118. A genius of such native force as Locke’s could not be applied to philosophy without determining the lines of future speculation, even though to itself they remained obscure. He stumbles upon truths when he is not looking for them, and the inconsistencies or accidents of his system are its most valuable part. Thus, in a certain sense, he may claim the authorship at once of the popular empiricism of the modern world, and of its refutation. He fixed the prime article of its creed, that thought has nothing to do with the constitution of facts, but only with the representation of them by signs and the rehearsal to itself of what its signs have signified--in brief, that its function is merely the analytical judgment; yet his admissions about mathematical knowledge rendered inevitable the Kantian question, ‘How are synthetic judgments á-priori possible?’--which was to lead to the recognition of thought as constituting the objective world, and thus to get rid of the antithesis between thought and reality. In his separation of the datum of experience from the work of thought he was merely following the Syllogistic Logic, which really assigns no work to the thought, whose office it professes to magnify, but the analysis of given ideas. Taking the work as that Logic conceived it (and as it must be conceived if the separation is to be maintained) he showed--conclusively as against Scholasticism-- the ‘trifling’ character of the necessary and universal truths with which it dealt. Experience, the manifestation of the real, regarded as a series of events which to us are sensations, can only yield propositions singular as the events, and having a truth like them contingent. By consequence, necessity and universality of connection can only be found in what the mind does for itself, without reference to reality, when it analyses the complex idea which it retains as the memorandum of its past single experiences; _i.e._, in a relation between ideas or propositions of which one explicitly includes the other. Upon this relation syllogistic reasoning rests, and, except so far as it may be of use for convicting an opponent (or oneself) of inconsistency, it has nothing to say against such nominalism as the above. Hence, with those followers of Locke who have been most faithful to their master, it has remained the standing rule to make the generality of a truth consist in its being analytical of the meaning of a name, and its necessity in its being included in one previously conceded. Yet if such were the true account of the generality and necessity of mathematical propositions, their truth according to Locke’s explicit statement would be ‘verbal and trifling,’ not, as it is, ‘real and instructive.’ Fatal to the notion that mathematical truths, though general, are got from experience: