The Politics of Aristotle

by Aristotle

  30 · The method is the same in all cases, in philosophy and in any art or study. We must look for the attributes and the subjects of both our terms, and we [5] must supply ourselves with as many of these as possible, and consider them by means of the three terms, refuting statements in one way, establishing them in another, in the pursuit of truth starting from an arrangement of the terms in accordance with truth, while if we look for dialectical deductions we must start from plausible propositions. The principles of deductions have been stated in [10] general terms, both how they are characterized and how we must hunt for them, so as not to look to everything that is said about the terms of the problem or to the same points whether we are establishing or refuting, or again whether we are establishing of all or of some, and whether we are refuting of all or some; we must look to fewer [15] points and they must be definite. We have also stated how we must select with reference to each thing that is, e.g. about good or knowledge. But in each science the principles which are peculiar are the most numerous. Consequently it is the business of experience to give the principles which belong to each subject. I mean for example that astronomical experience supplies the principles of astronomical science; for once the phenomena were adequately apprehended, the demonstrations [20] of astronomy were discovered. Similarly with any other art or science. Consequently, if the attributes of the thing are apprehended, our business will then be to exhibit readily the demonstrations. For if none of the true attributes of things had been omitted in the survey, we should be able to discover the proof and demonstrate [25] everything which admitted of proof, and to make that clear, whose nature does not admit of proof.

  Thus we have explained fairly well in general terms how we must select propositions: we have discussed the matter precisely in the treatise concerning [30] dialectic.15

  31 · It is easy to see that division by genera is a small part of the method we have described; for division is, so to speak, a weak deduction; for what it ought to prove, it begs, and it always deduces something more general than the attribute in [35] question. First, this very point had escaped all those who used the method of division; and they attempted to persuade men that it was possible to make a demonstration of substance and essence. Consequently they did not understand what it is possible to deduce by division, nor did they understand that it was possible to deduce in the manner we have described. In demonstrations, when there is a need to deduce that something belongs, the middle term through which the deduction is [46b1] formed must always be inferior to and not comprehend the first of the extremes. But division has a contrary intention; for it takes the universal as middle. Let animal be the term signified by A, mortal by B, and immortal by C, and let man, whose [5] definition is to be got, be signified by D. The man who divides assumes that every animal is either mortal or immortal: i.e. whatever is A is all either B or C. Again, always dividing, he lays it down that man is an animal, so he assumes A of D as belonging to it. Now the deduction is that every D is either B or C, consequently [10] man must be either mortal or immortal, but it is not necessary that man should be a mortal animal—this is begged: and this is what ought to have been deduced. And again, taking A as mortal animal, B as footed, C as footless, and D as man, he [15] assumes in the same way that A inheres either in B or in C (for every mortal animal is either footed or footless), and he assumes A of D (for he assumed man to be a mortal animal); consequently it is necessary that man should be either a footed or a footless animal; but it is not necessary that man should be footed—this he assumes: and it is just this again which he ought to have proved. Always dividing then in this [20] way it turns out that they assume as middle the universal term, and as extremes that which ought to have been the subject of proof and the differentiae. In conclusion, they do not make it clear, and show it to be necessary, that this is man or whatever the subject of inquiry may be; for they pursue the other method altogether, never even [25] suspecting the presence of the rich supply of evidence which might be used.

  It is clear that it is neither possible to refute by this method, nor to deduce about an accident or property of a thing, nor about its genus, nor in cases in which it is unknown whether it is thus or thus, e.g. whether the diagonal is incommensurate [30] or commensurate. For if he assumes that every length is either commensurate or incommensurate, and the diagonal is a length, he has deduced that the diagonal is either incommensurate or commensurate. But if he should assume that it is incommensurate, he will have assumed what he ought to have proved. He cannot then prove it; for this is his method, but proof is not possible by this method. (Let A [35] stand for incommensurate or commensurate, B for length, C for diagonal). It is clear then that this method of investigation is not suitable for every inquiry, nor is it useful in those cases in which it is thought to be most suitable.

  32 · From what has been said it is clear from what elements demonstrations are formed and in what manner, and to what points we must look in each problem. Our next business is to state how we can reduce deductions to the aforementioned figures; for this part of the inquiry still remains. If we should investigate the [47a1] production of deductions and had the power of discovering them, and further if we could resolve the deductions produced into the aforementioned figures, our original project would be brought to a conclusion. It will happen at the same time that what [5] has been already said will be confirmed and its truth made clearer by what we are about to say. For everything that is true must in every respect agree with itself.

  First then we must attempt to select the two propositions of the deduction (for [10] it is easier to divide into large parts than into small, and the composite parts are larger than the elements out of which they are made); next we must inquire which are universal and which particular, and if both have not been stated, we must ourselves assume the one which is missing. For sometimes men put forward the universal, but do not posit the proposition which is contained in it, either in writing [15] or in discussion: or men put these forward, but omit those through which they are inferred, and invite the concession of others to no purpose. We must inquire then whether anything unnecessary has been assumed, or anything necessary has been omitted, and we must posit the one and take away the other, until we have reached the two propositions; for unless we have these, we cannot reduce arguments put [20] forward in the way described. In some arguments it is easy to see what is wanting, but some escape us, and appear to be deductions, because something necessary results from what has been laid down, e.g. if the assumptions were made that substance is not annihilated by the annihilation of what is not substance, and that if [25] the elements out of which a thing is made are annihilated, then that which is made out of them is destroyed: these propositions being laid down, it is necessary that any part of substance is substance; this has not however been deduced from the assumptions, but propositions are wanting. Again if it is necessary that animal should exist, if man does, and that substance should exist, if animal does, it is necessary that substance should exist if man does; but as yet the conclusion has not [30] been deduced; for the propositions are not in the shape we described.

  We are deceived in such cases because something necessary results from what is assumed, since deduction also is necessary. But that which is necessary is wider than deduction; for every deduction is necessary, but not everything which is necessary is a deduction. Consequently, though something results when certain [35] propositions are assumed, we must not try to reduce it directly, but must first take the two propositions, then divide them into their terms. We must take that term as middle which is stated in both the propositions; for it is necessary that the middle should be found in both in all the figures.

  If then the middle term is a predicate and a subject of predication, or if it is a [47b1] predicate, and something else is denied of it, we shall have the first figure; if it both is a predicate and is denied of something, the middle figure; if other things are predicated of it, or one is denied, the other predicated, the last figure. For it was thus that we
found the middle term placed in each figure. It is placed similarly too if [5] the propositions are not universal; for the middle term is determined in the same way. Clearly then, if the same term is not said more than once in the course of an argument, a deduction cannot be made; for a middle term has not been taken. Since [10] we know what sort of problem is established in each figure, and in which the universal and in what sort the particular is established, clearly we must not look for all the figures, but for that which is appropriate to the problem in hand. If it is established in more figures than one, we shall recognize the figure by the position of the middle term.

  [15] 33 · Men are frequently deceived about deduction because the inference is necessary, as has been said above; sometimes they are deceived by the similarity in the positing of the terms; and this ought not to escape our notice. E.g. if A is said of B, and B of C: it would seem that a deduction is possible since the terms stand thus; [20] but nothing necessary results, nor does a deduction. Let A represent being eternal, B Aristomenes as an object of thought, C Aristomenes. It is true then that A belongs to B. For Aristomenes as an object of thought is eternal. But B also belongs to C; for [25] Aristomenes is Aristomenes as an object of thought. But A does not belong to C; for Aristomenes is perishable. For no deduction was made although the terms stood thus: that required that the proposition AB should be stated universally. But this is false, that every Aristomenes who is an object of thought is eternal, since [30] Aristomenes is perishable. Again let C stand of Miccalus, B for musical Miccalus, A for perishing to-morrow. It is true to predicate B for C; for Miccalus is musical Miccalus. Also A can be predicted of B; for musical Miccalus might perish to-morrow. But to say A of C is false at any rate. This argument then is identical [35] with the former; for it is not true universally that musical Miccalus perishes to-morrow; but unless this is assumed, no deduction (as we have shown) is possible.

  This deception then arises through ignoring a small distinction. For we accept the conclusion as though it made no difference whether we said ‘This belongs to that’ or ‘That belongs to all of that’.

  [48a1] 34 · Men will frequently fall into error through not setting out the terms of the proposition well, e.g. suppose A to be health, B disease, C man. It is true to say that A cannot belong to any B (for health belongs to no disease) and again that B [5] belongs to every C (for every man is capable of disease). It would seem to follow that health cannot belong to any man. The reason for this is that the terms are not set out well in expression, since if the things which are in the conditions are [10] substituted, no deduction can be made, e.g. if healthy is substituted for health and diseased for disease. For it is not true to say that being healthy cannot belong to one who is diseased. But unless this is assumed no conclusion results, save in respect of possibility; but such a conclusion is not impossible; for it is possible that health [15] should belong to no man. Again the falsity may occur in a similar way in the middle figure: it is not possible that health should belong to any disease, but it is possible that health should belong to every man, consequently it is not possible that disease should belong to any man. In the third figure the falsity results in reference to possibility. For health and disease, and knowledge and ignorance, and in general contraries, may belong to the same thing, but cannot belong to one another. This is [20] not in agreement with what was said before; for we stated that when several things could belong to the same thing, they could belong to one another.

  It is evident then that in all these cases the error arises from the setting out of the terms; for if the things that are in the conditions are substituted, no falsity [25] arises. It is clear then that in such propositions what possesses the condition ought always to be substituted for the condition and taken as the term.

  35 · We must not always seek to set out the terms in a single word; for we shall often have phrases to which no single name is equivalent. Hence it is difficult [30] to reduce deductions with such terms. Sometimes too error will result from such a search, e.g. the belief that deduction can establish something immediate. Let A stand for two right angles, B for triangle, C for isosceles triangle. A then belongs to C because of B; but A belongs to B not in virtue of anything else (for the triangle in [35] virtue of its own nature contains two right angles); consequently there will be no middle term for AB, although it is demonstrable. For it is clear that the middle must not always be assumed to be an individual thing, but sometimes a phrase, as happens in the case mentioned.

  36 · That the first term belongs to the middle, and the middle to the [40] extreme, must not be understood in the sense that they can always be predicated of one another or that the first term will be predicated of the middle in the same way as [48b1] the middle is predicated of the last term. The same holds if the premisses are negative. But we must suppose that ‘to belong’ has as many meanings as the ways in which ‘to be’ and ‘it is true to say this is that’ are used. Take for example the statement that there is a single science of contraries. Let A stand for there being a [5] single science, and B for things which are contrary to one another. Then A belongs to B, not in the sense that contraries are a single science, but in the sense that it is true to say of the contraries that there is a single science of them.

  It happens sometimes that the first term is said of the middle, but the middle is [10] not said of the third term, e.g. if wisdom is knowledge, and wisdom is of the good, the conclusion is that there is knowledge of the good. The good then is not knowledge, though wisdom is knowledge. Sometimes the middle term is said of the [15] third, but the first is not said of the middle, e.g. if there is a science of everything that has a quality, or is a contrary, and the good both is a contrary and has a quality, the conclusion is that there is a science of the good—but the good is not a science, nor is that which has a quality or is a contrary, though the good is both of these. Sometimes neither the first term is said of the middle, nor the middle of the third, [20] while the first is sometimes said of the third, and sometimes not; e.g. if there is a genus of that of which there is a science, and there is a science of the good, we conclude that there is a genus of the good. But nothing is predicated of anything. And if that of which there is a science is a genus, and there is a science of the good, [25] we conclude that the good is a genus. The first term then is predicated of the extreme, but the terms are not said of one another.

  The same holds good where the relation is negative. For ‘that does not belong [30] to this’ does not always mean that this is not that, but sometimes that this is not of that or for that, e.g. there is not a motion of a motion or a becoming of a becoming, but there is a becoming of pleasure; so pleasure is not a becoming. Or again it may be said that there is a sign of laughter, but there is not a sign of a sign, consequently laughter is not a sign. This holds in the other cases too, in which a problem is refuted [35] because the genus is asserted in a particular way in relation to it. Again take the inference: opportunity is not the right time; for opportunity belongs to God, but the right time does not, since nothing is useful to God. We must take as terms opportunity, right time, God; but the proposition must be understood according to the case of the noun. For we state this universally without qualification, that the [49a1] terms ought always to be stated in the nominative, e.g. man, good, contraries, not in oblique cases, e.g. of man, of good, of contraries, but the propositions ought to be understood with reference to the cases of each term—either the dative, e.g. ‘equal to this’, or the genitive, e.g. ‘double of this’, or the accusative, e.g. ‘that which strikes or sees this’, or the nominative, e.g. ‘man is an animal’, or in whatever other way the [5] word falls in the proposition.

  37 · The expressions ‘this belongs to that’ and ‘this holds true of that’ must be understood in as many ways as there are different categories, and these categories must be taken either with or without qualification, and further as simple or compound; the same holds good of negative expressions. We must consider these [10] points and define them better.<
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  38 · A term which is repeated in the propositions ought to be joined to the first extreme, not to the middle. I mean for example that if a deduction should be made proving that there is knowledge of justice, that it is good, the expression ‘that it is good’ (or ‘qua good’) should be joined to the first term. Let A stand for [15] knowledge that it is good, B for good, C for justice. It is true to predicate A of B. For of the good there is knowledge that it is good. Also it is true to predicate B of C. For justice is identical with a good. In this way an analysis of the argument can be made. But if the expression ‘that it is good’ were added to B, there will be no [20] analysis; for A will be true of B, but B will not be true of C. For to predicate of justice the term ‘good that it is good’ is false and not intelligible. Similarly if it should be proved that the healthy is an object of knowledge quâ good, or goat-stag an object of knowledge quâ not existing, or man perishable quâ an object of sense: in [25] every case in which an addition is made to the predicate, the repetition must be joined to the extreme.

  The position of the terms is not the same when something is deduced without qualification and when the deduction relates to some particular thing or way or condition, e.g. when the good is proved to be an object of knowledge and when it is proved to be an object of knowledge that it is good. If it has been proved to be an [30] object of knowledge without qualification, we must put as middle term that which is, but if we add the qualification ‘that it is good’, the middle term must be that which is something. Let A stand for knowledge that it is something, B stand for something, and C stand for good. It is true to predicate A of B; for ex hypothesi there is knowledge of that which is something, that it is something. B too is true of C; for that which C represents is something. Consequently A is true of C: there will [35] then be knowledge of the good, that it is good: for ex hypothesi the term something indicates the thing’s proper substance. But if being were taken as middle and being (without qualification) were joined to the extreme, not being something, we should not have had a deduction that there is knowledge of the good, that it is good, but that it is; e.g. let A stand for knowledge that it is, B for being, C for good. Clearly [49b1] then in particular deductions we must take the terms in the way stated.