The Politics of Aristotle

by Aristotle

  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 a
bout, 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 a
ssume 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.