The Politics of Aristotle

by Aristotle

  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 ou
r 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.