54Analyt. Prior. II. xxiii. p. 68, b. 27: δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ’ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων.
54Analyt. Prior. II. xxiii. p. 68, b. 27: δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ’ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων.
55Analyt. Prior. II.xxiii.p. 68, p. 23: εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β, καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν.Julius Pacius translates this: “Si igitur convertatur τὸ Γ cum B, nec medium excedat, necesse est τὸ Α τῷ Β inesse.â€� These Latin words include the same grammatical ambiguity as is found in the Greek original:medium, like τὸ μέσον, may be either an accusative case governed byexcedat, or a nominative case precedingexcedat. The same may be said of the other Latin translations, from Boethius downwards.But M. Barthélemy St. Hilaire in his French translation, and Sir W. Hamilton in his English translation (Lectures on Logic, Vol. II. iv. p. 358, Appendix), steer clear of this ambiguity. The former says: “Si donc C est réciproque à B, et qu’il ne dépasse pas le moyen, il est nécessaire alors que A soit à B:â€� to the same purpose, Hamilton,l. c.These words are quite plain and unequivocal. Yet I do not think that they convey the meaning of Aristotle. In my judgment, Aristotle meant to say: “If then C reciprocates with B, and if the middle term (B) does not stretch beyond (the minor C), it is necessary that A should be predicable of B.â€� To show that this must be the meaning, we have only to reflect on what C and B respectively designate. It is assumed that C designates the sum of individual bile-less animals; and that B designates the class or class-term bile-less, that is, the totality thereof. Now the sum of individuals included in the minor (C) cannot upon any supposition overpass the totality: but it may very possibly fall short of totality; or (to state the same thing in other words) the totality may possibly surpass the sum of individuals under survey, but it cannot possibly fall short thereof. B is here the limit, and may possibly stretch beyond C; but cannot stretch beyond B. Hence I contend that the translations, both by M. Barthélemy St. Hilaire and Sir W. Hamilton, take the wrong side in the grammatical alternative admissible under the words καὶ μὴ ὑπερτείνει τὸ μέσον. The only doubt that could possibly arise in the case was, whether the aggregate of individuals designated by the minor did, or did not, reach up to the totality designated by the middle term; or (changing the phrase) whether the totality designated by the middle term did, or did not, stretch beyond the aggregate of individuals designated by the minor. Aristotle terminates this doubt by the words: “And if the middle term doesnotstretch beyond (the minor).â€� Of course the middle term does not stretch beyond, when the terms reciprocate; but when they do not reciprocate, the middle term must be themoreextensive of the two; it canneverbe thelessextensive of the two, since the aggregate of individuals cannot possibly exceed totality, though it may fall short thereof.I have given in the text what I think the true meaning of Aristotle, departing from the translations of M. Barthélemy St. Hilaire and SirW. Hamilton.
55Analyt. Prior. II.xxiii.p. 68, p. 23: εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β, καὶ μὴ ὑπερτείνει τὸ μέσον, ἀνάγκη τὸ Α τῷ Β ὑπάρχειν.
Julius Pacius translates this: “Si igitur convertatur τὸ Γ cum B, nec medium excedat, necesse est τὸ Α τῷ Β inesse.â€� These Latin words include the same grammatical ambiguity as is found in the Greek original:medium, like τὸ μέσον, may be either an accusative case governed byexcedat, or a nominative case precedingexcedat. The same may be said of the other Latin translations, from Boethius downwards.
But M. Barthélemy St. Hilaire in his French translation, and Sir W. Hamilton in his English translation (Lectures on Logic, Vol. II. iv. p. 358, Appendix), steer clear of this ambiguity. The former says: “Si donc C est réciproque à B, et qu’il ne dépasse pas le moyen, il est nécessaire alors que A soit à B:â€� to the same purpose, Hamilton,l. c.These words are quite plain and unequivocal. Yet I do not think that they convey the meaning of Aristotle. In my judgment, Aristotle meant to say: “If then C reciprocates with B, and if the middle term (B) does not stretch beyond (the minor C), it is necessary that A should be predicable of B.â€� To show that this must be the meaning, we have only to reflect on what C and B respectively designate. It is assumed that C designates the sum of individual bile-less animals; and that B designates the class or class-term bile-less, that is, the totality thereof. Now the sum of individuals included in the minor (C) cannot upon any supposition overpass the totality: but it may very possibly fall short of totality; or (to state the same thing in other words) the totality may possibly surpass the sum of individuals under survey, but it cannot possibly fall short thereof. B is here the limit, and may possibly stretch beyond C; but cannot stretch beyond B. Hence I contend that the translations, both by M. Barthélemy St. Hilaire and Sir W. Hamilton, take the wrong side in the grammatical alternative admissible under the words καὶ μὴ ὑπερτείνει τὸ μέσον. The only doubt that could possibly arise in the case was, whether the aggregate of individuals designated by the minor did, or did not, reach up to the totality designated by the middle term; or (changing the phrase) whether the totality designated by the middle term did, or did not, stretch beyond the aggregate of individuals designated by the minor. Aristotle terminates this doubt by the words: “And if the middle term doesnotstretch beyond (the minor).â€� Of course the middle term does not stretch beyond, when the terms reciprocate; but when they do not reciprocate, the middle term must be themoreextensive of the two; it canneverbe thelessextensive of the two, since the aggregate of individuals cannot possibly exceed totality, though it may fall short thereof.
I have given in the text what I think the true meaning of Aristotle, departing from the translations of M. Barthélemy St. Hilaire and SirW. Hamilton.
56Analyt. Prior. II. xxiii. p. 68, b. 30-38: ἔστι δ’ ὁ τοιοῦτος συλλογισμὸς τῆς πρώτης καὶ ἀμέσου προτάσεως· ὧν μὲν γάρ ἐστι μέσον, διὰ τοῦ μέσου ὁ συλλογισμός, ὧν δὲ μή ἐστι, δι’ ἐπαγωγῆς. — φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ’ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.
56Analyt. Prior. II. xxiii. p. 68, b. 30-38: ἔστι δ’ ὁ τοιοῦτος συλλογισμὸς τῆς πρώτης καὶ ἀμέσου προτάσεως· ὧν μὲν γάρ ἐστι μέσον, διὰ τοῦ μέσου ὁ συλλογισμός, ὧν δὲ μή ἐστι, δι’ ἐπαγωγῆς. — φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ’ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.
From Induction he proceeds to Example. You here take in (besides the three terms, major, middle, and minor, of the Syllogism) a fourth term; that is, a new particular case analogous to the minor. Your purpose here is to show — not, as in the ordinary Syllogism, that the major term is predicable of the minor, but, as in the Inductive Syllogism — that the major term is predicable of the middle term; and you prove this conclusion, not (as in the Inductive Syllogism) through the minor term, but through the new case or fourth term analogous to the minor.57Let A represent evil or mischievous; B, war against neighbours, generally; C, war of Athens against Thebes, an event to come and under deliberation; D, war of Thebes against Phokis, a past event of which the issue is known to have been signally mischievous. You assume as known, first, that A is predicable of D,i.e.that the war of Thebes against Phokis has been disastrous; next, that B is predicable both of C and of D,i.e.that each of the two wars, of Athens against Thebes, and of Thebes against Phokis, is a war of neighbours against neighbours, or a conterminous war. Now from the premiss that A is predicable of D, along with the premiss that B is predicable of D, you infer that A is predicable of the class B, or of conterminous wars generally; and hence you draw the farther inference, that A is also predicable of C, another particular case under the same class B. The inference here is, in the first instance, from part to whole; and finally, through that whole, from the one part to another part of the same whole.Inductionincludes in its major premiss all the particulars, declaring all of them to be severally subjects of the major as predicate; hence it infers as conclusion, that the major is also predicable of the middle or class-term comprising all these particulars, but comprising no others.Exampleincludes not all, but only one or a few particulars; inferring from it or them, first, to the entireclass, next, to some new analogous particular belonging to the class.58
57Ibid. II. xxiv. p. 68, b. 38: παραδεῖγμα δ’ ἐστὶν ὅταν τῷ μέσῳ τὸ ἄκρον ὑπάρχον δειχθῇ διὰ τοῦ ὁμοίου τῷ τρίτῳ.
57Ibid. II. xxiv. p. 68, b. 38: παραδεῖγμα δ’ ἐστὶν ὅταν τῷ μέσῳ τὸ ἄκρον ὑπάρχον δειχθῇ διὰ τοῦ ὁμοίου τῷ τρίτῳ.
58Analyt. Prior. II. xxiv. p. 69, a. 1-19.Julius Pacius (p. 400) notes the unauthorized character of this so-called Paradeigmatic Syllogism, contradicting the rules of the figures laid down by Aristotle, and also the confused manner in which the scope of it is described: first, to infer from a single example to the universal; next, to infer from a single examplethroughthe universal to another parallel case. To which we may add the confused description in p. 69, a. 17, 18, where τὸ ἄκρον in the first of the two lines signifies themajorextreme — in the second of the two theminorextreme. See Waitz’s note, p. 533.If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on a different occasion disallowing altogether this so-called Syllogism from Example.
58Analyt. Prior. II. xxiv. p. 69, a. 1-19.Julius Pacius (p. 400) notes the unauthorized character of this so-called Paradeigmatic Syllogism, contradicting the rules of the figures laid down by Aristotle, and also the confused manner in which the scope of it is described: first, to infer from a single example to the universal; next, to infer from a single examplethroughthe universal to another parallel case. To which we may add the confused description in p. 69, a. 17, 18, where τὸ ἄκρον in the first of the two lines signifies themajorextreme — in the second of the two theminorextreme. See Waitz’s note, p. 533.
If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on a different occasion disallowing altogether this so-called Syllogism from Example.
These chapters respecting Induction and Example are among the most obscure and perplexing in the Aristotelian Analytica. The attempt to throw both Induction and Example into the syllogistic form is alike complicated and unfortunate; moreover, the unsatisfactory reading and diversities in the text, among commentators and translators, show that the reasoning of Aristotle has hitherto been imperfectly apprehended.59From some of his phrases, we see that he was aware of the essential antithesis between Induction and Syllogism; yet the syllogistic forms appear to have exercised such fascination over his mind, that he could not be satisfied without trying to find some abnormal form of Syllogism to represent and give validity to Induction. In explaining generally what the Syllogism is, andwhat Induction is, he informs us that the Syllogism presupposes and rests upon the process of Induction as its postulate. For there can be no valid Syllogism without an universal proposition in one (at least) of the premisses; and he declares, unequivocally, that universal propositions are obtained only through Induction. How Induction operates through the particular facts of sense, remembered, compared, and coalescing into clusters held together by associating similarity, he has also told us; it is thus that Experience, with its universal notions and conjunctions, is obtained. But this important process is radically distinct from that of syllogizing, though it furnishes the basis upon which all syllogizing is built.
59Sir W. Hamilton (Lectures on Logic, vol. i. p. 319) says justly, that Aristotle has been very brief and unexplicit in his treatment of Induction. Yet the objections that Hamilton makes to Aristotle are very different from those which I should make. In the learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369), he collects various interesting criticisms of logicians respecting Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ, VIII. xi.) says very truly:— “Quid vero sit Inductio, perobscure ab Aristotele declaratur; nec ab interpretibus intelligitur, quo modosyllogismusper medium concludat majus extremum de minore;inductio, majus de medio per minus.�The Inductive Syllogism, as constructed by Aristotle, requires a reciprocating minor premiss. It may, indeed, be cited (as I have already remarked) in support of Hamilton’s favourite precept of quantifying the predicate. The predicate of this minor must be assumed asquantified in thought, the subject being taken as co-extensive therewith. Therefore Hamilton’s demand that it shall bequantified in speechhas really in this case that foundation which he erroneously claims for it in all cases. He complains that Lambert and some other logicians dispense with the necessity of quantifying the predicate of the minor by making it disjunctive; and adds the remarkable statement that “the recent German logicians, Herbart, Twesten, Drobisch, &c., following Lambert, make the Inductive Syllogism a byeword� (p. 366). I agree with them in thinking the attempted transformation of Induction into Syllogism very unfortunate, though my reasons are probably not the same as theirs.Trendelenburg agrees with those who said that Aristotle’s doctrine about the Inductive Syllogism required that the minor should be disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi. pp. 262, 263; also Erläuterungen zu den Elementen der Aristotelischen Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System derLogik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference is to be twisted into Syllogism, it seems more naturally to fall into anhypotheticalsyllogism,e. g.:—If this, that, and the other magnet attract iron, all magnets attract iron;But this, that, and the other magnet do attract iron:Ergo, &c.
59Sir W. Hamilton (Lectures on Logic, vol. i. p. 319) says justly, that Aristotle has been very brief and unexplicit in his treatment of Induction. Yet the objections that Hamilton makes to Aristotle are very different from those which I should make. In the learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369), he collects various interesting criticisms of logicians respecting Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ, VIII. xi.) says very truly:— “Quid vero sit Inductio, perobscure ab Aristotele declaratur; nec ab interpretibus intelligitur, quo modosyllogismusper medium concludat majus extremum de minore;inductio, majus de medio per minus.�
The Inductive Syllogism, as constructed by Aristotle, requires a reciprocating minor premiss. It may, indeed, be cited (as I have already remarked) in support of Hamilton’s favourite precept of quantifying the predicate. The predicate of this minor must be assumed asquantified in thought, the subject being taken as co-extensive therewith. Therefore Hamilton’s demand that it shall bequantified in speechhas really in this case that foundation which he erroneously claims for it in all cases. He complains that Lambert and some other logicians dispense with the necessity of quantifying the predicate of the minor by making it disjunctive; and adds the remarkable statement that “the recent German logicians, Herbart, Twesten, Drobisch, &c., following Lambert, make the Inductive Syllogism a byeword� (p. 366). I agree with them in thinking the attempted transformation of Induction into Syllogism very unfortunate, though my reasons are probably not the same as theirs.
Trendelenburg agrees with those who said that Aristotle’s doctrine about the Inductive Syllogism required that the minor should be disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi. pp. 262, 263; also Erläuterungen zu den Elementen der Aristotelischen Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System derLogik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference is to be twisted into Syllogism, it seems more naturally to fall into anhypotheticalsyllogism,e. g.:—
If this, that, and the other magnet attract iron, all magnets attract iron;But this, that, and the other magnet do attract iron:Ergo, &c.
The central idea of the Syllogism, as defined by Aristotle, is that of a conclusion following from given premisses bynecessarysequence;60meaning by the termnecessarythus much and no more — that you cannot grant the premisses, and deny the conclusion, without being inconsistent with yourself, or falling into contradiction. In all the various combinations of propositions, set forth by Aristotle as the different figures and modes of Syllogism, this property of necessary sequence is found. But it is a property which no Induction can ever possess.61When Aristotle professes to point out a particular mode of Syllogism to which Induction conforms, he can only do so by falsifying the process of Induction, and by not accurately distinguishing between what is observed and what is inferred. In the case which he takes to illustrate the Inductive Syllogism — the inference from all particular bile-less animals to the whole class bile-less — he assumes that we have ascertained the attribute to belong toallthe particulars, and that the inductive inference consists in passing from all of them to the class-term; the passage from premisses to conclusion being here necessary, and thus falling under the definition of Syllogism; since, to grant the premisses, and yet to deny the conclusion, involves a contradiction. But this doctrine misconceives what the inductive inference really is. We never can observeallthe particulars of a class, which is indefinite as to number of particulars, and definite only in respect of the attributes connoted by the class-term. We can only observesomeof the particulars, a greater or smaller proportion. Now it is in the transition from thesetothe totality of particulars, that the real inductive inference consists; not in the transitionfromthe totality to the class-term which denotes that totality and connotes its determining common attribute. In fact, the distinction between the totality of particulars and the meaning of the class-term, is one not commonly attended to; though it is worthy of note in an analysis of the intellectual process, and is therefore brought to view by Aristotle. But he employs it incorrectly as an intermediate step to slur over the radical distinction between Induction and Syllogism. He subjoins:62— “You must conceive the minor term C (in the Inductive Syllogism) as composed of all the particulars; for Induction is through all of them.â€� You may say that Induction isthroughall the particulars, if you distinguish this totality from the class-term, and if you treat the class-term as the ultimateterminus ad quem. But the Induction must first traveltoall the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself.
60Alexander intimates that Aristotle enunciated “necessary sequenceâ€� as a part of his definition of Syllogism, for the express purpose of distinguishing it from Induction, which is a sequencenot necessary(Schol. ad Top. p. 253, a. 19, Br.): τὸ δ’ἐξ ἀνάγκηςπροσκείμενον ἐν τῷ ὅρῳ, τῆςἐπαγωγῆςχωρίζει τὸν συλλογισμόν·ἔστιμὲν γὰρ καὶ ἐπαγωγὴ λόγος ἐν ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων συμβαίνει, ἀλλ’οὐκἐξ ἀνάγκης.
60Alexander intimates that Aristotle enunciated “necessary sequenceâ€� as a part of his definition of Syllogism, for the express purpose of distinguishing it from Induction, which is a sequencenot necessary(Schol. ad Top. p. 253, a. 19, Br.): τὸ δ’ἐξ ἀνάγκηςπροσκείμενον ἐν τῷ ὅρῳ, τῆςἐπαγωγῆςχωρίζει τὸν συλλογισμόν·ἔστιμὲν γὰρ καὶ ἐπαγωγὴ λόγος ἐν ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων συμβαίνει, ἀλλ’οὐκἐξ ἀνάγκης.
61Alexander (in his Scholia on the Metaphysica,E. i. p. 406,ed. Bonitz) observes truly: ἀλλ’ εἰ ἐκ τῆς αἰσθήσεως καὶ τῆς ἐπαγωγῆς πίστις, οὐκ ἔστιν ἀπόδειξις, πρὸς πᾶσαν γὰρ ἐπαγωγὴν δύναταί τις ἐνίστασθαι καὶ μὴ ἐᾷν τὸ καθόλου συμπεραίνειν.
61Alexander (in his Scholia on the Metaphysica,E. i. p. 406,ed. Bonitz) observes truly: ἀλλ’ εἰ ἐκ τῆς αἰσθήσεως καὶ τῆς ἐπαγωγῆς πίστις, οὐκ ἔστιν ἀπόδειξις, πρὸς πᾶσαν γὰρ ἐπαγωγὴν δύναταί τις ἐνίστασθαι καὶ μὴ ἐᾷν τὸ καθόλου συμπεραίνειν.
62Analyt. Prior. II. xxiii. p. 68, b. 27: δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ’ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων. See Professor Bain’s ‘Inductive Logic,’ chap. i. s. 2, where this process is properly criticised.
62Analyt. Prior. II. xxiii. p. 68, b. 27: δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ’ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων. See Professor Bain’s ‘Inductive Logic,’ chap. i. s. 2, where this process is properly criticised.
Aristotle states very clearly:— “We believe everything either through Syllogism, or from Induction.�63Here, as well as in several other passages, he notes the two processes as essentially distinct. The Syllogism requires in its premisses at least one general proposition; nor does Aristotle conceive the “generalities as the original data:�64he derives them from antecedent Induction. The two processes are (as he says) opposite in a certain way; that is, they are complementary halves of the same whole; Induction being the establishment of those universals which are essential for the deductive march of the Syllogism; while the two together make up the entire process of scientific reasoning. But he forgets or relinquishes this antithesis, when he presents to us the Inductive process as a given variety of Syllogism. And the objection to such a doctrine becomes the more manifest,since in constructing his Inductive Syllogism, he is compelled to admit either that there is no middle term, or that the middle term is subject of the conclusion, in violation of the syllogistic canons.65
63Ibid. II. xxiii. p. 68, b. 13: ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς. Here Induction includes Example, though in the next stage he puts the two apart. Compare Anal. Poster. I. i. p. 71, a. 9.
63Ibid. II. xxiii. p. 68, b. 13: ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς. Here Induction includes Example, though in the next stage he puts the two apart. Compare Anal. Poster. I. i. p. 71, a. 9.
64See Mr. John Stuart Mill’s System of Logic, Bk. II. ch. iii. a. 4, p. 219, 5th ed.
64See Mr. John Stuart Mill’s System of Logic, Bk. II. ch. iii. a. 4, p. 219, 5th ed.
65Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating the argument of Induction as a defective or informal Syllogism: see also to the same purpose SirW. Hamilton, Lectures on Logic, vol. i. p. 322. Aldrich treats it as a Syllogism inBarbara, with the minor suppressed; but Whately rejects this, because the minor necessary to be supplied is false. He maintains that the premiss suppressed is the major, not the minor. I dissent from both. It appears to me that the opinion which Whately pronounces to be a fallacy is the real truth: “Induction is a distinct kind of argument from the Syllogism� (p. 208). It is the essential property of the Syllogism, as defined by Aristotle and by every one after him, that the truth of the conclusion followsnecessarilyfrom the truth of its premisses: that you cannot admit the premisses and reject the conclusion without contradicting yourself. Now this is what the best Induction never attains; and I contend that the presence or absence of this important characteristic is quite enough to constitute “twodistinct kindsof argument.� Whately objects to Aldrich (whom Hamilton defends) for supplying a suppressedminor, because it is “manifestly false� (p. 209). I object to Whately’s suppliedmajor, because it is uncertified, and therefore cannot be used to prove any conclusion. By clothing arguments from Induction in syllogistic form, we invest them with a character of necessity which does not really belong to them. The establishment of general propositions, and the interpretation of them when established (to use the phraseology of Mr. Mill), must always be distinct mental processes; and the forms appropriate to the latter, involving necessary sequence, ought not to be employed to disguise the want of necessity — the varying and graduated probability, inherent in the former. Mr. Mill says (Syst. Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:) — “As Whately remarks, every induction is a syllogism with the major premiss suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premiss.� Even in this modified phraseology, I cannot admit the propriety of throwing Induction into syllogistic forms of argument. By doing this we efface the special character of Induction, as the jump from particular cases, more or fewer, to an universal proposition comprising them and an indefinite number of others besides. To state this in forms which imply that it is a necessary step, involving nothing more than the interpretation of a higher universal proposition, appears to me unphilosophical. Mr. Mill says with truth (in his admirable chapter explaining the real function of the major premiss in a Syllogism, p. 211), that the individual cases are all the evidence which we possess; the step from them to universal propositions ought not to be expressed in forms which suppose universal propositions to be already attained.I will here add that, though Aldrich himself (as I stated at the beginning of this note) treats the argument from Induction as a defective or informal Syllogism, his anonymous Oxonian editor and commentator takes a sounder view. He says (pp. 176, 177, 184, ed. 1823. Oxon.):—“The principles acquired by human powers may be considered as twofold. Some areintuitive, and are commonly called Axioms; the other class of general principles are those acquired by Induction. But it may be doubted whether this distinction is correct. It is highly probable, if not certain, that those primary Axioms generally esteemedintuitive, are in fact acquired by an inductive process; although that process is less discernible, because it takes place long before we think of tracing the actings of our own minds. It is often found necessary to facilitate the understanding of those Axioms, when they are first proposed to the judgment, by illustrations drawn from individual cases. But whether it is, as is generally supposed, the mereenunciationof the principle, or theprinciple itself, which requires the illustration, may admit of a doubt. It seems probable, however that, such illustrations are nothing more than a recurrence to the original method by which the knowledge of those principles was acquired. Thus, the repeated trial or observation of the necessary connection between mathematical coincidence and equality, first authorizes the general position or Axiom relative to that subject. If this conjecture is founded in fact, it follows that bothprimaryandultimateprinciples have the same nature and are alike acquired by the exercise of the inductive faculty.� “Those who acquiesce in the preceding observations will feel a regret to findInductionclassed among defective or informal Syllogisms. It is in fact prior in its order to Syllogism; nor can syllogistic reasoning he carried on to any extent without previous Induction� (p. 184).
65Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating the argument of Induction as a defective or informal Syllogism: see also to the same purpose SirW. Hamilton, Lectures on Logic, vol. i. p. 322. Aldrich treats it as a Syllogism inBarbara, with the minor suppressed; but Whately rejects this, because the minor necessary to be supplied is false. He maintains that the premiss suppressed is the major, not the minor. I dissent from both. It appears to me that the opinion which Whately pronounces to be a fallacy is the real truth: “Induction is a distinct kind of argument from the Syllogism� (p. 208). It is the essential property of the Syllogism, as defined by Aristotle and by every one after him, that the truth of the conclusion followsnecessarilyfrom the truth of its premisses: that you cannot admit the premisses and reject the conclusion without contradicting yourself. Now this is what the best Induction never attains; and I contend that the presence or absence of this important characteristic is quite enough to constitute “twodistinct kindsof argument.� Whately objects to Aldrich (whom Hamilton defends) for supplying a suppressedminor, because it is “manifestly false� (p. 209). I object to Whately’s suppliedmajor, because it is uncertified, and therefore cannot be used to prove any conclusion. By clothing arguments from Induction in syllogistic form, we invest them with a character of necessity which does not really belong to them. The establishment of general propositions, and the interpretation of them when established (to use the phraseology of Mr. Mill), must always be distinct mental processes; and the forms appropriate to the latter, involving necessary sequence, ought not to be employed to disguise the want of necessity — the varying and graduated probability, inherent in the former. Mr. Mill says (Syst. Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:) — “As Whately remarks, every induction is a syllogism with the major premiss suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premiss.� Even in this modified phraseology, I cannot admit the propriety of throwing Induction into syllogistic forms of argument. By doing this we efface the special character of Induction, as the jump from particular cases, more or fewer, to an universal proposition comprising them and an indefinite number of others besides. To state this in forms which imply that it is a necessary step, involving nothing more than the interpretation of a higher universal proposition, appears to me unphilosophical. Mr. Mill says with truth (in his admirable chapter explaining the real function of the major premiss in a Syllogism, p. 211), that the individual cases are all the evidence which we possess; the step from them to universal propositions ought not to be expressed in forms which suppose universal propositions to be already attained.
I will here add that, though Aldrich himself (as I stated at the beginning of this note) treats the argument from Induction as a defective or informal Syllogism, his anonymous Oxonian editor and commentator takes a sounder view. He says (pp. 176, 177, 184, ed. 1823. Oxon.):—
“The principles acquired by human powers may be considered as twofold. Some areintuitive, and are commonly called Axioms; the other class of general principles are those acquired by Induction. But it may be doubted whether this distinction is correct. It is highly probable, if not certain, that those primary Axioms generally esteemedintuitive, are in fact acquired by an inductive process; although that process is less discernible, because it takes place long before we think of tracing the actings of our own minds. It is often found necessary to facilitate the understanding of those Axioms, when they are first proposed to the judgment, by illustrations drawn from individual cases. But whether it is, as is generally supposed, the mereenunciationof the principle, or theprinciple itself, which requires the illustration, may admit of a doubt. It seems probable, however that, such illustrations are nothing more than a recurrence to the original method by which the knowledge of those principles was acquired. Thus, the repeated trial or observation of the necessary connection between mathematical coincidence and equality, first authorizes the general position or Axiom relative to that subject. If this conjecture is founded in fact, it follows that bothprimaryandultimateprinciples have the same nature and are alike acquired by the exercise of the inductive faculty.� “Those who acquiesce in the preceding observations will feel a regret to findInductionclassed among defective or informal Syllogisms. It is in fact prior in its order to Syllogism; nor can syllogistic reasoning he carried on to any extent without previous Induction� (p. 184).
We must presume Syllogisms without a middle term, when we read:— “The Syllogism through a middle term isby natureprior, and of greater cognitive efficacy; butto usthe Syllogism through Induction is plainer and clearer.�66Nor, indeed, is the saying, when literally taken, at all well-founded; for the pretended Syllogisms from Induction and Example, far from being clear and plain, are more involved and difficult to follow thanBarbaraandCelarent. Yet the substance of Aristotle’s thought is true and important, when considered as declaring the antithesis (not between varieties of Syllogisms, but) between Induction and Example on the one part, and Syllogism (Deduction) on the other. It is thus that he sets out the same antithesis elsewhere, both in the Analytica Posteriora and the Topica.67Prior and more cognizableby natureorabsolutely, prior and more cognizableto usorin relation to us— these two are not merely distinct, but the one is the correlate and antithesis of the other.
66Analyt. Prior. II. xxiii. p. 68, b. 35: φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ’ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.
66Analyt. Prior. II. xxiii. p. 68, b. 35: φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ’ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.
67Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik. VI. iii.p. 1139, b. 28: ἡ μὲν δὴ ἐπαγωγὴ ἀρχή ἐστι καὶ τοῦ καθόλοῦ, ὁ δὲ συλλογισμὸς ἐκ τῶν καθόλου. εἰσὶν ἄρα ἀρχαὶ ἐξ ὧν ὁ συλλογισμός, ὧν οὐκ ἔστι συλλογισμός· ἐπαγωγὴ ἄρα. Compare Topica, I. xii. p. 105, a. 11; VI. iv. pp. 141, 142;Physica, I. i. p. 184, a. 16; Metaphysic.E.iv. p. 1029, b.4-12. Compare also Trendelenburg’s explanation of this doctrine, Erläuterungen zu den Elementen der Aristotelischen Logik, sects. 18, 19, 20, p. 33, seq.
67Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik. VI. iii.p. 1139, b. 28: ἡ μὲν δὴ ἐπαγωγὴ ἀρχή ἐστι καὶ τοῦ καθόλοῦ, ὁ δὲ συλλογισμὸς ἐκ τῶν καθόλου. εἰσὶν ἄρα ἀρχαὶ ἐξ ὧν ὁ συλλογισμός, ὧν οὐκ ἔστι συλλογισμός· ἐπαγωγὴ ἄρα. Compare Topica, I. xii. p. 105, a. 11; VI. iv. pp. 141, 142;Physica, I. i. p. 184, a. 16; Metaphysic.E.iv. p. 1029, b.4-12. Compare also Trendelenburg’s explanation of this doctrine, Erläuterungen zu den Elementen der Aristotelischen Logik, sects. 18, 19, 20, p. 33, seq.
To usthe particulars of sense stand first, and are the earliest objects of knowledge.To us, means to the large variety of individual minds, which grow up imperceptibly from the simple capacities of infancy to the mature accomplishments of adult years; each acquiring its own stock of sensible impressions, remembered, compared, associated; and each learning a language, which both embodies in general terms and propositions the received classification of objects, and communicates the current emotional beliefs. We all begin by being learners; and we ascend by different paths to those universal notions and beliefs which constitute the common fund of the advanced intellect; developed in some minds intoprincipiaof philosophy with their consequences.By nature, orabsolutely, theseprincipiaare considered as prior, and as forming the point of departure: the advanced position is regarded as gained, and the march taken is not that of the novice, but that of the trained adult, who having already learnt much, is doubly equipped either for learning more or for teaching others; who thus stands on a summitfrom whence he surveys nature as a classified and coherent whole, manifesting herself in details which he can interpret and sometimes predict. The path of knowledge, seenrelatively to us, is one through particulars, by way of example to fresh particulars, or by way of induction to universals. The path of knowledge,by natureorabsolutely, is from universals by way of deduction either to new universals or to new particulars. By the cognitivenatureof man, Aristotle means the full equipment, of and for cognition, which our mature age exhibits;notiora naturâare the acquisitions, points of view, and processes, familiar in greater or less perfection to such mature individuals and societies.Notiora nobisare the facts and processes with which all of us begin, and which belong to the intellect in its highest as well as its lowest stage; though, in the higher stages, they are employed, directed, and modified, by an acquired intellectual capital, and by the permanent machinery of universal significant terms in which that capital is invested.
Such is the antithesis betweennotiora naturâ(orsimpliciter) andnotiora nobis(orquoad nos), which Aristotle recognizes as a capital point in his philosophy, and insists upon in many of his writings. The antithesis is represented by Example and Induction, in the point of view —quoad nos— last mentioned; by Syllogism or Deduction, in the other point of view —naturâ. Induction (he says),68or the rising from particulars to universals, is plainer, more persuasive, more within the cognizance of sensible perception, more within the apprehension of mankind generally, than Syllogism; but Syllogism is more cogent and of greater efficacy against controversial opponents. What he affirms here about Induction is equally true about the inference from Example, that is, the inference from one or some particulars, to other analogous particulars; the rudimentary intellectual process, common to all human and to many animal minds, of which Induction is an improvement and an exaltation. While Induction will be more impressive, and will carry assent more easily with an ordinary uncultivated mind, an acute disputant may always deny the ultimate inference, for the denialinvolves no contradiction. But the rightly constructed Syllogism constrains assent;69the disputant cannot grant the premisses and deny the conclusion without contradicting himself. The constraining force, however, does not come into accurate and regulated working until the principles and conditions of deductive reasoning have been set forth — until the Syllogism has been analysed, and the characteristics of its validity, as distinguished from its invalidity, have been marked out. This is what Aristotle teaches in the Analytica and Topica. It admits of being set out in regular figure and mode — forms of premisses with the conclusion appropriate to each; and the lesson must be learnt before we can know how far the force of deductive reasoning, which begins with thenotiora naturâ, is legitimately binding and trustworthy.
68Aristot. Topica, I. xii. p. 105, a. 13-19: ἐπαγωγὴ δὲ ἡ ἀπὸ τῶν καθ’ ἕκαστον ἐπὶ τὰ καθόλου ἔφοδος· οἷον εἰ ἔστι κυβερνήτης ὁ ἐπιστάμενος κράτιστος καὶ ἡνίοχος, καὶ ὅλως ἐστὶν ὁ ἐπιστάμενος περὶ ἕκαστον ἄριστος. ἔστι δ’ ἡ μὲν ἐπαγωγὴ πιθανώτερον καὶ σαφέστερον καὶ κατὰ τὴν αἴσθησιν γνωριμώτερον,καὶ τοῖς πολλοῖς κοινόν· ὁ δὲ συλλογισμὸς βιαστικώτερον καὶ πρὸς τοὺς ἀντιλογικοὺς ἐνεργέστερον. Also the same treatise. VI. iv. p. 141, b. 17.The inductive interrogations of Sokrates relating to matters of common life, and the way in which they convinced ordinary hearers, are strikingly illustrated in the Memorabilia of Xenophon, especially IV. vi.: πολὺ μάλιστα ὧν ἐγὼ οἶδα, ὅτε λέγοι, τοὺς ἀκούοντας ὁμολογοῦντας παρεῖχεν (15). The same can hardly be said of the Platonic dialogues.
68Aristot. Topica, I. xii. p. 105, a. 13-19: ἐπαγωγὴ δὲ ἡ ἀπὸ τῶν καθ’ ἕκαστον ἐπὶ τὰ καθόλου ἔφοδος· οἷον εἰ ἔστι κυβερνήτης ὁ ἐπιστάμενος κράτιστος καὶ ἡνίοχος, καὶ ὅλως ἐστὶν ὁ ἐπιστάμενος περὶ ἕκαστον ἄριστος. ἔστι δ’ ἡ μὲν ἐπαγωγὴ πιθανώτερον καὶ σαφέστερον καὶ κατὰ τὴν αἴσθησιν γνωριμώτερον,καὶ τοῖς πολλοῖς κοινόν· ὁ δὲ συλλογισμὸς βιαστικώτερον καὶ πρὸς τοὺς ἀντιλογικοὺς ἐνεργέστερον. Also the same treatise. VI. iv. p. 141, b. 17.
The inductive interrogations of Sokrates relating to matters of common life, and the way in which they convinced ordinary hearers, are strikingly illustrated in the Memorabilia of Xenophon, especially IV. vi.: πολὺ μάλιστα ὧν ἐγὼ οἶδα, ὅτε λέγοι, τοὺς ἀκούοντας ὁμολογοῦντας παρεῖχεν (15). The same can hardly be said of the Platonic dialogues.
69Bacon, Novum Organ. I. Aphor. 13:— “Syllogismus assensum constringit, non res.�
69Bacon, Novum Organ. I. Aphor. 13:— “Syllogismus assensum constringit, non res.�
Both the two main points of Aristotle’s doctrine — the antithesis between Induction and Deduction, and the dependence of the latter process upon premisses furnished by the former, so that the two together form the two halves of complete ratiocination and authoritative proof — both these two are confused and darkened by his attempt to present the Inductive inference and the Analogical or Paradeigmatic inference as two special forms of Syllogistic deduction.70But when we put aside this attempt, and adhere to Aristotle’s main doctrine — of Induction as a process antithetical to and separate from Deduction, yet as an essential preliminary thereto, — we see that it forms the basis of that complete and comprehensive System of Logic, recently elaborated in the work of Mr. John Stuart Mill. The inference from Example (i.e.from some particulars to other similar particulars) is distinguished by Aristotle from Induction, and is recognized by him as the primitive intellectual energy, common to all men, through which Induction is reached; its results he calls Experience (ἐμπειρία), and he describes it as the real guide, more essential than philosophical generalities, to exactness ofperformance in detail.71Mr. John Mill has been the first to assign to Experience, thus understood, its full value and true position in the theory of Ratiocination; and to show that the Paradeigmatic process exhibits the prime and ultimate reality of all Inference, the real premisses and the real conclusion which Inference connects together. Between these two is interposed the double process of which Induction forms the first half and Deduction the second; neither the one nor the other being indispensable to Inference, but both of them being required as securities for Scientific inference, if we desire to have its correctness tested and its sufficiency certified; the real evidence, whereby the conclusion of a Syllogism is proved, being the minor premiss, together with (not the major premiss itself, but) the assemblage of particular facts from which by Induction the major premiss is drawn. Now Aristotle had present to his mind the conception of Inference as an entire process, enabling us from some particular truths to discover and prove other particular truths: he considers it as an unscientific process, of which to a limited extent other animals besides man are capable, and which, as operative under the title of Experience in mature practical men, is a safer guide than Science amidst the doubts and difficulties of action. Upon this foundation he erects the superstructure of Science; the universal propositions acquired through Induction, and applied again to particulars or to lower generalities, through the rules of the deductive Syllogism. He signalizes, with just emphasis, the universalizing point of view called Science or Theory; but he regards it as emerging from particular facts, and as travelling again downwards towards particular facts. The misfortune is, that he contents himself with barely recognizing, though he distinctly proclaims the necessity of, the inductive part of this complex operation; while he bestows elaborate care upon the analysis of the deductive part, and of the rules for conducting it. From this disproportionate treatment, one half of Logic is made to look like the whole; Science is disjoined from Experience, and is presented as consisting in Deduction alone; every thing which is not Deduction, is degraded into unscientific Experience; the major premiss of the Syllogism being considered as part of the proof of the conclusion, and the conclusion being necessarily connectedtherewith, we appear to have acquired alocus standiand a binding cogency such as Experience could never supply; lastly, when Aristotle resolves Induction into a peculiar variety of the Syllogism, he appears finally to abolish all its separate dignity and jurisdiction. This one-sided view of Logic has been embraced and perpetuated by the Aristotelian expositors, who have carefully illustrated, and to a certain extent even amplified, the part which was already in comparative excess, while they have added nothing to the part that was in defect, and have scarcely even preserved Aristotle’s recognition of it as being not merely legitimate but essential. The vast body of Inductive Science, accumulated during the last three centuries, has thus, until recently, been allowed to grow up, as if its proofs and processes had nothing to do with Logic.
70Heyder (in his learned treatise, Darstellung der Aristotelischen und Hegelschen Dialektik, p. 226), after having considered the unsatisfactory process whereby Aristotle attempts to resolve Induction into a variety of Syllogism, concludes by a remark which I think just:— “Aus alle dem erhellt zur Genüge, dass sich Aristoteles bei dem Versuch die Induction auf eine Schlussform zurückzuführen, selbst sich nicht recht befriedigt fühlte, und derselbe wohl nur aus seinem durchgängigen Bestreben zu erklären ist, alles wissenschaftliche Verfahren in die Form des Schlusses zu bringen; dass dagegen, seiner eigentlichen Meinung und der strengen Consequenz seiner Lehre zu Folge, die Induction zum syllogistischen und beweisenden Verfahren einen in dem Begriff der beiden Verfahrungsweisen liegenden Gegensatz bildete, was sich ihm dann auch auf das Verhältniss der Induction zur Begriffsbestimmung ausdehnen musste.�
70Heyder (in his learned treatise, Darstellung der Aristotelischen und Hegelschen Dialektik, p. 226), after having considered the unsatisfactory process whereby Aristotle attempts to resolve Induction into a variety of Syllogism, concludes by a remark which I think just:— “Aus alle dem erhellt zur Genüge, dass sich Aristoteles bei dem Versuch die Induction auf eine Schlussform zurückzuführen, selbst sich nicht recht befriedigt fühlte, und derselbe wohl nur aus seinem durchgängigen Bestreben zu erklären ist, alles wissenschaftliche Verfahren in die Form des Schlusses zu bringen; dass dagegen, seiner eigentlichen Meinung und der strengen Consequenz seiner Lehre zu Folge, die Induction zum syllogistischen und beweisenden Verfahren einen in dem Begriff der beiden Verfahrungsweisen liegenden Gegensatz bildete, was sich ihm dann auch auf das Verhältniss der Induction zur Begriffsbestimmung ausdehnen musste.�
71Aristot. Analyt. Prior. II. xxiii. p. 68, b. 12; xxvi. p. 69, a. 17. Analyt. Post. II. xix. p. 99, b. 30, seq.; xiii. p. 97, b. 7. Topica, VIII. i. p. 155, b. 35; p. 156, b. 10; p. 157, a. 14-23; p. 160, a. 36. Metaphys.A. i. p. 980, b. 25-p. 981, a. 30. This first chapter of the Metaphysica is one of the most remarkable passages of Aristotle, respecting the analytical philosophy of mind.
71Aristot. Analyt. Prior. II. xxiii. p. 68, b. 12; xxvi. p. 69, a. 17. Analyt. Post. II. xix. p. 99, b. 30, seq.; xiii. p. 97, b. 7. Topica, VIII. i. p. 155, b. 35; p. 156, b. 10; p. 157, a. 14-23; p. 160, a. 36. Metaphys.A. i. p. 980, b. 25-p. 981, a. 30. This first chapter of the Metaphysica is one of the most remarkable passages of Aristotle, respecting the analytical philosophy of mind.
But though this restricted conception of Logic or the theory of Reasoning has arisen naturally from Aristotle’s treatment, I maintain that it does not adequately represent his view of that theory. In his numerous treatises on other subjects, scarcely any allusion is made to the Syllogism; nor is appeal made to the rules for it laid down in the Analytica. His conviction that the formalities of Deduction were only one part of the process of general reasoning, and that the value of the final conclusion depended not merely upon their being correctly performed, but also upon the correctness of that initial part whereby they are supplied with matter for premisses — is manifested as well by his industry (unrivalled among his contemporaries) in collecting multifarious facts, as by his specific declarations respecting Induction. Indeed, a recent most erudite logician, Sir William Hamilton, who insists upon the construction of Logic in its strictest sense as purely formal, blames Aristotle72for having transgressed this boundary, and for introducing other considerations bearing on diversities of matter and of material evidence. The charge so made, to whatever extent it is well-founded, does rather partake of the nature of praise; inasmuch as it evinces Aristotle’s larger views of the theory of Inference, and confirms his own statement that the Deductive process was only the last half of it, presupposing a prior Induction. It is only this last half that Aristotle has here analysed, setting forth its formal conditions with precepts founded thereupon; while he claims to have accomplished the work by long and patient investigation, having found not the smallest foundation laid by others, andbespeaks indulgence73as for a first attempt requiring to be brought to completion by others. He made this first step for himself; and if any one would make a second step, so as to apply the same analysis to the other half, and to bring out in like manner the formal conditions and principles of Induction, we may fairly believe that Aristotle would have welcomed the act, as filling up what he himself recognized to be a gap in the entire compass of Reasoning. As to his own achievement, it is certain that he could not have composed the Analytica and Topica, if he had not had before him many specimens of the deductive process to study and compare. Neither could the inductive process have been analysed, until after the examples of successful advance in inductive science which recent years have furnished. Upon these examples, mainly, has been based the profound System of Mr. John Stuart Mill, analysing and discriminating the formalities of Induction in the same way as those of Deduction had before been handled by Aristotle; also fusing the two together as co-operative towards one comprehensive scheme of Logic — the Logic of Evidence generally, or of Truth as discoverable and proveable. In this scheme the Syllogistic Theory, or Logic of Consistency between one proposition and others, is recognized as an essential part, but is no longer tolerated as an independent whole.74
72See his Discussions on Philosophy, p. 139, seq.; Lectures on Logic, vol. i. p. 27.
72See his Discussions on Philosophy, p. 139, seq.; Lectures on Logic, vol. i. p. 27.
73See the remarkable paragraph at the close of the Sophistici Elenchi, already quoted (supra,p. 140, note).
73See the remarkable paragraph at the close of the Sophistici Elenchi, already quoted (supra,p. 140, note).
74Mr. John Stuart Mill says (Bk. II. ch. i. sect. 3):“Induction is inferring a proposition from premissesless generalthan itself, and Ratiocination is inferring a proposition from premissesequally or more general.� Again in another passage: “We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions; that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of logic — the question which includes all others. It is however one which professed writers on logic have almost entirely passed over. The generalities of the subject, indeed, have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for Induction itself what the rules of the Syllogism are for interpretation of Induction� (Bk. III. ch. i. s. 1. p. 313.) — “The business of Inductive Logic is to provide rules and models (such as the Syllogism and its rules are for ratiocination) to which if inductive arguments conform, those arguments are conclusive, and not otherwise. This is what the Four Methods profess to be, and what I believe they are universally considered to be by experimental philosophers, who had practised all of them long before any one sought to reduce the practice to theory� (Bk. III. ch. ix. s. 5, p. 471, 5th ed.) — See also the same point of view more copiously set forth, in Mr. Mill’s later work, ‘Examination of Sir W. Hamilton’s Philosophy’ (ch. xx. pp. 454-462, 3rd ed.): “It is only as a means to material truth that the formal (or to speak more clearly, the conditional) validity of an operation of thought is of any value; and even that value is only negative: we have not made the smallest positive advance towards right thinking, by merely keeping ourselves consistent in what is perhaps systematic error. This by no means implies that Formal Logic, even in its narrowest sense, is not of very great, though purely negative value.� — “Not only however is it indispensable that the larger Logic, which embraces all the general conditions of the ascertainment of truth, should be studied in addition to the smaller Logic, which only concerns itself with the conditions of consistency; but the smaller Logic ought to be (at least, finally) studied as part of the greater — as a portion of the means to the same end; and its relation to the other parts — to the other means — should be distinctly displayed.�
74Mr. John Stuart Mill says (Bk. II. ch. i. sect. 3):“Induction is inferring a proposition from premissesless generalthan itself, and Ratiocination is inferring a proposition from premissesequally or more general.� Again in another passage: “We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions; that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of logic — the question which includes all others. It is however one which professed writers on logic have almost entirely passed over. The generalities of the subject, indeed, have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for Induction itself what the rules of the Syllogism are for interpretation of Induction� (Bk. III. ch. i. s. 1. p. 313.) — “The business of Inductive Logic is to provide rules and models (such as the Syllogism and its rules are for ratiocination) to which if inductive arguments conform, those arguments are conclusive, and not otherwise. This is what the Four Methods profess to be, and what I believe they are universally considered to be by experimental philosophers, who had practised all of them long before any one sought to reduce the practice to theory� (Bk. III. ch. ix. s. 5, p. 471, 5th ed.) — See also the same point of view more copiously set forth, in Mr. Mill’s later work, ‘Examination of Sir W. Hamilton’s Philosophy’ (ch. xx. pp. 454-462, 3rd ed.): “It is only as a means to material truth that the formal (or to speak more clearly, the conditional) validity of an operation of thought is of any value; and even that value is only negative: we have not made the smallest positive advance towards right thinking, by merely keeping ourselves consistent in what is perhaps systematic error. This by no means implies that Formal Logic, even in its narrowest sense, is not of very great, though purely negative value.� — “Not only however is it indispensable that the larger Logic, which embraces all the general conditions of the ascertainment of truth, should be studied in addition to the smaller Logic, which only concerns itself with the conditions of consistency; but the smaller Logic ought to be (at least, finally) studied as part of the greater — as a portion of the means to the same end; and its relation to the other parts — to the other means — should be distinctly displayed.�
After adverting to another variety of ratiocinative procedure, which he callsApagogeor Abduction (where the minor is hardly more evident than the conclusion, and might sometimes conveniently become a conclusion first to be proved),75Aristotle goes on to treat of Objection generally — the function of the dialectical respondent. TheEnstasisor Objection is a proposition opposed not to a conclusion, but to the proposition set up by the defendant. When the proposition set up by him is universal, as it must be if he seeks to establish an universal conclusion, your objection may be either universal or particular: you may deny either the whole of his proposition, or only one portion of the particulars contained under it; the denial of one single particular, when substantiated, being enough to overthrow his universal. Accordingly, your objection, being thus variously opposed to the proposition, will lie in the syllogistic figures which admit opposite conclusions; that is, either in the First or Third; for the Second figure admits only negative conclusions not opposed to each other. If the defendant has set up an Universal Affirmative, you may deny the whole and establish a contrary negative, in the First figure; or you may deny a part only, and establish a contradictory negative, in the Third figure. The like, if he has set up an Universal Negative: you may impugn it either by an universal contrary affirmative, in the First figure; or by a particular contradictory affirmative, in the Third figure.76