ton are summarily comprehended by him in the three following particulars: 1. The syllogism proceeds not, as had been previously taught, in one, but in the two correlative and counter wholes of comprehension and of extension; - the doctrine as it is familiarly but inadequately denominated, of " the quantification of the predicate." 2. The enunciation and application of the simple logical postulate, that what is thought implicitly be stated explicitly; a doctrine wide-sweeping and entirely revolutionary of the whole science as a formal system. 3. A new logical notation. There is certainly but little show of uncommon power or marvellous achievement here. Yet we shall see that there is here precisely the mark and characteristic of great power,the comprehension as simple of what weakness can deal with only as the multifarious and chaotic. Not more mighty or far-reaching, nor more revolutionary, was the promulgation by Newton, as ascertained law, of the simple principle of universal gravitation to the science of physical astronomy, than this simple promulgation by Hamilton of the nature of the syllogismn to the science of logic. In both cases we have a discovery that is not merely corrective of existing systems, but creative of new scienees. Science makes a new development. The human mind reaches a new stage of growth. Thought, both as system and as discipline, is revolutionized. In the case of logic, the revolution is only more radical, more wide-sweeping, because of the nature of its object, because the laws of thought are more fundamental to man than the laws of motion. Sir William Hamilton has by no means left us, in any of his literary remains, the new forms of the science as necessarily determined to it by these new promulgations. His Lectures do not contain his latest evolutions of his doctrine; and in the loose fragments gathered in his Discussions, and the posthumous papers collected by his editors (Professors. Mansel and Veitch), we find only vague hints and une laborated suggestions. His Lectures, as we shall see, are strangely immature. His new doctrines, here and there, are given in certain forms of application; nowhere thoroughly developed. His Lectures contain divers teachings that are directly contradictory to his fundamental doctrine. We find this imperfection and inconsistency as well in his own origi nal expositions of the science, as in the large draughts be has drawn from German logicians. 1 We may, at once, dismiss from our examination, all the claimed improvement in logical notation. With some modi fication we may accept Professor Mansel's criticism on attempts at representing logical relations by special forms. "If logic," he says, "is exclusively concerned with thought, and thought is exclusively concerned with concepts, it is impossible to approve of a practice sanctioned by some eminent logicians, of representing the relation of terms in a syllogism by that of figures in a diagram. To illustrate, for example, the position of the terms in Barbara, by a diagram of three circles, one within another, is to lose sight of the distinctive mark of a concept,that it cannot be presented to the sense, and tends to confuse the mental inclusion of one notion in the sphere of another, with the local inclusion of a smaller portion of space in a larger." This remark is cer tainly too sweeping; for there is a close analogy between quantities in concepts and quantities in space. That the relations in quantity in the one case may be properly sym. bolized in the represented relations in quantity in the other case, we cannot question. Special diagrams may be ser viceable in helping to a right view of the nature of concepts; but the help so rendered is very limited; and there is danger of the evil intimated by Professor Mansel from an extended use of any such system of notation. It was precisely this kind of subjection to outward form in word and symbol that, as it occasioned the overlooking of the contained thought in the symbolism, smothered the life out of the old logic, and forced the living mind of the last century to de Prolegomena Logica, Chap. L mand that the dead be buried out of its sight. Herein, indeed, lay the marvellous power of that simple postulate propounded by Hamilton, that it demanded for the admitted principles of the science an embodiment in which they could live and express themselves. The mighty hold which this dead symbolism of logic retained upon the minds of its few remaining cultivators is well exemplified in the case of Hamilton, both elsewhere, in his steadfast adherence to an antiquated nomenclature, but especially here, in his unabated veneration for logical diagrams. His own elaborated scheme of notation is an admirable instance of constructive genius; but it is a scientific toy, not a scientific instrument. That Hamilton should have held it in such estimation is one of many proofs that his genius was not destructive, but conservative; he loved the old, and accepted its teachings even when erroneous, till the truth within forced him to let them go. He was no iconoclast, while a true renovator, a noble model of a true radical and, at the same time, of a true conservative. The truth of this will appear more signally in a consideration of the second of those improvements which Hamilton claims to have contributed to logical science. "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." We do not know where to find, in the history of philosophy, an instance to be compared with this of the power of the simplest truth to overthrow the most formidable system of error, provided only that they be brought into actual engagement. The whole stately structure of the scholastic logic was shaken to its foundations at the first shock of the encounter. One is appalled at the long detail of results which, inter alia, as Hamilton says, we obtain from a single application of this unquestionable postulate; the application from which "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 judg - ment." We must refer to the Discussions,' for the full enumeration. We can only state generally that, in the first place, before the magic touch of this postulate, the whole magnificent system of logical mood and figure vanishes into thin air, leaving scarcely a shred behind. Not only is it shown to be wholly useless as a scientific instrument, -absolutely worthless except as a fossil for antiquarian study, or as a philosophical amusement, but actually unsound, defective, leading inevitably to error. Mood and figure, in logic, respect only the external, accidental form of a reasoning, and therefore must be held to be of insignificant importance as compared with its essential nature. Further than this, admitting the natural and easy distinction of syllogisms in respect to the order of stating its propositions into analytic and synthetic, we have no irregularity in form to provide for, except "the single case where the conclusion is placed between the premises," and consequently no further use of a doctrine of mood in logic. And as to logical figure, it is demonstrated in an elaboration of proof to which only a Hamilton was competent, that "there is but one figure, or more properly but one process, of categorical reasoning." The whole doctrine of logical mood and figure being thus eviscerated from the science, as it has been hitherto taught, we have little left. The stateliness, the charm of the scholastic art, disappear, when Barbara and all her cabalistic train take their departure. They bear away, however, few regrets from the springing age of thought. Logic lives still; and its true life will develop itself, now that the winter bands of scholastic mood and figure are burst. Another grand result claimed by Hamilton to be obtained from this application of the newly enounced postulate is, the reduction of all the laws of syllogism to a single canon, and the consequent evolution of all varieties of syllogism from that one canon, and the abrogation of all the special laws of syllogism. It is much to be deplored that Hamilton has 1 Appendix II. Logical. A. Of Syllogism, etc. (Am. ed.), p. 602. given us no expanded evolution of the results thus summarily stated; that he has left even the true import of these brief statements to be conjectured or laboriously deduced from the merest germs of doctrinal statement. The single canon of the syllogism is thus enounced: What worst relation of subject and predicate subsists between either of the two terms and a common third term with which one, at least, is positively related; that relation subsists between the two terms them selves; in other words: In as far as two notions both agree, or, one agreeing, the other disagrees, with a common third notion; in so far those notions agree or disagree with each other." "But we cannot believe this to be the highest canon of syllogism as necessarily resulting from the application of the postulate. If it can be interpreted by any possibility to include all that such a canon, as supreme, should compre hend; still its whole form and shape are ill-suited to express such a fundamental principle. The terms "related," in the first form, and "agreeing," in the second, are altogether too vague, too rhetorical, for such a universal canon. Only as these terms are limited to quantity, is the canon, in either form, tenable. If this be regarded as Hamilton's last exposition of the syllogistic law, and his use of it in his scheme of logical notation seems to favor this supposition, then we must apply to him the language he uses of Aristotle: that "it contains the truth; but the truth partially and in complexity, even in confusion. And why? Because [Hamil ton] by an oversight, marvelous certainly in him, was prematurely arrested in his analysis." If Hamilton could justly claim that this postulate necessarily involves "the reduction of all the general laws of categorical syllogisms to a single canon," he certainly has not left us, in his published works, any actual "evolution from that one canon of the species and varieties of syllogism," or the "abrogation of all the special laws of syllogism.” Indeed, the canon called by Hamilton, in his letter to Mr. De Morgan, his "supreme canon," cannot, by any liberality of 'Lectures on Logic, Appendix (Am. ed.), p. 587. |