(Physique Particulière, ch. xxxiii.):-"Il y a donc certainement des lois eternelles, inconnues, suivant lesquelles tout s'opère, sans qu'on puisse les expliquer par la matière et par le mouvement. Il y a dans toutes les Académies une chaire vacante pour les vérités inconnues, comme Athènes avait un autel pour les dieux ignorés." Besides the few testimonies adduced, I would refer, in general, for some excellent observations on the point, to Fernelius "De Abditis Rerum Causis," and to the "Hypomnemata" of Sennertus. (A.) OF SYLLOGISM, ITS KINDS, CANONS, NOTATIONS, &c. TOUCHING the principle of an explicitly Quantified Predicate, I had by 1833 become convinced of the necessity to extend and correct the logical doctrine upon this point. In the article on Logic, reprinted above, and first published in April 1833, the theory of Induction there maintained proceeds on a thoroughgoing quantification of the predicate, in affirmative propositions. (P. 161, sq.) Before 1840, I had, however, become convinced, that it was necessary to extend the principle equally to negatives; for I find by academical documents, that in that year, at latest, I had publicly taught the unexclusive doctrine. The following is an extract from the "Prospectus of Essay towards a New Analytic of Logical Forms," appended to the edition of Reid's Works, published by me in 1846 :— "In the first place, in the Essay there will be shown, that the Syllogism proceeds, not as has hitherto, virtually at least, been taught, in one, but in the two correlative and counter wholes, (Metaphysical) of Comprehension, and (Logical) of Extension;—the major premise in the one whole, being the minor premise in the other, &c.—Thus is relieved a radical defect and vital inconsistency in the present logical system. In the second place, the self-evident truth,-That we can only rationally deal with what we already understand, determines the simple logical postulate,-To state explicitly what is thought implicitly. From the consistent application of this postulate, on which Logic ever insists, but which Logicians have never fairly obeyed, it follows:-that, logically, we ought to take into account the quantity, always understood in thought, but usually, and for manifest reasons, elided in its expression, not only of the subject, but also of the predicate, of a judgment. This being done, and the necessity of doing it will be proved against Aristotle and his repeaters, we obtain, inter alia, the ensuing results :— 1°, That the preindesignate terms of a proposition, whether subject or predicate, are never, on that account, thought as indefinite (or indeterminate) in quantity. The only indefinite, is particular, as opposed to definite, quantity; and this last, as it is either of an extensive maximum undivided, or of an extensive minimum indivisible, constitutes quantity universal (general,) and quantity singular (individual.) In fact, definite and indefinite are the only quantities of which we ought to hear in Logic; for it is only as indefinite that particular, it is only as definite that individual and general, quantities have any (and the same) logical avail. 2o, The revocation of the two terms of a Proposition to their true relation; a proposition being always an equation of its subject and its predicate. 3°, The consequent reduction of the Conversion of Propositions from three species to one-that of Simple Conversion. 4°, The reduction of all the General Laws of Categorical Syllogisms to a Single Canon. 5°, The evolution from that one canon of all the Species and varieties of Syllogisms. 6°, The abrogation of all the Special Laws of Syllogism. 7°, A demonstration of the exclusive possibility of Three syllogistic Figures; and (on new grounds) the scientific and final abolition of the Fourth. 8°, A manifestation that Figure is an unessential variation in syllogistic form; and the consequent absurdity of Reducing the syllogisms of the other figures to the first. 9°, An enouncement of one Organic Principle for each Figure. 10°, A determination of the true number of the legitimate Moods; with 11°, Their amplification in number (thirty-six); 12°, Their numerical equality under all the figures; and, 13°, Their relative equivalence, or virtual identity, throughout every schematic difference. 14°, That, in the second and third figures, the extremes holding both the same relation to the middle term, there is not, as in the first, an opposition and subordination between a term major and a term minor, mutually containing and contained, in the counter wholes of Extension and Comprehension. 15°, Consequently, in the second and third figures, there is no determinate major and minor premise, and there are two indifferent conclusions; whereas, in the first the premises are determinate, and there is a single proximate conclusion. 16°, That the third, as the figure in which Comprehension is predominant, is more appropriate to Induction. 17°, That the second, as the figure in which Extension is predominant, is more appropriate to Deduction. 18°, That the first, as the figure in which Comprehension and Extension are in equilibrium, is common to Induction and Deduction, indifferently." What follows was subjoined, as a note, to the "Essay on the New Analytic of Logical Forms," by Mr Thomas Spencer Baynes, which obtained the prize proposed in 1846, but was not published until 1850. The foot-notes are now added. "The ensuing note contains a summary of my more matured doctrine of the Syllogism, in so far as it is relative to the preceding Essay. All mediate inference is one-that incorrectly called Categorical; for the Conjunctive and Disjunctive forms of Hypothetical reasoning are reducible to immediate inferences. Mentally one, the Categorical Syllogism, according to its order of enouncement, is either Analytic (A) or Synthetic (B). Analytic, if (what is inappropriately styled) the conclusion be expressed first, and (what are inappropriately styled) the premises be then stated as its reasons. (These might be called the Preassertion and the Proofs, or Probandum and Probationes; Proof or Probation would apply to the whole process, whether analytic or synthetic.) -Synthetic, if the premises precede, and, as it were, effectuate the conclusion.*-These general forms of the syllogism can with ease be distinguished by a competent notation; and every special variety in the one has its corresponding variety in the other. Though the following division applies equally to the Analytic and to the Synthetic syllogism, yet taking it under the latter form (B), (which, though perhaps less natural,† has been alone cultivated by logicians, and to which, [This, in the first place, relieves the syllogism of two one-sided views. The Aristotelic syllogism is exclusively synthetic; the Epicurean (or Neoclesian) syllogism was—for it has been long forgotten-exclusively analytic; whilst the Hindoo syllogism is merely a clumsy agglutination of these counter forms, being nothing but an operose repetition of the same reasoning, enounced, 1°, analytically; 2°, synthetically. I say clumsy, for the example interpolated is an extralogical superfluity, and may be thrown out of account. In thought, the syllogism is organically one; and it is only stated in an analytic or synthetic form, from the necessity of adopting the one order or the other, in accommodation to the vehicle of its expression-Language. For the conditions of language require, that a reasoning be distinguished into parts, and these detailed before and after other. The analytic and synthetic orders of enouncement are, thus, only accidents of the syllogistic process. This is, indeed, shown in practice; for our best reasonings proceed indifferently in either order. In the second place, this central view vindicates the Syllogism from the objection of Petitio Principii, which professing logically to annul logic, or at least to reduce it to an idle tautology, defines syllogistic-the art of avowing in the conclusion what has been already confessed in the premises. This objection (which has at least an antiquity of three centuries and a half) is only applicable to the synthetic or Aristotelic order of enouncement, which the objectors, indeed, contemplate as alone possible. It does not hold against the analytic syllogism; it does not hold against the syllogism considered aloof from the accident of its expression; and being proved irrelevant to these, it is easily shown in reference to the synthetic syllogism itself, that it applies only to an accident of its external form.] [I say less natural. For if it be asked-" Is C'in A?" surely it is more natural to reply,-Yes, (or C′ is in A), for C is in B and B in A, (or, for B is in A and C in B); than to reply,-B is in A, and C in B, (or, C is in B and B in A), therefore, C is in A. In point of fact, the analytic syllogism is not only the more natural, it is even presupposed by the synthetic. To express in words, we must first analyse in thought the organic whole-the mental simultaneity of a simple reasoning; and then, we may reverse in thought the process, by a synthetic return. Further, we may now enounce the reasoning in either order; but, certainly, to express it in the essential, primary, or analytic order, is not only more natural, but more direct therefore, exclusively all logical nomenclature is relative,)—the syllogism is again divided into the Unfigured (a) and the Figured (b). The Unfigured Syllogism (a) is that in which the terms compared do not stand to each other in the reciprocal relation of subject and predicate, being in the same proposition, either both subjects or (possibly) both predicates.* Here the dependency of Breadth and Depth, (Extension and Intension, Extension and Comprehension, &c.) does not subsist, and the order, accordingly, of the premises is wholly arbitrary. This form has been overlooked by the logicians, though equally worthy of development as any other; in fact, it affords a key to the whole mystery of Syllogism. And what is curious, the Canon by which this syllogism is regulated, (what may be called that of logical Analogy or Proportion,) has, for above five centuries, been commonly stated as the one principle of reasoning, whilst the form of reasoning itself, to which it properly applies, has never been generalized. This Canon, which has been often erroneously, and never adequately enounced, in rules four, three, two, or one, is as follows:-In as far as two notions, (notions proper or individuals,) either both agree, or one agreeing, the other does not, with a common third notion; in so far, these notions do or do not agree with each other. (This Canon thus excludes:-1°, an undistributed, as then no common notion; 2°, two negative premises, as then no agreement of the other and simple, than to express it in the accidental, secondary, or synthetic. This also avoids the objection of Petitio Principii, at least as it has been stated by modern logicians; for the objection as taken by the ancient sceptics applies to either form. [Subjects, as: * All C and some B are (some) convertible; All B and all A are (some) convertible; All C and some A are (some) convertible. (Some) convertibles are all C and some B; (Some) convertibles are all C and some A. I need hardly repeat, that the Premises or Proofs may be reversed in order of enouncement, that order being indifferent; and that for convertible may be used identical, same, equal, &c., or any term expressing an equation. "This Dr Reid in his Account of Aristotle's Logic (Works, p. 702) says:simple reasoning, A is equal to B, and B to C, therefore A is equal to C, cannot be brought into any syllogism in figure and mode." To this I appended the following Note::- "Not as it stands; for, as expressed, this reasoning is elliptical. Explicitly stated, it is as follows: What are equal to the same, are equal to each other; A and Care equal to the same (B); Therefore, A and C are equal to each other." I would now explicate this as a mere Unfigured syllogism, thus: A and B are equal; B and C are equal; Therefore A and C are equal. Or in an analytic form :— A and C are equal; for A and B are equal; and B and C are equal.] |