The Basic Works of Aristotle (Modern Library Classics)

by Mckeon, Richard

  One science differs from another when their basic truths have neither a common source nor are derived those of the one science from those of the other. This is verified when we reach the indemonstrable premisses of a science, for they must be within one genus with its conclusions: and this again is verified if the conclusions proved by means of them fall within one genus—i. e. are homogeneous. [87b]

  29 One can have several demonstrations of the same connexion not only by taking from the same series of predication middles which are other than the immediately cohering term—e. g. by taking C, D, (5) and F severally to prove A–B—but also by taking a middle from another series. Thus let A be change, D alteration of a property, B feeling pleasure, and G relaxation. We can then without falsehood predicate D of B and A of D, for he who is pleased suffers alteration of a property, (10) and that which alters a property changes. Again, we can predicate A of G without falsehood, and G of B; for to feel pleasure is to relax, and to relax is to change. So the conclusion can be drawn through middles which are different, i. e. not in the same series—yet not so that neither of these middles is predicable of the other, for they must both be attributable to some one subject. (15)

  A further point worth investigating is how many ways of proving the same conclusion can be obtained by varying the figure.

  30 There is no knowledge by demonstration of chance conjunctions; for chance conjunctions exist neither by necessity nor as general connexions but comprise what comes to be as something distinct from these. (20) Now demonstration is concerned only with one or other of these two; for all reasoning proceeds from necessary or general premisses, the conclusion being necessary if the premisses are necessary and general if the premisses are general. (25) Consequently, if chance conjunctions are neither general nor necessary, they are not demonstrable.

  31 Scientific knowledge is not possible through the act of perception. Even if perception as a faculty is of ‘the such’ and not merely of a ‘this somewhat’, yet one must at any rate actually perceive a ‘this somewhat’, (30) and at a definite present place and time: but that which is commensurately universal and true in all cases one cannot perceive, since it is not ‘this’ and it is not ‘now’; if it were, it would not be commensurately universal—the term we apply to what is always and everywhere. Seeing, therefore, that demonstrations are commensurately universal and universals imperceptible, we clearly cannot obtain scientific knowledge by the act of perception: nay, (35) it is obvious that even if it were possible to perceive that a triangle has its angles equal to two right angles, we should still be looking for a demonstration—we should not (as some48 say) possess knowledge of it; for perception must be of a particular, whereas scientific knowledge involves the recognition of the commensurate universal. So if we were on the moon, and saw the earth shutting out the sun’s light, (40) we should not know the cause of the eclipse: we should perceive the present fact of the eclipse, but not the reasoned fact at all, since the act of perception is not of the commensurate universal. [88a] I do not, of course, deny that by watching the frequent recurrence of this event we might, after tracking the commensurate universal, possess a demonstration, for the commensurate universal is elicited from the several groups of singulars. (5)

  The commensurate universal is precious because it makes clear the cause; so that in the case of facts like these which have a cause other than themselves universal knowledge49 is more precious than sense-perceptions and than intuition. (As regards primary truths there is of course a different account to be given.50) Hence it is clear that knowledge of things demonstrable cannot be acquired by perception, (10) unless the term perception is applied to the possession of scientific knowledge through demonstration. Nevertheless certain points do arise with regard to connexions to be proved which are referred for their explanation to a failure in sense-perception: there are cases when an act of vision would terminate our inquiry, not because in seeing we should be knowing, but because we should have elicited the universal from seeing; if, for example, we saw the pores in the glass and the light passing through, the reason of the kindling would be clear to us51 because we should at the same time see it in each instance and intuit that it must be so in all instances. (15)

  32 All syllogisms cannot have the same basic truths. This may be shown first of all by the following dialectical considerations. (1) Some syllogisms are true and some false: for though a true inference is possible from false premisses, (20) yet this occurs once only—I mean if A, for instance, is truly predicable of C, but B, the middle, is false, both A–B and B–C being false; nevertheless, if middles are taken to prove these premisses, they will be false because every conclusion which is a falsehood has false premisses, while true conclusions have true premisses, (25) and false and true differ in kind. Then again, (2) falsehoods are not all derived from a single identical set of principles: there are falsehoods which are the contraries of one another and cannot coexist, e. g. ‘justice is injustice’, and ‘justice is cowardice’; ‘man is horse’, and ‘man is ox’; ‘the equal is greater’, and ‘the equal is less’. From our established principles we may argue the case as follows, (30) confining ourselves therefore to true conclusions. Not even all these are inferred from the same basic truths; many of them in fact have basic truths which differ generically and are not transferable; units, for instance, which are without position, cannot take the place of points, which have position. The transferred terms could only fit in as middle terms or as major or minor terms, or else have some of the other terms between them, (35) others outside them.

  Nor can any of the common axioms—such, I mean, as the law of excluded middle—serve as premisses for the proof of all conclusions. For the kinds of being are different, and some attributes attach to quanta and some to qualia only; and proof is achieved by means of the common axioms taken in conjunction with these several kinds and their attributes. [88b]

  Again, it is not true that the basic truths are much fewer than the conclusions, for the basic truths are the premisses, (5) and the premisses are formed by the apposition of a fresh extreme term or the interposition of a fresh middle. Moreover, the number of conclusions is indefinite, though the number of middle terms is finite; and lastly some of the basic truths are necessary, others variable.

  Looking at it in this way we see that, since the number of conclusions is indefinite, the basic truth cannot be identical or limited in number. (10) If, on the other hand, identity is used in another sense, and it is said, e. g., ‘these and no other are the fundamental truths of geometry, these the fundamentals of calculation, these again of medicine’; would the statement mean anything except that the sciences have basic truths? To call them identical because they are self-identical is absurd, since everything can be identified with everything in that sense of identity. (15) Nor again can the contention that all conclusions have the same basic truths mean that from the mass of all possible premisses any conclusion may be drawn. That would be exceedingly naïve, for it is not the case in the clearly evident mathematical sciences, nor is it possible in analysis, since it is the immediate premisses which are the basic truths, and a fresh conclusion is only formed by the addition of a new immediate premiss: but if it be admitted that it is these primary immediate premisses which are basic truths, (20) each subject-genus will provide one basic truth. If, however, it is not argued that from the mass of all possible premisses any conclusion may be proved, nor yet admitted that basic truths differ so as to be generically different for each science, it remains to consider the possibility that, while the basic truths of all knowledge are within one genus, special premisses are required to prove special conclusions. (25) But that this cannot be the case has been shown by our proof that the basic truths of things generically different themselves differ generically. For fundamental truths are of two kinds, those which are premisses of demonstration and the subject-genus; and though the former are common, the latter—number, for instance, and magnitude—are peculiar.

  33 Scientific knowledge and
its object differ from opinion and the object of opinion in that scientific knowledge is commensurately universal and proceeds by necessary connexions, (30) and that which is necessary cannot be otherwise. So though there are things which are true and real and yet can be otherwise, scientific knowledge clearly does not concern them; if it did, things which can be otherwise would be incapable of being otherwise. (35) Nor are they any concern of rational intuition—by rational intuition I mean an originative source of scientific knowledge—nor of indemonstrable knowledge, which is the grasping of the immediate premiss. [89a] Since then rational intuition, science, and opinion, and what is revealed by these terms, are the only things that can be ‘true’, it follows that it is opinion that is concerned with that which may be true or false, and can be otherwise: opinion in fact is the grasp of a premiss which is immediate but not necessary. This view also fits the observed facts, for opinion is unstable, (5) and so is the kind of being we have described as its object. Besides, when a man thinks a truth incapable of being otherwise he always thinks that he knows it, never that he opines it. He thinks that he opines when he thinks that a connexion, though actually so, may quite easily be otherwise; for he believes that such is the proper object of opinion, while the necessary is the object of knowledge. (10)

  In what sense, then, can the same thing be the object of both opinion and knowledge? And if any one chooses to maintain that all that he knows he can also opine, why should not opinion be knowledge? For he that knows and he that opines will follow the same train of thought through the same middle terms until the immediate premisses are reached; because it is possible to opine not only the fact but also the reasoned fact, (15) and the reason is the middle term; so that, since the former knows, he that opines also has knowledge.

  The truth perhaps is that if a man grasp truths that cannot be other than they are, in the way in which he grasps the definitions through which demonstrations take place, he will have not opinion but knowledge: if on the other hand he apprehends these attributes as inhering in their subjects, but not in virtue of the subjects’ substance and essential nature, he possesses opinion and not genuine knowledge; and his opinion, (20) if obtained through immediate premisses, will be both of the fact and of the reasoned fact; if not so obtained, of the fact alone. The object of opinion and knowledge is not quite identical; it is only in a sense identical, just as the object of true and false opinion is in a sense identical. The sense in which some maintain that true and false opinion can have the same object leads them to embrace many strange doctrines, (25) particularly the doctrine that what a man opines falsely he does not opine at all. There are really many senses of ‘identical’, and in one sense the object of true and false opinion can be the same, in another it cannot. Thus, to have a true opinion that the diagonal is commensurate with the side would be absurd: but because the diagonal with which they are both concerned is the same, (30) the two opinions have objects so far the same: on the other hand, as regards their essential definable nature these objects differ. The identity of the objects of knowledge and opinion is similar. Knowledge is the apprehension of, e. g. the attribute ‘animal’ as incapable of being otherwise, opinion the apprehension of ‘animal’ as capable of being otherwise—e. g. the apprehension that animal is an element in the essential nature of man is knowledge; the apprehension of animal as predicable of man but not as an element in man’s essential nature is opinion: man is the subject in both judgments, (35) but the mode of inherence differs.

  This also shows that one cannot opine and know the same thing simultaneously; for then one would apprehend the same thing as both capable and incapable of being otherwise—an impossibility. [89b] Knowledge and opinion of the same thing can coexist in two different people in the sense we have explained, but not simultaneously in the same person. That would involve a man’s simultaneously apprehending, e. g., (1) that man is essentially animal—i. e. cannot be other than animal—and (2) that man is not essentially animal, (5) that is, we may assume, may be other than animal.

  Further consideration of modes of thinking and their distribution under the heads of discursive thought, intuition, science, art, practical wisdom, and metaphysical thinking, belongs rather partly to natural science, partly to moral philosophy.

  34 Quick wit is a faculty of hitting upon the middle term instantaneously. (10) It would be exemplified by a man who saw that the moon has her bright side always turned towards the sun, and quickly grasped the cause of this, namely that she borrows her light from him; or observed somebody in conversation with a man of wealth and divined that he was borrowing money, or that the friendship of these people sprang from a common enmity. In all these instances he has seen the major and minor terms and then grasped the causes, (15) the middle terms.

  Let A represent ‘bright side turned sunward’, B ‘lighted from the sun’, C the moon. Then B, ‘lighted from the sun’, is predicable of C, the moon, and A, ‘having her bright side towards the source of her light’, (20) is predicable of B. So A is predicable of C through B.

  * * *

  1 Plato, Meno, 80 E.

  2 Cf. An. Pr. ii, ch. 21.

  3 Cf. the following chapter and more particularly ii, ch. 19.

  4 An. Pr. i, ch. 25.

  5 Ibid. ii, ch. 5.

  6 Ibid. ii, cc. 5 and 6.

  7 Plato, Euthydemus, 277 B.

  8 Cf. Met. 1039a 9.

  9 Cf. i, cc. 9 and 13.

  10 sc. axioms.

  11 Cf. Plato, Theaetetus, 189 E ff.

  12 Lit. ‘even if the middle is itself and also what is not itself’; i. e. you may pass from the middle term man to include not-man without affecting the conclusion.

  13 Cf. 75a 42 ff. and 76b 13.

  14 An. Pr. i. 1. The ‘opposite facts’ are those which would be expressed in the alternatively possible answers to the dialectical question, the dialectician’s aim being to refute his interlocutor whether the latter answers the question put to him affirmatively or in the negative.

  15 i. e. a premiss put in the form of a question.

  16 sc. ‘which require two sciences for their proof’. Cf. 78b 35.

  17 i. e. in Celarent.

  18 i. e. in Cesare or Camestres.

  19 Cf. 80a 29.

  20 Cf. 80b 17–26.

  21 Cf. 80b 26–32.

  22 sc. a predicate above which is no wider universal.

  23 sc. ‘that no C is B’.

  24 i. e. each of the successive prosyllogisms required to prove the negative minors contains an affirmative major in which the middle is affirmed of a subject successively ‘higher’ or more universal than the subject of the first syllogism. Thus:

  Syllogism: All B is D

  No C is D

  No C is B

  Proyllogisms: All D is E All E is F

  No C is E No C is F

  No C is D No C is E

  B, D, E, &c., are successively more universal subjects; and the series of affirmative majors containing them must ex hypothesi terminate.

  25 Since the series of affirmative majors terminates and since an affirmative major is required for each prosyllogism, we shall eventually reach a minor incapable of proof and therefore immediate.

  26 If the attributes in a series of predication such as we are discussing are substantial, they must be finite in number, because they are then the elements constituting the definition of a substance.

  27 The first of three statements preliminary to a proof that predicates which are accidental—other than substantial—cannot be unlimited in number: Accidental is to be distinguished from essential or natural predication [cf. i, ch. 4, 73b 5 ff. and An. Pr. i, ch. 25, 43a 25–6]. The former is alien to demonstration: hence, provided that a single attribute is predicated of a single subject, all genuine predicates fall either under the category of substance or under one of the adjectival categories.

  28 Second preliminary statement: The precise distinction of substantive from adjectival predication makes clear (implicitly) the two distinctions, (a)
that between natural and accidental predication, (b) that between substantival and adjectival predication, which falls within natural predication. This enables us to reject the Platonic Forms.

  29 Third preliminary statement merging into the beginning of the proof proper: Reciprocal predication cannot produce an indefinite regress because it is not natural predication.

  30 Expansion of third preliminary statement: Reciprocals A and B might be predicated of one another (a) substantially; but it has been proved already that because a definition cannot contain an infinity of elements substantial predication cannot generate infinity; and it would disturb the relation of genus and species: (b) as qualia or quanta &c; but this would be unnatural predication, because all such predicates are adjectival, i. e. accidents, or coincidents, of substances.

  31 The ascent of predicates is also finite; because all predicates fall under one or other of the categories, and (a) the series of predicates under each category terminates when the category is reached, and (b) the number of the categories is limited. [(a) seems to mean that an attribute as well as a substance is definable by genus and differentia, and the elements in its definition must terminate in an upward direction at the category, and can therefore no more form an infinite series than can the elements constituting the definition of a substance.]

  32 To reinforce this brief proof that descent and ascent are both finite we may repeat the premisses on which it depends. These are (1) the assumption that predication means the predication of one attribute of one subject, and (2) our proof that accidents cannot be reciprocally predicated of one another, because that would be unnatural predication. It follows from these premisses that both ascent and descent are finite. [Actually (2) only reinforces the proof that the descent terminates.]