Prior Analytics II. 16, § 1. Now begging and assuming the original question,' to take it generically, falls under the head of not demonstrating what is proposed for proof. Now this happens in several ways besides: (a) if there is no conclusion proved at all; (B) if it is proved by premisses more unknown than itself, or equally unknown; or (y) if what is prior is proved by what is later; for demonstration starts from what is more certain and prior. Now none of these is begging the original question, but since some things are naturally ascertained on their own evidence, and some by means of other things (for the first principles 2 are ascertained on their own ἐν ἀρχῇ προκειμένον (originally proposed for · ἐν ἀρχῇ here proof). = 2 First principles, or ultimate major premisses, are those truths which are not capable of being deduced; e.g. 'Socrates has life' follows from all men have life; Socrates is a man.' In the same way 'all men have life' follows from all animals having life, and that from all organised beings having life; this, however, cannot be deduced, and is therefore an apxh. Aristotle in Post. Anal. I. 10. 1, defines first principles' thus : λέγω δ' ἀρχὰς ἐν ἑκάστῳ γένει ταύτας, ἃς ὅτι ἔστι μὴ ἐνδέχεται δεῖξαι. They are: (1) Axioms, tà koivà Xeyóμeva džiŵμata (Post. Anal. I. 10. 4), or (2) Hypotheses, voléσeis, which imply the actual existence or non- The faculty which apprehends apxaí is said to be vous (Post. 64. 65. evidence, all subordinate to them by means of others), whenever we try to show on its own evidence that which is not self-evident, then we beg the question. Prior Analytics II. 23, §§ 1-4. How then terms are related to one another, in respect of conversions, and the being more eligible or more to be avoided, is manifest. We ought now to state that not only are demonstrative and dialectical syllogisms formed by the figures described above, but rhetorical syllogisms also, and generally speaking all belief whatever, and belief arrived at by whatever method. For we arrive at all our beliefs either by syllogism or from induction.. Induction then, and the inductive syllogism, is to prove the major term of the middle1 by means of the minor; for instance, if B is the middle of the terms 1 The middle term in this description seems to mean the term which is such in extent. The major is the most general of the three, and is proved of the middle by examining the minor, which consists of all the individuals that compose the middle. We must make sure whether our minor term does include all the individuals of the middle—εἰ ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον—if we are to have a valid induction, as Aristotle understands the word. It is clear that such an induction can easily be put into syllogistic form : All men, horses, and mules are long-lived, All the gall-less animals are men, horses, and mules; All gall-less animals are long-lived. Many logicians regard this induction as the only perfect type; but Mill's idea of induction is not the same as Aristotle's: he examines some of the individuals composing the middle, and endeavours to lay down canons, which will enable us rightly to infer the 'major of the middle by the minor,' though it is not so convertible with the middle-is only a part of the middle. AC, to prove A of B by means of C; for it is thus that we make our inductions. For instance, let A be long-lived; B1 the class of things that has no gall; C the individual long-lived creatures, as man, horse, mule. Now A belongs to the whole of C, for every gallless creature is long lived. But B also the having no gall-belongs to all C. If, then, C is convertible with B, and the middle is not more extensive (than the minor), A must of necessity belong to B. For we have shown before that if any two predicates belong to the same subject, and it is convertible with one of them, the other of the predicates will also belong to the convertible term. But we must take into consideration the C, which is composed of all the individuals; for Induction works by means of all. This kind of syllogism belongs to the primary and immediate3 proposition; for propositions which have a middle are proved by the middle, those which have not, by Induction. And in a certain way Induction is opposed to Syllogism; for Syllogism proves the major of the minor by means of the middle; Induction the major of the middle by means of the minor. Accordingly the Syllogism, which works by means of the middle, is by nature prior and better known, but that by means of Induction is clearer to us.4 2 1 Tò èp' & B; that which is denoted by B, lit. that on which is B.' All C is A, All C is B; .. All B is A (if C and B are convertible). i.e. That has no middle term by which we can prove it. It would be hard to find a passage showing a truer and more profound insight into the relation of Induction and Deduction than this. It is true that nature works deductively (so to speak); the 66 Prior Analytics II. 24, §§ 1-3. Now Example1 is when the major is shown to belong to the middle by means of a term resembling the minor. But both the middle must be known to belong to the minor, and the major to the term resembling the minor. law of gravitation is the cause of the apple falling; the apple does not cause the law. But we can only learn the general laws by our experience of the particular facts. For the antithesis expressed in the text, cf. Post. Anal. I. 2. §§ 4, 5. 1 Aristotle's Taрáderyμa is much the same as our 'argument from analogy,' and perhaps comes nearer to the modern notion of Induction than his waywyń, in that whilst it argues not from all the particulars to the collective whole, but from particulars to particulars, it implies the truth of some general principle embracing both particulars (e.g. in his own example, Aŋtтéov åтɩ tò tyds dμópovs Kakóν). Example is described in similar terms, but perhaps more clearly, Rhet i. 2, 19; i. 2, 8. We may analyse the argument in the text thus: The war of the Thebans against the Phocians (4) was evil (A), The war of the Thebans against the Phocians (4) was a war between neighbours (B); .. Wars between neighbours (B) are evil (A). But the war between the Athenians and Thebans (F) is a war between neighbours (B); .. The war between the Athenians and the Thebans (г) is evil (A). It is clear that in the first of these syllogisms there is, strictly speaking, an illicit process of the minor; in practice, however, we are constantly obliged to use arguments of this kind; they may have any degree of cogency, from the slightest and vaguest presumption, to virtual certainty. In judging of their value we have mainly to consider the following questions: (1) Are there many or few points in which the terms agree? (2) Are there many or few points in which they differ? (3) Are there many or few points in which we do not know whether they agree or differ? (4) Do these points of agreement and difference seem fundamental or superficial? connected or unconnected with the quality which we are inferring of the one because we know it of the other? 6 For instance, let A be evil;' B making war against neighbours' C 'the Athenians making war against the Thebans ;' and D 'the Thebans against the Phocians:' if, then, we wish to prove that to make war against the Thebans is evil (for the Athenians), we must get as a premiss that to make war against one's neighbours is evil. Now of this we are persuaded by similar cases; e.g., the war against the Phocians was evil for the Thebans. Since then to make war against one's neighbours is evil, and war against the Thebans is a war against neighbours, it is manifest that war with the Thebans is evil. It is then manifest that B belongs to C and to D (for both are cases of making war against neighbours), and that A belongs to D (for the war against the Phocians did not advantage the Thebans), and that A belongs to B will be proved by means of D. We should proceed in the same way also if the similar cases by which we had to prove the relation of the middle to the major (i.e. that the major is an attribute of the middle) were more than one. It is manifest then that Example has neither the relation of part to whole, nor of whole to part, but of part to part, when both terms fall under the same head, and one of them is known. And it differs from Induction, in that the latter proved the major to belong to the middle by an enumeration of all the individuals, and did not add to it the (de· ductive) inference; whereas Example does so add the inference, and does not make its proof by enumeration of all the individuals.1 . 'The meaning of this passage appears to be that Induction, examining all the individuals, finds a proposition to be universally true of the class, but does not go on to apply it, arguing back deductively, D |