that the man is a horse or a cow, and that what is equal is greater or less. [30]

From what we have laid down we argue as follows: not even all truths have the same principles. For the principles of many of them are different in genus and do not apply—e.g. units do not apply to points, for the former do not have the position while the latter do. But it is necessary for them to apply either as middle terms or from above or from below, or for some of the terms to be inside and some [35] outside.

Nor is it possible for there to be some of the common principles from which everything will be proved. (I call common e.g. that everything is affirmed or denied.) For the genera of the things there are are different, and some predicates [88b1] belong to quantities and some to qualities alone, with the help of which proofs are conducted through the common items.

Again, the principles are not much fewer than the conclusions; for the propositions are principles, and the propositions are formed either by taking an [5] additional term or by interpolating one.

Again, the conclusions are infinite, the terms finite.

Again, some principles are necessary and others possible.

Now if we inquire in this way, it is impossible for them to be the same and finite if the conclusions are infinite. If anyone means it in some other way, e.g. that [10] these are the principles of geometry, these of calculations, these of medicine, what else will he be saying other than that the sciences have principles? It is ridiculous to say they are the same because they are the same as themselves—for in this way everything comes to be the same.

Nor yet is the contention that anything is proved from everything the same as [15] seeking the same principles for everything; for that is too silly. For neither does this come about in the evident parts of mathematics, nor is it possible on analysis; for the immediate propositions are principles, and a different conclusion comes about if an additional immediate proposition is taken. And if someone were to say that it is the [20] primitive immediate propositions that are principles, then there is one in each genus.

If it is claimed neither that anything must be proved from all of them, nor that they are different in the sense of being different for each science, it remains to consider whether the principles of everything are of the same kind, but this depends on these and this on these. It is evident that this too is not possible; for it has been [25] proved that the principles of things different in genus are different in genus. For the principles are twofold, those from which and those about which; now while those from which are common, those about which are proper—e.g. number, magnitude.

[30] 33 · What is understandable, and understanding, differ from what is opinable, and opinion, because understanding is universal and through necessities, and what is necessary cannot be otherwise. But there are some things which are true and are the case, but which can also be otherwise. So it is clear that understanding is [35] not about these things; for then what can be otherwise could not be otherwise. But nor is comprehension concerned with them—for by comprehension I mean a principle of understanding—nor is non-demonstrative understanding (this is belief in an immediate proposition). But it is comprehension and understanding and [89a1] opinion and what is named from these that are true; hence it remains that opinion is about what is true or false but can also be otherwise. This is belief in a proposition which is immediate and not necessary.

[5] And this agrees with the appearances; for opinion is unstable, and so too is the nature of the things in question. In addition, no one thinks that he opines when he thinks that it is impossible for it to be otherwise, but that he understands; but when he thinks that it is so but that nothing prevents if from being otherwise, then he [10] thinks he opines, supposing opinion to be about that sort of thing and understanding about what is necessary.

So how can one opine and understand the same thing? and why will not opinion be understanding if one posits that it is possible to opine everything that one knows? For the knower and the opiner will follow one another through the middle terms until they come to the immediates; so that since the former knows, the opiner too [15] knows. For just as one can opine the fact, so too one can opine the reason why; and that is the middle term.

Or if he believes what cannot be otherwise in the way in which he does the definitions through which the demonstrations come about, will he not opine but understand? While if he believes that they are true but not that they belong to them [20] in virtue of their substance and in virtue of their form, he will opine and not truly understand—both the fact and the reason why if he opines through the immediates, but if not through immediates, he will opine only the fact.

There is not opinion and understanding of the same thing in every sense; but just as there is in a way both false and true opinion of the same thing, so there is both [25] understanding and opinion of the same thing. For if there is true and false opinion of the same thing in the way some say, it results that one is committed to absurdities, and in particular to the absurdity that a man does not opine what he opines falsely. But since things are called the same in several ways, in a sense it is possible and in a [30] sense it is not. For to opine truly that the diagonal is commensurate is absurd; but because the diagonal about which the opinions are is the same, in this way they are of the same thing—but what it is to be each of them in respect of its account is not the same.

Similarly, there is both knowledge and opinion of the same thing. For the one is of animal in such a way that it cannot not be an animal, and the other in such a way that it can be—e.g. if the one is of just what is man, and the other of man but not of [35] just what is man. For it is the same because man is the same, but the manner is not the same.

It is also evident from this that it is not possible to opine and to understand the same thing at the same time. For one would at the same time hold the belief that the same thing can be otherwise and cannot be otherwise, which is not possible. For in [89b1] different men it is possible for there to be each of these attitudes with regard to the same thing, as has been said; but in the same man it is not possible even in this way; for he will at the same time hold a belief, e.g. that a man is just what is an animal (for this is what it was for it not to be possible for something not to be an animal), and that man is not just what is an animal (for let that be what it is for it to be [5] possible).

As for how the rest should be distributed among thought and comprehension and understanding and skill and prudence and wisdom—that is rather the task partly of nature and partly of moral theory.

34 · Acumen is a talent for hitting upon the middle term in an imperceptible [10] time; e.g. if someone sees that the moon always holds its bright side toward the sun and quickly grasps why this is—because it gets light from the sun; or he is aware that someone is talking to a rich man because he is borrowing from him; or why they are friends—because they are enemies of the same man. For seeing the extremes he [15] becomes familiar with all the explanatory middle terms.

The bright side’s being toward the sun, A: getting light from the sun, B; the moon, C. Well, B, getting light from the sun, belongs to C, the moon; and A, the bright side’s being toward that from which it gets light, to B; hence A belongs to C, through B. [20]

BOOK II

1 · The things we seek are equal in number to those we understand. We seek four things: the fact, the reason why, if it is, what it is.

For when we seek whether it is this or this, putting it into a number (e.g. [25] whether the sun is eclipsed or not), we seek the fact. Evidence for this: on finding that it is eclipsed we stop; and if from the start we know that it is eclipsed, we do not seek whether it is. When we know the fact we seek the reason why (e.g. knowing that it is eclipsed and that the earth moves, we seek the reason why it is eclipsed or [30] why it moves).

Now while we seek these things in this way, we seek some things in another fashion—e.g. if a centaur or a god is or is not (I mean if one is or not simpliciter and not if one is white or not). And knowing that it is, we seek what it is (e.g. so what is a god? or what is a man?). [35]

2 · Now what we seek and what on finding we know are these and thus many. We seek, whenever we seek the fact or if it is simpliciter, whether there is or is not a middle term for it; and whenever we become aware of either the fact or if it [90a1] is—either partially or simpliciter—and again seek the reason why or what it is, then we seek what the middle term is. (I mean by the fact that it is partially and simpliciter—partially: Is the moon eclipsed? or is it increasing? (for in such cases we seek if it is something or is not something); simpliciter: if the moon or night is or [5] is not.) It results, therefore, that in all our searches we seek either if there is a middle term or what the middle term is.

For the middle term is the explanation, and in all cases that is sought. Is it eclipsed?—Is there some explanation or not? After that, aware that there is one, we [10] seek what this is. For the explanation of a substance being not this or that but simpliciter, or of its being not simpliciter but one of the things which belong to it in itself or accidentally—that is the middle term. I mean by simpliciter the underlying subject (e.g. moon or earth or sun or triangle) and by one of the things eclipse, equality, inequality, whether it is in the middle or not.

For in all these cases it is evident that what it is and why it is are the same. [15] What is an eclipse? Privation of light from the moon by the earth’s screening. Why is there an eclipse? or Why is the moon eclipsed? Because the light leaves it when the earth screens it. What is a harmony? An arithmetical ratio between high and [20] low. Why does the high harmonize with the low? Because an arithmetical ratio holds between the high and the low. Can the high and the low harmonize?—Is there an arithmetical ratio between them? Assuming that there is, what then is the ratio?

That the search is for the middle term is made clear by the cases in which the [25] middle is perceptible. For if we have not perceived it, we seek, e.g. for the eclipse, if there is one or not. But if we were on the moon we would seek neither if it comes about nor why, but it would be clear at the same time. For from perceiving, it would come about that we knew the universal too. For perception tells us that it is now [30] screening it (for it is clear that it is now eclipsed); and from this the universal would come about.

So, as we say, to know what it is is the same as to know why it is—and that either simpliciter and not one of the things that belong to it, or one of the things that belong to it, e.g. that it has two right angles, or that it is greater or less.

[35] 3 · Now, that everything we seek is a search for a middle term is clear; let us now say how one proves what a thing is, and what is the fashion of the reduction, [90b1] and what definition is and of what, first going through the puzzles about them. Let the start of what we are about to say be whatever is most appropriate to the neighbouring arguments.

A man might puzzle over whether one can know the same thing in the same respect by definition and by demonstration, or whether that is impossible.

For definition seems to be of what a thing is, and what a thing is is in every case [5] universal and affirmative, but deductions are some of them negative and some not universal—e.g. those in the second figure are all negative and those in the third not universal.

Next, there is not definition even of all the affirmatives in the first figure—e.g. that every triangle has angles equal to two right angles. The argument for this is that to understand what is demonstrable is to have a demonstration; so that since [10] there is demonstration of such things, clearly there will not also be definition of them—for someone might understand them in virtue of the definition without having the demonstration; for nothing prevents him from not having them together.

An induction, too, is sufficiently convincing; for we have never yet become aware of anything by giving a definition—neither of anything belonging in itself nor [15] of any accidental.

Again, if definition is becoming familiar with some substance, it is evident that such things are not substances.

So it is clear that there is not definition of everything of which there is demonstration.

Well then, is there demonstration of everything of which there is definition, or not?

Well, one argument is the same in this case too. For of one thing, as one, there [20] is one mode of understanding. Hence, if to understand what is demonstrable is to have a demonstration, something impossible will result; for anyone who has the definition without the demonstration will understand.

Again, the principles of demonstrations are definitions, and it has been proved [25] earlier that there will not be demonstrations of these—either the principles will be demonstrable and there will be principles of the principles, and this will go on ad infinitum, or the primitives will be non-demonstrable definitions.

But if the objects of definition and demonstration are not all the same, are some of them the same? or is this impossible? For there is no demonstration of that of which there is definition. For definition is of what a thing is and of substance; but [30] all demonstrations evidently suppose and assume what a thing is—e.g. mathematical demonstrations assume what a unit is and what odd, and the others similarly.

Again, every demonstration proves something of something, i.e. that it is or is not; but in a definition one thing is not predicated of another—e.g. neither animal of [35] two-footed nor this of animal, nor indeed figure of plane (for plane is not figure nor is figure plane).

Again, proving what a thing is and that it is are different. So the definition makes clear what it is, and the demonstration that this is or is not true of that. And [91a1] of different things there are different demonstrations—unless they are related as a part to the whole (I mean by this that the isosceles has been proved to have two right angles if every triangle has been proved to be so; for one is a part and the other a whole). But these things—that it is and what it is—are not related to one another in [5] this way; for neither is part of the other.

It is evident, therefore, that neither is there demonstration of everything of which there is definition, nor is there definition of everything of which there is demonstration, nor in general is it possible to have both of the same thing. Hence it [10] is clear that definition and demonstration are neither identical nor the one included in the other; for then their underlying subjects would be similarly related.

4 · Now so much for these puzzles; but is there deduction and demonstration of what a thing is, or is there not, as the argument just now supposed?

For deduction proves something of something through the middle term. But [15] what a thing is both is proper to it and is predicated in what it is. And these necessarily convert; for if A is proper to C it is clear that it is also proper to B and this to C; so that all are proper to one another. And if A belongs to every B in what it [20] is, and B is said universally of every C in what it is, necessarily A is said of C in what it is. But if you do not assume them in this double way, it will not be necessary for A to be predicated of C in what it is (if A holds of B in what it is, but of what B is said of B does not hold in what it is). But both these will contain what it is; therefore B [25] too will hold of C in what it is.

Thus if both contain what a thing is and what it is to be it, what it is to be it will be prior in the case of the middle term. And in general if one can prove what a man is, let C be man, and A what man is—whether two-footed animal or something else. If, then, it is deduced, it is necessary for A to be predicated of every B, and there will [30] be an intermediate account other than this,35 so that this too will be what man is. So you assume what you have to prove; for B is what man is.

We must inquire in the case of two propositions and of what is primitive and immediate; for there what we are saying becomes especially evident.

[35] Now those who prove through conversion what soul is, or what man is, or anything else that there is, postulate the point at issue—e.g. if someone were to claim that soul is what is explanatory of its own being alive, and that this is a number that moves itself; for it is necessary to postulate that soul is just what is a [91b1] number that moves itself, in the sense of its being the same thing.

For it is not the case that if A follows B and this C, A will be what it is to be C, but it is true36 to say only A will be C—even if A is just what is some B and is [5] predicated of every B. For what it is to be an animal is predicated of what it is to be a man (for it is true that every case of what it is to be a man is what it is to be an animal, just as every man is an animal), but not in the sense of their being one thing.

If, then, you do not assume in this way, you will not deduce that A is what it is to be C and its substance; and if you do assume in this way, you will already have [10] assumed what is what it is to be C, viz. B. Hence it has not been demonstrated; for you have assumed the point of issue.

5 · But neither does the method of division deduce, as we said in our analysis of the figures.37 For it nowhere becomes necessary for the object to be that if these are the case—just as someone who is giving an induction does not demonstrate. For [15] one must not ask the conclusion, nor must it be the case by being granted; but it is necessary for it to be the case if those are the case, even if the answerer denies it.

Is man an animal or inanimate? If38 he assumed animal, he has not deduced it. Again, every animal is either terrestrial or aquatic: he assumed terrestrial. And that man is the whole—a terrestrial animal—is not necessary from what he has said, but [20] he assumes this too. It makes no difference whether he does this in many steps or in few; for it is the same. (Indeed those who proceed in this way actually make non-deductive use even of what can be deduced.) For what prevents all this from being true of man yet not making clear what a man is or what it is to be a man? [25] Again, what prevents you from positing something additional, or from abstracting something, or from passing over something in its substance?

Now these points are ignored; but it is possible to solve them if one assumes everything in what the thing is, and makes the division consecutive by postulating what is primitive, and leaves nothing out. [This is necessary if everything falls into [30] the division and nothing is omitted; and this is necessary, for it must already by atomic.]39

But nevertheless there is no deduction in it; but it makes us familiar with what the thing is, if at all, in some other fashion. And this is nothing absurd; for neither, presumably, does someone who gives an induction demonstrate, but he nevertheless makes something clear. And someone who states the definition as a result of the [35] division does not state a deduction. For just as in the case of conclusions without middle terms if someone says that if these are the case it is necessary that this is the case, it is possible to ask why; so too this is possible in the case of divisional definitions. What is man? An animal, mortal, footed, two-footed, wingless. Why (at [92a1] each additional posit)? For he will say, and prove by the division as he thinks, that everything is either mortal or immortal. But a whole argument of this sort is not a definition, so that even if it were demonstrated by the division, that does not make the definition a deduction. [5]

6 · But can one actually demonstrate what a thing is in respect of substance, but do so on a supposition, by assuming that what it is to be something is the property composed from the things in what it is, and that these alone are in what it is, and that the whole is proper to it? For this is what it is to be that thing.

Or do you again assume what it is to be the thing in this case too? For it is [10] necessary to prove it through the middle term.

Again, just as in a deduction you do not assume what being deduced is (for the proposition on which the deduction depends is always whole or part), so too what it is to be something must not be in the deduction, but this must be separate from what is laid down. And if anyone disputes whether something has been deduced or not, we [15] meet him by saying that “that is what a deduction is”; and if anyone says that what it is to be it has not been deduced we can say that “Yes it has; for that is what we supposed what it is to be something is.” Hence it is necessary for something to have been deduced without assuming what deduction is or what it is to be something.

[20] And even if you prove it from a supposition—e.g. if being bad is being divisible, and for things which have a contrary being their contrary is being contrary to what they are,40 and the good is contrary to the bad, and the indivisible to the divisible—therefore being good is being indivisible.

For here too you prove by assuming what it is to be something, and you assume [25] it in order to prove what it is to be it.—Yet something different.—Granted; for in demonstrations too one assumes that this is true of this—but not itself, and not something that has the same account and converts.

And in both cases—if you prove in virtue of a division and if you produce a deduction in this way—there is the same puzzle: why will man be a two-footed [30] terrestrial animal and not animal and terrestrial? For from the assumption there is no necessity for what is predicated to become a unity, but it might be as if the same man were musical and literate.

7 · Well now, how will a definer prove a thing’s substance or what it is?

[35] For neither, as in demonstration, will he make it clear from what is agreed to be the case because necessarily if these are the case something else is (for this is demonstration); nor, as in induction, will he show through the particulars, which are clear, that everything is thus since nothing is otherwise (for in induction you do not [92b1] prove what a thing is, but that either it is or it is not).

Now what other way is left? For you will hardly prove it by perception or by pointing with your finger.

Again, how will you prove what a thing is? For it is necessary for anyone who [5] knows what a man or anything else is to know too that it is (for of that which is not, no one knows what it is—you may know what the account or the name signifies when I say goatstag, but it is impossible to know what a goatstag is). But if you are to prove what it is and that it is, how will you prove them by the same argument? [10] For both the definition and the demonstration make one thing clear; but what a man is and that a man is are different.

Next, we say it is necessary that everything that a thing is should be proved through demonstration, unless it is its substance. But being is not the substance of anything; for what is is not a genus. Therefore there will be a demonstration that it [15] is. And that is what the sciences as a matter of fact do; for the geometer assumes what triangle signifies and proves that it is. So when you define what it is, what will you prove? Triangle?41 Then you will know by definition what it is, but you will not know if it is. But that is impossible.

It is evident too from the present fashions of definition that definers do not [20] prove that a thing is. For if it is in fact what is42 equidistant from the middle, why should what has been defined be? and why is this a circle? For one might say that it was a definition of mountain-copper. For definitions do not in addition make clear either that what is said is possible, or that it is that of which they say they are definitions, but it is always possible to say “Why?” [25]

If, therefore, the definer proves either what a thing is or what its name signifies, then if a definition has nothing at all to do with what a thing is, it will be an account signifying the same as a name. But that is absurd.

For, first, there would be definitions even of non-substances, and of things that are not—for one can signify even things that are not.

Again, all accounts would be definitions; for one could posit a name for any [30] account whatever, so that we would all talk definitions and the Iliad would be a definition.

Again, no demonstration would demonstrate that this name makes this clear; nor then do definitions make this clear in addition.

From this, then, it is evident that definition and deduction are not the same, [35] and that deduction and definition are not of the same thing; and in addition, that definition neither demonstrates nor proves anything, and that you can become aware of what a thing is neither by definition nor by demonstration.

8 · We must inquire again which of these points is correctly argued and [93a1] which not correctly; and what a definition is; and whether there is in some way demonstration and definition of what a thing is, or in no way at all.

Since, as we said, to know what something is and to know the explanation of the fact that it is are the same—the argument for this is that there is some [5] explanation, and this is either the same thing or something else, and if it is something else it is either demonstrable or non-demonstrable—if, then, it is something else and it is possible to demonstrate it, it is necessary for the explanation to be a middle term and to be proved in the first figure; for what is being proved is both universal and affirmative.

Well, one way would be the one just examined—proving what a thing is [10] through another definition. For in the case of what a thing is, it is necessary for the middle term to state what the thing is (and in the case of what is proper it must be proper). Hence you will prove the one but you will not prove the other instance of what it is to be the same object. Now that this way will not be a demonstration was said earlier (but it is a general deduction of what the thing is). [15]

But let us say in what way a demonstration is possible, speaking again from the beginning. Just as we seek the reason why when we grasp the fact—sometimes they actually become clear together, but it is not possible to become familiar with the reason why before the fact—it is clear that similarly we cannot grasp what it is to be something without grasping the fact that it is; for it is impossible to know what a [20] thing is if we are ignorant of whether it is. But as to whether it is, sometimes we grasp this accidentally, and sometimes when grasping something of the object itself—e.g. of thunder, that it is a sort of noise of the clouds; and of eclipse, that it is a sort of privation of light; and of man, that he is a sort of animal; and of soul, that it is something moving itself.

[25] Now in cases in which we know accidentally that a thing is, necessarily we have no hold on what it is; for we do not even know that it is, and to seek what it is without grasping that it is, is to seek nothing. But in the cases in which we grasp something, it is easier. Hence in so far as we grasp that it is, to that extent we also have some hold on what it is.

So in cases in which we grasp something of what the thing is, let it be first like [30] this:—eclipse A, moon C, screening by the earth B. So to ask whether it is eclipsed or not is to seek whether B is or not. And this is no different from seeking whether there is an account of it; and if this is, we say that that is too. (Or: of which of the contradictory pair does the account hold—of its having two right angles or of its not having them?)

[35] When we discover it, we know at the same time the fact and the reason why, if it is through immediates; if not, we know the fact but not the reason why. Moon, C; eclipse, A; not being able to produce a shadow during full moon though there is nothing evident between us, B. Then if B—not being able to produce a shadow [93b1] though there is nothing evident between us—belongs to C, and A—being eclipsed—to this, then it is clear that it is eclipsed but not yet why; and we know that an eclipse is but we do not know what it is.

When it is clear that A belongs to C, then to seek why it belongs is to seek what [5] B is—whether screening or rotation of the moon or extinction. And this is the account of the one extreme, i.e. in this case of A. For an eclipse is a screening by the earth.

What is thunder? Extinction of fire in cloud. Why does it thunder? Because the fire in the cloud is extinguished. Cloud C, thunder A, extinction of fire B. Thus B [10] belongs to C, the cloud (for the fire is extinguished in it); and A, noise, to this; and B is indeed an account of A, the first extreme. And if again there is another middle term for this, it will be from among the remaining accounts.

[15] We have said, then, how what a thing is is grasped and becomes familiar, hence no deduction and no demonstration of what a thing is comes about—yet it is clear through deduction and through demonstration. Hence without a demonstration you cannot become aware of what a thing is (in cases where the explanation is something else), yet there is no demonstration of it (as we said when we went [20] through the puzzles).

9 · Of some things there is something else that is their explanation, of others there is not. Hence it is clear that in some cases what a thing is is immediate and a principle; and here one must suppose, or make apparent in some other way, both [25] that they are and what they are (which the arithmetician does; for he supposes both what the unit is and that it is); but in those cases which have a middle term and for which something else is explanatory of their substance, one can, as we said, make them clear through a demonstration, but not by demonstrating what they are.

10 · Since a definition is said to be an account of what a thing is, it is evident [30] that one type will be an account of what the name, or a different name-like account, signifies—e.g. what triangle signifies. And when we grasp that this is, we seek why it is; but it is difficult to grasp in this way why a thing is if we do not know that it is. The explanation of the difficulty has been stated already—that we do not even know whether it is or not, except accidentally. (An account is a unity in two [35] ways—either by connection, like the Iliad, or by making one thing clear of one thing non-accidentally.)

Thus one definition of definition is the one stated; another definition is an account which makes clear why a thing is. Hence the former type of definition signifies but does not prove, whereas the latter evidently will be a sort of [94a1] demonstration of what a thing is, differing in position from the demonstration. For there is a difference between saying why it thunders and what thunder is; for in the one case you will say: Because the fire is extinguished in the clouds. What is thunder?—A noise of fire being extinguished in the clouds. Hence the same account [5] is put in a different way, and in this way it is a continuous demonstration, in this way a definition.

Again, a definition of thunder is noise in the clouds; and this is a conclusion of the demonstration of what it is.

The definition of immediates is an undemonstrable positing of what they are. [10]

One definition, therefore, is an undemonstrable account of what a thing is; one is a deduction of what it is, differing in aspect from the demonstration; a third is a conclusion of the demonstration of what it is.

So it is evident from what has been said, both in what way there is a demonstration of what a thing is, and in what way there is not; and in what cases [15] there is and in what cases there is not; and again in how many ways something is called a definition, and in what way it proves what a thing is and in what way it does not, and in what cases it does and in what cases it does not; and again how it is related to demonstration and in what way it is possible for them to be of the same thing and in what way it is not possible.

11 · Since we think we understand when we know the explanation, and there [20] are four types of explanation (one, what it is to be a thing; one, that if certain things hold it is necessary that this does; another, what initiated the change; and fourth, the aim), all these are proved through the middle term.

The case in which if something holds it is necessary that this does, does not occur if one proposition is assumed, but only if at least two are; and this occurs when [25] they have one middle term. So when this one thing is assumed it is necessary for the conclusion to hold. It is clear too as follows: Why is the angle in the semicircle right? It is right if what holds? Well, let right be A; half of two rights B; the angle in the semicircle C. Thus B is the explanation of why A, right, belongs to C, the angle in [30] the semicircle. For this is equal to A and C to B; for it is half of two rights. So if B, half of two rights, holds, then A belongs to C (that is, the angle in the semicircle is right). And what it is to be it is the same as this, since this is what its account signifies.

And the middle term has also been proved to be explanatory of what it is to be [35] something.43

And why did the Persian war come upon the Athenians? What is the explanation of the Athenians’ being warred upon? Because they attacked Sardis [94b1] with the Eretrians; for that initiated the change. War, A; being the first to attack, B; Athenians, C. Thus B belongs to C (being the first to attack to the Athenians), and A to B (for men make war on those who have first done them wrong). Therefore A [5] belongs to B (being warred upon to those who first began), and this—B—to the Athenians (for they first began). Therefore here too the explanation, what initiated the change, is a middle term.

In cases in which the aim is explanatory—e.g. why does he walk about? In order to be healthy. Why is there a house? In order that his belongings may be [10] preserved—in the one case with the aim of being healthy, in the other with the aim of their being preserved. (Why must he walk about after dinner? and With what aim must he? do not differ.) Walk after dinner, C; the foodstuffs’ not remaining on the surface, B; being healthy, A. Well, let there belong to walking about after [15] dinner, making the foodstuffs not to remain on the surface at the mouth of the stomach; and let this be healthy. For B, the foodstuffs’ not remaining on the surface, seems to belong to walking about, C; and A, healthy, to this. So what is explanatory—the aim—for C of A’s belonging to it?—B, their not remaining on the [20] surface. And this is as it were an account of it; for A will be set out in this way. Why is B explanatory for C? Because this, being in such a state, is what being healthy is. (One must transpose the accounts, and in this way everything will be more evident.)

Here the events are the other way about from those in the case of explanations [25] in respect of change; for there the middle term must come about first, but here C, the last term, comes about first, and the final term to come about is the aim.

It is possible for the same thing to be the case both with some aim and from necessity—e.g. the light through the lantern; for the finer body passes through the [30] larger pores both from necessity (if light comes about by passing through), and with some aim (in order that we shan’t stumble).

Now if it is possible for something to be the case in this way, is it also possible for something to come about thus? E.g. if it thunders: when the fire is extinguished, it is necessary for it to sizzle and make a noise, and also (if things are as the Pythagoreans say) it has the aim of threatening those in Hell in order to make them afraid.

[35] There are very many things of this sort, especially among things which are constituted by nature or are being so constituted; for one nature makes them with some aim and another from necessity. (Necessity is twofold: one, in accordance with [95a1] nature and impulse; the other, by force and44 contrary to impulse—e.g. a stone travels both upwards and downwards from necessity, but not because of the same necessity.) Among the products of thought, some never occur spontaneously—e.g. a [5] house or a statute—nor from necessity either, but with some aim; but others occur by chance too—e.g. health and preservation. But it is especially among things which can be both thus and otherwise, when their coming about, not being by chance, is such that the end is good, that things come about with some aim, and then either by nature or by skill, but by change nothing comes about with any aim.

12 · The same thing is explanatory for what is coming about and what has [10] come about and what will be as for what is the case (for the middle term is explanatory)—except that for what is the case, it is the case; for what is coming about, it is coming about; for what has come about, it has come about; and for what will be, it will be.

E.g. why has an eclipse come about? Because the earth has come to be in the middle. And it is coming about because it is coming to be there; and it will be because it will be in the middle; and it is because it is. [15]

What is ice? Well, assume that it is solidified water. Water, C; solidified, A; the explanatory middle term B—utter lack of heat. Thus B belongs to C, and being solidified, A, to this. And ice is coming about if B is coming about; and it has come about if it has come about; and it will be if it will be. [20]

Now what is explanatory in this way and what is explanatory of come about together when they come about, and are the case together when they are; and similarly for having come about and going to be. But what of things that do not go together—can it be that in continuous time, as it seems to us, one should be [25] explanatory of another? something else that has come about of the fact that this has come about, and something else that will be of the fact that this will be, and of the fact that this is coming about something that came to be before?

Well, the deduction proceeds from what has come about later (but the principle of these things is actually what has come about—and similarly in the case of what is coming about), and it does not proceed from what is earlier (e.g. since this [30] has come about, that this has come about later). And similarly for what will be the case. For whether the time is indeterminate or determined it will not be the case that since it is true to say that this has come about it is true to say that this, the later thing, has come about. For in between it will be false to say this, when the one has already come about. And the same account also goes for what will be the case. [35]

Neither can one deduce that since this has come about this will be. For the middle term must be coeval—something that came about for what came about, something that will be for what will be, something that is coming about for what is coming about, something that is for what is; but it is not possible for anything to be coeval with “it has come about” and “it will be”.

Again, the time in between can be neither determinate or determined; for it [95b1] will be false to say it in between.

We must inquire what it is that holds things together so that after what has come about there are objects that are coming about. Or is it clear that what is coming about is not next to what has come about? For neither is what came about next to what came about; for they are limits and atomic. So just as points are not [5] next to one another, neither are things that came about; for both are indivisible. Thus neither is what is coming about next to what has come about, for the same reason; for what is coming about is divisible, but what has come about is indivisible. So just as a line is related to a point, in the same way what is coming about is related [10] to what has come about; for infinitely many things that have come about inhere in what is coming about.

But we must speak more clearly about this in our general account of change.

Now as to the character of the explanatory middle term when events occur [15] consecutively, let this much be assumed. For here too it is necessary for the middle and the first term to be immediate.

E.g. A has come about since C has come about (C has come about later, A before; but C is the principle since it is nearer to the present, which is the principle of time); and C has come about if D has come about. Thus if D has come about it is [20] necessary that A has come about; and C is the explanation—for if D came about it is necessary that C has come about, and if C has come about it is necessary that A has come about earlier.

If we take things in this way, will the middle term come to a stop anywhere at an immediate, or will there always be something falling in between because of the infinite nature of the past? For what has come about is not next to what has come about, as has been said. But nevertheless it is necessary to begin from something [25] that is immediate and first from the present.

The same goes too for “it will be”. For if it is true to say that D will be, then necessarily it was earlier true to say that A will be. And C is explanatory of this; for if D will be, C will be earlier; and if C will be, A will be earlier. And similarly the [30] division is infinite in these cases too; for things that will be are not next to one another. But in these cases too an immediate principle must be got.

And it is like this in actual cases—if a house has come about it is necessary for stones to have been cut and to have come about. Why is this? Because it is necessary for a foundation to have come about if a house has come about; and if a foundation [35] has come about, it is necessary for stones to have come about earlier.

Again, if there is going to be a house, in the same way there will be stones earlier. It is proved similarly through the middle term; for there will be a foundation earlier.

Since we see that among the things that come about there is a sort of circular coming about, it is possible for this to be the case if the middle term and the extremes follow one another; for in these cases there is conversion (this has been [96a1] proved in our first chapters45 because the conclusions convert; and this is what being circular is.

In actual cases it appears as follows: if the earth is soaked, necessarily steam came about; and if that came about, cloud; and if that came about, water: and if [5] that came about, it is necessary for the earth to be soaked. But this was what we started from; so that it has come round in a circle—for if any whatever of them is the case, another is; and if that, another; and if that, the first.

Some things come about universally (for always and in every case either it holds or it comes about in this way), others not always but for the most part—e.g. not every male man has hair on his chin, but for the most part they do. Well, in such [10] cases it is necessary for the middle term also to hold for the most part. For if A is predicated universally of B and this universally of C, it is necessary for A to be predicated of C always and in every case; for that is what the universal is—what holds in every case and always. But it was supposed to hold for the most part. [15] Therefore it is necessary for the middle term, B, also to hold for the most part. There will be immediate principles, then, also in the case of what is for the most part, which hold or come about in this way for the most part.

13 · Now we have already said how what a thing is is set out in the terms, [20] and in what way there is or is not demonstration or definition of it; let us now say how one should hunt out what is predicated in what a thing is.

Well, of the things which belong always to something, some extend further—yet not outside its genus. (I say they belong further if they belong to the thing [25] universally but also belong to something else.) E.g. there is something which belongs to every triplet but also to non-triplets—as being belongs to the triplet but also to non-numbers, but odd both belongs to every triplet and belongs further (for [30] it also belongs to the quintuplet), but not outside its genus; for the quintuplet is a number, and nothing outside number is odd.

Well, such things must be taken up to the first point at which just so many are taken that each will belong further but all of them together will not belong further; for necessarily this will be the substance of the object.

E.g. number belongs to every triplet, and so do odd, prime (in both [35] ways—both as not being measured by number and as not being compounded from numbers). This, then, is precisely what a triplet is: a number that is odd, prime, and prime in this way. For each of these belongs in some cases to all the odds as well and in the last case to pairs as well—but all of them together belong to nothing other than the [96b1] triplet.

Since we have made clear above46 that what is predicated in what a thing is is necessary47 (and what is universal is necessary), and in the case of the triplet (and of anything else for which we take terms in this way) what is taken is in what it is, in this way a triplet will be these things from necessity. [5]

And that they constitute its substance is clear from this: necessarily, if this is not what being a triplet is, it is some sort of genus, either named or nameless. It will, then, belong further than to the triplet—for let it be supposed that a genus is such as potentially to belong further. Then if it belongs to nothing other than the atomic [10] triplets, this will be what being a triplet is—for let this too be supposed, that the substance of a thing is the last such predication to hold of the atoms. Hence in the case of anything else proved in this way, the same will go for what being it is.

When you are dealing with some whole, you should divide the genus into what [15] is atomic in species—the primitives—(e.g. number into triplet and pair); then in this way attempt to get definitions of these (e.g. of straight line and circle and right angle); and after that, grasping what the genus is (e.g. whether it is a quantity or a [20] quality), consider the proper affections through the first common items.

For what holds for what is compounded from the atoms will be clear from the definitions, because definitions and what is simple are principles of everything, and what holds belongs in themselves to the simples alone, and to the other things in virtue of them.

[25] Divisions made according to the differentiae are useful for this sort of pursuit: while the sense in which they prove has been discussed earlier,48 they will be useful for deducing what a thing is only as follows.

Yet they might seem to be of no use, but to assume everything straight off—just as if one were to assume it from the beginning without the division. But it [30] makes a difference which of the predicates are predicated first and which later—e.g. to say animal tame two-footed or two-footed animal tame. For if everything depends on two things and animal tame is a single thing, and again man (or whatever the single thing in question may be) depends on this and the [35] differentia, then it is necessary to postulate by dividing.

Again, only in this way is it possible to ensure that you leave nothing out in what the thing is. For when the first genus has been taken, if you take one of the lower divisions not everything will fall into it—e.g. not every animal is either whole-winged or split-winged, but every winged animal (for it is this of which it is a [97a1] differentia). The first differentia of animal is that into which every animal falls; and similarly of each of the others, both the genera outside it and those under it—e.g. the first differentia of bird is that into which every bird falls, and of fish, that into which every fish.

[5] Now if you proceed in this way you can know that nothing has been left out; but in any other way you will of necessity both leave something out and not know it.

There is no need for one who is defining and dividing to know everything there is. Yet some say that it is impossible to know a thing’s differences from something without knowing that thing; but that without the differences one cannot know that [10] thing—for it is the same as that from which it does not differ and different from that from which it does differ.

Now, first, this is false; for a thing is not different in virtue of every difference; for many differences belong to things that are the same species—though not in respect of their substance, nor in themselves.

Next, when you assume the opposites and the differentia and that everything [15] falls here or here, and assume that what you are seeking is in one of them, and are aware of this, it makes no difference whether you know or do not know the other things of which the differentiae are predicated. For it is evident that if, proceeding in this way, you come to things of which there is no longer a differentia, you will [20] have the account of its substance. (And that everything falls into the division—if they are opposites which have nothing between them—is not a postulate; for it is necessary for everything to be in one of them, if it is a differentia of that thing.)

To establish a definition through divisions, one must aim for three things—grasping what is predicated in what the thing is, ordering these as first or second, [25] and ensuring that these are all there are.

The first one of these is achieved through being able to establish conclusions through the genus, just as in the case of accidentals one can deduce that they belong.49

And ordering them as one should will be achieved if you take the first term; and this will be achieved by taking the one which follows all the others but is not followed by them all (for of necessity there will be some such term). And when this [30] is taken the same now goes for the lower terms; for second will be that which is first of the others, and third that which is first of the next; for if the upmost one is abstracted, the next will be first of the others. And similarly in the other cases too.

And that these are all there are is evident; for you assume of the first term in [35] the division that every animal is either this or this, and that this belongs to it, and again you take the differentia of this whole, and you assume that there is no further differentia of the final whole—or that straightaway after the final differentia this no longer differs in species from the complex. For it is clear both that nothing extra has been posited (for all of these terms have been taken in what the thing is) and [97b1] that nothing is missing (for it would be either a genus or a differentia: now both the first term, and this taken together with the differentiae, constitute the genus; and the differentiae are all grasped—for there is no later one left; for then the final term [5] would differ in species, but it has been said not to differ).

We should look at what are similar and undifferentiated, and seek, first, what they all have that is the same; next, we should do this again for other things which are of the same genus as the first set and of the same species as one another but of a [10] different species from those. And when we have grasped what all these have that is the same, and similarly for the others, then we must again inquire if what we have grasped have anything that is the same—until we come to a single account; for this will be the definition of the object. And if we come not to one but to two or more accounts, it is clear that what we are seeking is not a single thing but several. [15]

I mean, e.g., if we were to seek what pride is we should inquire, in the case of some proud men we know, what one thing they all have as such. E.g. if Alcibiades is proud, and Achilles and Ajax, what one thing do they all have? Intolerance of insults; for one made war, one waxed wroth, and the other killed himself. Again in [20] the case of others, e.g. Lysander and Socrates. Well, if here it is being indifferent to good and bad fortune, I take these two things and inquire what both indifference to fortune and not brooking dishonour have that is the same. And if there is nothing, then there will be two sorts of pride.

Every definition is always universal; for the doctor does not say what is healthy [25] in the case of some individual eye, but either in the case of every eye, or determining some species of eye.

And it is easier to define the particular than the universal—that is why one should cross from the particulars to the universals. For homonymies escape notice in [30] what is universal more than in what is undifferentiated.

Just as in demonstrations a deduction must have been made, so in definitions there must be clarity. And this will be achieved if, through the stated50 particulars, one can define separately for each genus (e.g. if one defines similarity not for every [35] case but for colour and for shape, and sharpness for sound), and can then proceed in this way to what is common, taking care not to fall into homonymy.

And if one should not argue in metaphors, it is clear too that one should not define either by metaphors or what is said in metaphors; for then one will necessarily argue in metaphors.

[98a1] 14 · In order to grasp problems, one should excerpt both the anatomies and the divisions; and in this way, laying down the genus common to all the subject-matter, one should excerpt (if e.g. animals are under consideration) whatever [5] belongs to every animal; and having got this, again excerpt whatever follows every case of the first of the remaining terms (e.g. if it is bird, whatever follows every bird), and always excerpt in this way whatever follows the nearest term. For it is clear that we shall now be in a position to state the reason why what follows the items under the common genus belongs to them—e.g. why it belongs to man or to [10] horse. Let A be animal, B what follows every animal, and C, D, E individual animals. Well, it is clear why B belongs to D; for it does so because of A. Similarly in the other cases too. and the same account will always hold for the others.51

Now at present we argue in terms of the common names that have been handed down; but we must not only inquire in these cases, but also if anything else [15] has been seen to belong in common, we must extract that and then inquire what it follows and what follows it—e.g. having a manyplies and not having upper incisors follow having horns; again, we should inquire what having horns follows. For it is clear why what we have mentioned will belong to them; for it will belong because they have horns.

[20] Again, another way is excerpting in virtue of analogy; for you cannot get one identical thing which pounce and spine and bone should be called; but there will be things that follow them too, as though there were some single nature of this sort.

15 · Problems are the same in some cases through having the same middle [25] term, e.g. because they are all cases of reciprocity. And of these some are the same in genus—those which have differences through holding of different things or in different ways: e.g. Why does it echo? or Why is it mirrored? and Why is there a rainbow?—for all these are the same problem in genus (for they are all cases of reflection), but different in species.

[30] Other problems differ in that the middle term of the one is under the other middle term; e.g. Why does the Nile flow more at the end of the month? Because the end of the month is more stormy. And why is the end more stormy? Because the moon is waning. For these are related in this way to one another.

16 · About explanations and what they are explanatory of, one might puzzle [35] whether when the explanandum belongs to something the explanation belongs too. E.g. if it sheds its leaves or if it suffers eclipse, will the explanation of the eclipse or the shedding also hold—if this is, e.g. having broad leaves, and (for the eclipse) the [98b1] earth’s being in the middle? For if they do not hold, something else will be explanatory of them. And if the explanation belongs to it, does the explanandum also belong at the same time? e.g. if the earth is in the middle, it suffers eclipse; or if it is broad-leaved, it sheds its leaves.

If this is so, they will hold at the same time and will be proved through one [5] another. For let shedding leaves be A, broad-leaved B, vine C. Well, if A belongs to B (for everything broad-leaved 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. B, the middle [10] term, is explanatory. But one can also demonstrate that the vine is broad-leaved through the fact that it sheds its leaves. For let D be broad-leaved, E shedding leaves, F vine. Well, E belongs to F (for every vine sheds its leaves) and D to E (for everything that sheds its leaves is broad-leaved); therefore vine is broad-leaved. [15] Shedding its leaves is explanatory.

But if it is not possible for things to be explanatory of one another (for the explanation is prior to what it is explanatory of), and the earth’s being in the middle is explanatory of the eclipse, but the eclipse is not explanatory of the earth’s being in the middle—so if the demonstration through the explanation gives the reason why, and the one not through the explanation gives the fact, you know that it is in the [20] middle but not why. And that the eclipse is not explanatory of its being in the middle but the latter of the eclipse is evident; for its being in the middle belongs in the account of the eclipse; so that it is clear that the latter becomes familiar through the former and not the former through the latter.

Or is it possible for there to be several explanations of one thing? For if the [25] same thing can be predicated of several things primitively—let A belong to B primitively and to another term, C, primitively; and these to D, E. Therefore A will belong to D, E; and B is explanatory for D, and C for E. Hence when the explanation belongs, it is necessary for the object to belong; but when the object belongs it is not [30] necessary for everything which is explanatory to belong—something, yet not everything, explanatory must belong.

Or if problems are always universal, must the explanation be some whole and what it is explanatory of universal? E.g. shedding leaves is determined to some whole, even if that has species, and it belongs to these universally (either plants or plants of such and such a sort); hence in these cases the middle term and what it is [35] explanatory of must be equal and convert. E.g. why do trees shed their leaves? Well, if it is because of solidification of their moisture, then if a tree sheds its leaves solidification must belong to it, and if solidification belongs—not to anything whatever but to a tree—it must shed its leaves.

[99a1] 17 · Is it possible for there not to be the same explanation of the same thing for every case, but a different one? or not? Perhaps if it has been demonstrated in itself and not in virtue of a sign or accidentally it is not possible (for the middle term is the account of the extreme), but if it has not been demonstrated in this way, it is [5] possible? One can inquire accidentally both about what it is explanatory of and about what it is explanatory for—but these do not seem to be problems. Otherwise, the middle term will have a similar character—if they are homonymous, the middle will be homonymous; if they are in a genus, it will have a similar character.

E.g. why do proportionals alternate? For the explanation in the cases of lines [10] and of numbers is different—and the same: as lines it is different, as having such and such an increase it is the same. And so in all cases.

The explanation of a colour’s being similar to a colour and a figure to a figure is different in the different cases. For what is similar is homonymous in these cases; for here it is presumably having proportionate sides and equal angles, but in the [15] case of colours it is that perception of them is single, or something else of that sort.

And things which are the same by analogy will have their middle term the same by analogy too.

The explanation and what it is explanatory of and what it is explanatory for are interrelated like this: taking them severally, what it is explanatory of extends further (e.g. having external angles equal to four right angles extends further than [20] either triangle or quadrangle), but for all of them together it extends equally (for they comprise everything that has external angles equal to four right angles); and similarly for the middle term. (But the middle term is an account of the first extreme: that is why all the sciences come about through definition.)

E.g. shedding leaves follows together with the vine and exceeds it; and with the fig, and exceeds it—but not all of them, but it is equal.

[25] Thus if you were to take the primitive middle term, it is an account of shedding leaves. For there will be a middle term in the other direction (that all are such and such); and then a middle for this (that the sap solidifies or something else of that sort). What is shedding leaves? The solidifying of the sap at the connection of the seed.

[30] Schematically it will come out as follows for anyone seeking the interrelation between the explanation and what it is explanatory of: Let A belong to every B, and B to each of the D’s, and further. Thus B will hold universally of the D’s (for I call universal that with which they do not convert, and primitive universal that with [35] which severally they do not convert but taken all together they do convert and extend alongside). Thus B is explanatory of A for the D’s. Therefore A must extend alongside further than B; for if it does not, why will this be explanatory rather than that?

Well, if A belongs to all the E’s, all of them together will be some one thing different from B. For if not, how will one be able to say that A belongs to everything [99b1] to which E belongs but E does not belong to everything to which A belongs? For why will there not be some explanation, as of its belonging to all the D’s? (But will the DE’s be some one thing? We must inquire into this; let it be C.)

Thus it is possible for there to be several explanations of the same thing, but not for things of the same species—e.g. the explanation of longevity for quadrupeds [5] is their not having bile, but for birds their being dry or something else.

18 · If they do not come at once to what is atomic and there is not only one middle term but several, the explanations too are several. But which of the middle terms is explanatory for the particulars—that which is primitive in the direction of the universal or that which is primitive in the direction of the particular? Well, it is [10] clear that it is the one nearest to what it is explanatory for. For this explains why the primitive term belongs under the universal—i.e. C is explanatory for D of B’s belonging to it. So for D C is explanatory of A, and for C B, and for this itself.

19 · Now as for deduction and demonstration, it is evident both what each is [15] and how it comes about—and at the same time this goes for demonstrative understanding too (for that is the same thing). But as for the principles—how they become familiar and what is the state that becomes familiar with them—that will be clear from what follows, when we have first set down the puzzles.

Now, we have said earlier that it is not possible to understand through [20] demonstration if we are not aware of the primitive, immediate, principles. But as to knowledge of the immediates, one might puzzle both whether it is the same or not the same—whether there is understanding of each, or rather understanding of the one and some other kind of thing of the other—and also whether the states are not present in us but come about in us, or whether they are present in us but escape [25] notice.

Well, if we have them, it is absurd; for it results that we have pieces of knowledge more precise than demonstration and yet this escapes notice. But if we get them without having them earlier, how might we become familiar with them and learn them from no pre-existing knowledge? For that is impossible, as we said in the case of demonstration too. It is evidently impossible, then, both for us to have [30] them and for them to come about in us when we are ignorant and have no such state at all. Necessarily, therefore, we have some capacity, but do not have one of a type which will be more valuable than these in respect of precision.

And this evidently belongs to all animals; for they have a connate discriminatory [35] capacity, which is called perception. And if perception is present in them, in some animals retention of the percept comes about, but in others it does not comes about. Now for those in which it does not come about, there is no knowledge outside perceiving (either none at all, or none with regard to that of which there is no retention); but for some52 perceivers, it is possible to grasp it in their minds. And when many such things come about, then a difference comes about, so that some [100a1] come to have an account from the retention of such things, and others do not.

So from perception there comes memory, as we call it, and from memory (when it occurs often in connection with the same thing), experience; for memories [5] that are many in number from a single experience. And from experience, or from the whole universal that has come to rest in the soul (the one apart from the many, whatever is one and the same in all those things), there comes a principle of skill and of understanding—of skill if it deals with how things come about, of understanding if it deals with what is the case.

[10] Thus the states neither belong in us in a determinate form, nor come about from other states that are more cognitive; but they come about from perception—as in a battle when a rout occurs, if one man makes a stand another does and then another, until a position of strength53 is reached. And the soul is such as to be capable of undergoing this.

[15] What we have just said but not said clearly, let us say again: when one of the undifferentiated things makes a stand, there is a primitive universal in the mind (for though one perceives the particular, perception is of the universal—e.g. of man but [100b1] not of Callias the man); again a stand is made in these, until what has no parts and is universal stands—e.g. such and such an animal stands, until animal does, and in this a stand is made in the same way. Thus it is clear that it is necessary for us to become familiar with the primitives by induction; for perception too54 instils the [5] universal in this way.

Since of the intellectual states by which we grasp truth some are always true and some admit falsehood (e.g. opinion and reasoning—whereas understanding and comprehension are always true), and no kind other than comprehension is more precise than understanding, and the principles of demonstrations are more familiar, [10] and all understanding involves an account—there will not be understanding of the principles; and since it is not possible for anything to be truer than understanding, except comprehension, there will be comprehension of the principles—both if we inquire from these facts and because demonstration is not a principle of demonstration so that understanding is not a principle of understanding either—so if we have [15] no other true kind apart from understanding, comprehension will be the principle of understanding. And the principle will be of the principle, and understanding as a whole will be similarly related to the whole object.