by Aristotle
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 understandin
g—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.