« ForrigeFortsett »
the subject-matter of the premisses bears to that of the conclusion.” (P. 110.)— The second :-" In the process of reasoning by which we deduce, from our observation of certain known cases, an inference with respect to unknown ones, we are employing a syllogism in Barbara with the major premiss suppressed ; that being always substantially the same, as it asserts, that, 'what belongs to the individual or individuals we have examined, belongs to the whole class under which they come.' (P. 216.)
This agrees, neither with the Aristotelic doctrine, nor with truth.
We must presume, from his silence, that our author, in his analysis of the inductive process, was not aware of any essential deviation from the doctrine of Aristotle. This he does not seem to have studied, either in the Organon, or in any of its authentic expositors; and nothing can be conceived more contradictory, than the statements of the philosopher on this subject and those of Dr Whately.- Aristotle views the Inductive and the Deductive syllogisms as, in certain respects, similar in form ; in others, as diametrically opposed. Dr Whately regards them as formally identical, and only discriminated by a material difference, i. e. logically considered, by no difference at all.–Aristotle regards the Deductive syllogism as the analysis of a logical whole into its parts,-as a descent from the (more) general to the (more) particular; the Inductive as a synthesis of logical parts into a logical whole,-as an ascent from the (more) particular to the (more) general. Dr Whately, on the other hand, virtually annihilates the latter process, and identifies the Inductive with the Deductive inference.—Aristotle makes Deduction necessarily dependent on Induction; he maintains that the highest or most universal axioms which constitute the primary and immediate propositions of the former, are all conclusions previously furnished by the latter. Whately, on the contrary, implicitly asserts the independence of the syllogism proper, as he considers the conclusions of Induction to be only inferences evolved from a more universal major.–Aristotle recognises only a perfect Induction, i. e. an enumeration (actual or presumed) of all the parts ; Whately only an imperfect, i.e. an enumeration professedly only of some.—To Aristotle, Induction is a syllogism, apparently, of the third figure; to Whately, it is a syllogism of the first
In short, if Whately be right, Aristotle is fundamentally wrong: wrong in admitting Inductive reasoning within the sphere of logic at all; wrong in discriminating Induction from Syllogism proper ; wrong in all the particulars of the contrast.
But that the Philosopher is not in error, is evident at once ; whereas the Archbishop's doctrine is palpably suicidal. On that doctrine, the inductive reasoning is "a syllogism in Barbara, the major premiss being always substantially the same :- What belongs to the individual or individuals we have examined, belongs to the whole class under which they come.”
Now, we ask :-In what manner do we obtain this major, in the evolution of which all Induction consists? Here there are only four possible answers.—1°, This proposition, (like the dictum de omni et de nullo, and the axiom of the convertibility of the whole and its parts,) it may be said, is (analytically) selfevident, its negation implying a contradiction. This answer is manifestly false. For so far from being necessitated by the laws of thought, it is in opposition to them; the whole of the consequent not being determined in thought by the some of the antecedent.–2°, It may be said to be acquired by Induction. This, however, would be absurd ; inasmuch as Induction itself is, ex hypothesi, only possible, through and after the principle it is thus adduced to construct. This of the proposition as a whole. The same is also true of its parts. “Class” is a notion, itself the result of an Induction ; it cannot, therefore, be postulated as a pre-requisite or element of that process itself. A similar remark applies to " property.”—3°, It may be said to be deduced from a higher axiom. What then is such axiom? That has not been declared. And if such existed, the same questions would remain to be answered regarding the higher proposition which are now required in relation to the lower.—4o, It may be asserted to be (as Kant would say, synthetically) given as an ultimate principle of our intellectual constitution. This will not do. In the first place, if such principle exist, it only inclines, it does not necessitate. In the second, by appealing to it, we should transcend our science, confound the logical and formal with the metaphysical and material. In the third, we should thus attempt to prove a logical law from a psychological observation; i.e. establish an a priori, a necessary science on a precarious experience,—an experience admitted perhaps by the disciples of Reid and Royer-Collard, but scouted by those of Gassendi and Locke.*
* " It is by induction that all axioms are known, such as :- Things that are cqual to the same are equal to one another ;' 'A whole is greater than its parts ;' Logicians, we already observed, have been guilty of a fundamental error, in bringing the distinction of perfect and of imperfect Induction within the sphere of their science, as this distinction proceeds on a material, consequently on an extralogical difference. In this error, however, Dr Whately exceeds all other logicians, recognising, as he does, exclusively, that Induction, which is only precariously valid, and valid only through an extralogical presumption. This common major premise, if stated as necessary, is (formally and materially) false; if stated as probable, it is (formally) illegitimate, even if not (materially) untrue, both because an inferior degree of certainty is incompatible with an apodictic science, and because the amount of certainty itself must, if not capriciously assumed, be borrowed from evidence dependent on material conditions beyond the purview of a formal science.
Dr Whately is not less unfortunate in refuting the opinions of other logicians touching Induction, than in establishing his own.
“In this process,” he says, we are employing a syllogism in Barbara with the major premiss suppressed ; not the minor, as Aldrich represents it. The instance he gives will sufficiently prove this :- This, that, and the other magnet, attract iron; therefore so do all.' If this were, as he asserts, an enthymeme whose minor is suppressed, the only premise which we could supply to fill it up would be, 'all magnets are this, that, and the other ;' which is manifestly false.” (P. 217.)
Aldrich has faults sufficient of his own, without taking burden of the sins of others. He is here singly reprehended for saying only what, his critic seems not aware, had been said by all logicians before him. The suppressed minor premise even obtained in the schools the name of the Constantia ; and it was not until the time of Wolf* that a new-fangled doctrine, in this respect the same as Whately's, in some degree superseded the older and correcter theory. “In the example of Aldrich,” says our author, “the suppressed minor premiss, all magnets are and all other mathematical axioms.” Huyshe, p. 132. The same doctrine is held by Hill, p. 176.—Is such the Oxford Metaphysic? [This doctrine, the ingenious author of “The Regeneration of Metaphysics” (pp. 81, 104), charges also on Dr Whately.]
* (I said generally "the time of Wolf;" for I recollected that some German logicians, prior to him, had held the same doctrine. It was however Wolf's authority which rendered the innovation general.-M. Peisse has here the following note :-" The germ of this doctrine is to be found in Gassendi. (Inst. Log. Pars iii. canon 11. Opera, i. 113.)"]
this, that, and the other,' is manifestly false.” Why ?-Is it because the proposition affirms that a certain three magnets (“this, that, and the other") are all magnets ? Even admitting this, the objection is null. The logician has a perfect right to suppose this or any other material falsity for an example; all that is required of him is, that his syllogism should be formally correct. Logic only proves on the hypothetical truth of its antecedents. As Magentinus notices, Aristotle's example of Induction is physiologically false; but it is not on that account a whit the worse as a dialectical illustration. The objection is wholly extralogical.—But this is not, in fact, the meaning of the proposition. The words in the original “ hic, et ille, et iste magnes") are intended to denote every several magnet. Aldrich borrows the instance from Sanderson, by whom it is also more fully expressed :—“Iste magnes trahit ferrum, et ille, et hic, et pariter se habet in reliquis,” &c.—Perhaps, however, and this is the only other alternative, Dr Whately thinks the assumption "manifestly false," on the ground that no extent of observation could possibly be commensurate with “all magnets.” This objection likewise lies beyond the domain of the science. The logician, qua logician, knows nothing of material possibility and impossibility. To him all is possible that does not involve a contradiction in terms. At the same time, the present is merely the logical manner of wording the proposition. The physical observer asserts on the analogy of his science, “This, that, the other magnet, &c., represent, all magnets ;” which the logician accepting, brings under the conditions, and translates into the language of his—"This, that, the other magnet, &c., are all mayneth," i,c. are conceivedl as constituting the whole-Magnet.
Dr Whately's errors relative to Induction are, however, surjanned by those of another able writer, Mr Hampden, in regard both to that process itself, and to the Aristotelic exposition of its nature ;-orrors the more inconceivable, as he professes to have devoted peculiar attention to the subject, which he says, “deMOPON A more particular notice, as throwing light on Aristotle's wholo mothod of philosophising, while it shows how far he approximated to the induction of modern philosophy." His words
"To obtain an accurate notion of the being of anything, we require a definition of it. A definition of the thing corresponds, in dialectic, with the unsential notion of it in metaphysics, This abstract notion, then, accord
ing to Aristotle, constituting the true scientific view of a thing—and all the real knowledge consequently of the properties of the thing depending on the right limitation of this notion-some exact method of arriving at definitions which should express these limitations, and serve as the principles of sciences, became indispensable in such a system of philosophy. But in order to attain such definitions, a process of induction was required,—not merely an induction of that kind, which is only a peculiar form of syllogism, enumerating all the individuals implied in a class instead of the whole class collectively, but an induction of a philosophical character, and only differing from the induction of modern philosophy so far as it is employed about language. We shall endeavour to show this more fully. There are, then, two kinds of induction treated of by Aristotle. The first, that of simple enumeration.”—After explaining with ordinary accuracy the first, in fact the only, species of induction, he proceeds :)—“But there is also a higher kind of induction employed by Aristotle, and pointed out by him expressly in its subserviency to the exact notions of things, by its leading to the right definitions of them in words. As it appears that words, in a dialectical point of view, are classes more or less comprehensive of observations on things, it is evident that we must gradually approximate towards a definition of any individual notion, by assigning class within class, until we have narrowed the extent of the expression as far as language will admit. (Analyt. Post. ii. c. 13, § 21.) The first definitions of any object are vague, founded on some obvious resemblance which it exhibits compared with other objects. This point of resemblance we abstract in thought, and it becomes, when expressed in language, a genus or class, under which we regard the object as included. A more attentive examination suggests to us less obvious points of resemblance between this object and some of those with which we had classed it before. Thus carrying on the analysis—and by the power of abstraction giving an independent existence to those successive points of resemblance—we obtain subaltern genera or species, or subordinate classes included in that original class with which the process of abstraction commenced. As these several classifications are relative to each other, and dependent on the class with which we first commenced, the definition of any notion requires a successive enumeration of the several classes in the line of abstraction, and hence is said technically to consist of genus and differentia ; the genus being the first abstraction, or class to which the object is first referred, and the differentia being the subordinate classes in the same line of abstraction. Now, the process by which we discover these successive genera, is strictly one of philosophical induction. As in the philosophy of nature in general, we take certain facts as the basis of enquiry, and proceed by rejection and exclusion of principles involved in the enquiry, until at last-there appearing no ground for further rejection—we conclude that we are in possession of the true principle of the object examined ; so, in the philosophy of language, we must proceed by a like rejection and exclusion of notions implied in the general term with which we set out, until we reach the very confines of that notion of it with which our enquiry is concerned. This exclusion is effected in language, by annexing to the general term denoting the class to which the object is primarily referred, oth terms not including under them those other objects or notions to which the