His influence on his successors has rather lain in the general stimulus of his enthusiasm for experience, or in the success with which he represents the cause of nominalism and in certain special devices of method handed down till, through Hume or Herschel, they affected the thought of Mill. For the rest he was too Aristotelian, if we take the word broadly enough, or, as the result of his Cambridge studies, too Ramist,[99] when the interest in scholastic issues was fading, to bring his original ideas to a successful market.
Bacon’s Logic, then, like Galilei’s, intended as a contribution to scientific method, a systematization of discovery by which, given the fact of knowledge, new items of knowledge may be acquired, failed to convince contemporaries and successors alike of its efficiency as an instrument. It was an ideal that failed to embody itself and justify itself by its fruits. It was otherwise with the mathematical instrument of Galilei.
Descartes stands in the following of Galilei. It is concurrently with signal success in the work of a pioneer in the mathematical advance that he comes to reflect on method, generalizes the method of mathematics to embrace knowledge as Descartes. a whole, and raises the ultimate issues of its presuppositions. In the mathematics we determine complex problems by a construction link by link from axioms and simple data clearly and distinctly conceived. Three moments are involved. The first is an induction, i.e. an exhaustive enumeration of the simple elements in the complex phenomenon under investigation. This resolution or analysis into simple, because clear and distinct, elements may be brought to a standstill again and again by obscurity and indistinctness, but patient and repeated revision of all that is included in the problem should bring the analytic process to fruition. It is impatience, a perversity of will, that is the cause of error. Upon the analysis there results intuition of the simple data. With Descartes intuition does not connote givenness, but its objects are evident at a glance when induction has brought them to light. Lastly we have deduction the determination of the most complex phenomena by a continuous synthesis or combination of the simple elements. Synthesis is demonstrative and complete. It is in virtue of this view of derived or mediate knowledge that Descartes speaks of the (subsumptive) syllogism as “of avail rather in the communication of what we already know.” Syllogism is not the synthesis which together with analysis goes to constitute the new instrument of science. The celebrated Regulae of Descartes are precepts directed to the achievement of the new methodological ideal in any and every subject matter, however reluctant.
It is the paradox involved in the function of intuition, the acceptance of the psychological characters of clearness and distinctness as warranty of a truth presumed to be trans-subjective, that leads to Descartes’s distinctive contribution to the theory of knowledge. In order to lay bare the ground of certainty he raises the universal doubt, and, although, following Augustine,[100] he finds its limit in the thought of the doubter, this of itself is not enough. Cogito, ergo sum. That I think may be admitted. What I think may still need validation. Descartes’s guarantee of the validity of my clear and distinct perceptions is the veracity of God.[101] Does the existence of God in turn call for proof? An effect cannot contain more than its cause, nor the idea of a perfect Being find adequate source save in the actuality of such a Being. Thus the intuition of the casual axiom is used to prove the existence of that which alone gives validity to intuitions. Though the logical method of Descartes has a great and enduring influence, it is the dualism and the need of God to bridge it, the doctrine of “innate” ideas, i.e. of ideas not due to external causes nor to volition but only to our capacity to think, our disposition to develop them, and finally the ontological proof, that affect the thought of the next age most deeply. That essence in the supreme case involves existence is a thought which comes to Spinoza more easily, together with the tradition of the ordo geometricus.
D. Modern Logic
i. The Logic of Empiricism
The path followed by English thought was a different one. Hobbes developed the nominalism which had been the hallmark of revolt against scholastic orthodoxy, and, when he brings this into relation with the analysis and synthesis of scientific method, it is at the expense of the latter.[102] Locke, when Cartesianism had raised the problem of the contents of consciousness, and the spirit of Baconian positivism could not accept of anything that bore the ill-omened name of innate ideas, elaborated a theory of knowledge which is psychological in the sense that its problem is how the simple data with which the individual is in contact in sensation are worked up into a system. Though he makes his bow to mathematical method, he, even more than Hobbes, misses its constructive character. The clue of mathematical certainty is discarded in substance in the English form of “the new way of ideas.”
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 communicate with his fellows. He alone is Hobbes. capable of truth in the due conjunction or disjunction of names in propositions. Syllogism is simply summation of propositions, its function being communication merely. Analysis is the sole way of invention or discovery. There is more, however, in Hobbes, than the paradox of nominalism. Spinoza could draw upon him for the notion of genetic definition.[103] Leibnitz probably owes to him the thought of a calculus of symbols, and the conception of demonstration as essentially a chain of definitions.[104] His psychological account of syllogism[105] is taken over by Locke. Hume derived from him the explanatory formula of the association of ideas,[106] which is, however, 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,[107] which played no small part in the applied logic of the 19th century.
Locke is of more importance, if not for his logical doctrine, at least for the theory of knowledge from which it flows. With Locke the mind is comparable to white paper on which the world of things records itself in ideas of sensation. Locke. Simple ideas of sensation are the only points of contact we have with things. They are the atomic elements which “the workmanship of the understanding” can thereafter do no more than systematically compound and the like. It is Locke’s initial attribution of the primary rôle in mental process to the simple ideas of sensation that precludes him from the development of the conception of another sort of ideas, or mental contents that he notes, which are produced by reflection on “the operations of our own mind within us.” It is in the latter group that we have the explanation of all that marks Locke as a forerunner of the critical philosophy. It contains in germ a doctrine of categories discovered but not generated in the psychological processes of the individual. Locke, however, fails to “deduce” his categories. He has read Plato’s Theaetetus in the light of Baconian and individualist preconceptions. Reflection remains a sort of “internal sense,” whose ideas are of later origin than those of the external sense. His successors emphasize the sensationist elements, not the workmanship of the mind. When Berkeley has eliminated the literal materialism of Locke’s metaphors of sense-perception, Hume finds no difficulty in accepting the sensations as present virtually in their own right, any nonsensible ground being altogether unknown. From a point of view purely subjectivist he is prepared to explain all that is to be left standing of what Locke ascribes to the workmanship of the mind by the principle of association or customary conjunction of ideas, which Locke had added a chapter to a later edition of his Essay explicitly to reject as an explanatory formula. Condillac goes a step farther, and sees no necessity for the superstructure at all, with its need of explanation valid or invalid. Drawing upon Gassendi for his psychological atomism and upon Hobbes for a thoroughgoing nominalism, he reproduces, as the logical conclusion from Locke’s premises, the position of Antisthenes. The last word is that “une science bien traitée n’est qu’une langue bien faite.”[108]
Locke’s logic comprises, amid much else, a theory of general terms[109] and of definition, a view of syllogism[110] and a declaration as to the possibility of inference from particular to particular,[111] a distinction between propositions which are certain but trifling, and those which add to our knowledge though uncertain, and a doctrine of mathematical certainty.[112] 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 individuals than one.” This doctrine has found no acceptance. Not from the point of view for which idea means image. Berkeley, though at length the notions of spirits, acts and relations[113] 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,”[114] 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 leave 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 perception, 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 himself 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 general 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,[115] which has an obviously Cartesian ring, lays down four 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 intermediate ideas. He is prepared readily to “own that all right reasoning may be reduced to Aristotle’s forms 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.