I the Logic of Empiricism

I. THE LOGIC OF EMPIRICISM Hobbes.—With Hobbes logic is a calculus of marks and signs in the form of names. Naming is what distinguishes man from the brutes. It enables him to fix fleeting memories and to com municate with his fellows. He alone is capable of truth in the due conjunction or disjunction of names in propositions. Syllogism is simply summation of propositions, its function being com munication merely. Analysis is the sole way of invention or dis covery. There is more, however, in Hobbes, than the paradox of nominalism. Spinoza could draw upon him for the notion of genetic definition. Leibniz probably owes to him the thought of a calculus of symbols, and the conception of demonstration as essentially a chain of definitions. His psychological account of syllogism is taken over by Locke. Hume derived from him the explanatory formula of the association of ideas, which is, how ever, still with Hobbes a fact to be accounted for, not a theory to account for facts, being grounded physically in "coherence of the matter moved." Finally Mill took from him his definition of cause as sum of conditions, which played no small part in the applied logic of the i9th century.

Locke.

Locke's logic comprises, amid much else, a theory of general terms and of definition, a view of syllogism, and a dec laration as to the possibility of inference from particular to par ticular, a distinction between propositions which are certain but trifling, and those which add to our knowledge though uncertain, and a doctrine of mathematical certainty. As to the first, "words become general by being made the signs of general ideas, and ideas become general by separating from them" all "that may determine them to this or that particular existence. By this way of abstraction they are made capable of representing more in dividuals than one." This doctrine has found no acceptance. Not from the point of view for which idea means image. Berke ley, though at length the notions of spirits, acts and relations give him pause, prefers the formula which Hume expresses in the phrase that "some ideas are particular in their nature but general in their representation," and the after-history of "abstraction" is a discussion of the conditions under which one idea "stands for" a group. Not from those for whom general ideas mean schematic concepts, not imageable. The critic from this side has little difficulty in showing that abstraction of the kind alleged still leaves the residuum particular, this redness, e.g., not redness. It

is, however, of the sorts constituted by the representation which his abstraction makes possible that definition is given, either by enumeration of the simple ideas combined in the significance of the sortal name, or "to save the labour of enumerating," and "for quickness and despatch sake," by giving the next wider general name and the proximate difference. We define essences of course in a sense, but the essences of which men talk are abstractions, "creatures of the understanding." Man determines the sorts or nominal essences, nature the similitudes. The fundamentally enumerative character of the process is clearly not cancelled by the recognition that it is possible to abbreviate it by means of technique. So long as the relation of the nominal to the real essence has no other background than Locke's doctrine of per ception the conclusion that what Kant afterwards calls analytical judgments a priori and synthetic judgments a posteriori exhaust the field follows inevitably, with its corollary, which Locke him self has the courage to draw, that the natural sciences are in strictness impossible. Mathematical knowledge is not involved in the same condemnation, solely because of the "archetypal" character, which, not without indebtedness to Cumberland, Locke attributes to its ideas. The reality of mathematics, equally with that of the ideals of morals drawn from within, does not extend to the "ectypes" of the outer world. The view of reasoning which Locke enunciates coheres with these views. Reasoning from particular to particular, i.e., without the necessity of a gen eral premise, must be possible, and the possibility finds warranty in a consideration of the psychological order of the terms in syllogism. As to syllogism specifically, Locke in a passage which has an obviously Cartesian ring, lays down f our stages or degrees of reasoning, and points out that syllogism serves us in but one of these, and that not the all-important one of finding the inter mediate ideas. He is prepared readily to "own that all right reasoning may be reduced to Aristotle's form of syllogism," yet holds that "a man knows first, and then he is able to prove syllogistically." The distance from Locke to Stuart Mill along this line of thought is obviously but small.