Journal of the History of Philosophy

Locke on Mathematical Knowledge PREDRAG CICOVACKI 1. KANTPOINTS OUT that he had found in Locke's EssayconcerningHuman Understanding an indication of a general division of judgments into analytic and synthetic. He also notes that in the same work he had found an indication that some of our judgments are (in his terms) synthetic a priori.' What Kant says about Locke is peculiar for several reasons. First, Locke himself never used the terms 'analytic', 'synthetic', 'a priori', and 'a posteriori'. Second, when Kant goes on to explain more precisely where he finds an analogy between Locke's and his own view, he refers to passages which do not serve his purpose in the best way.' We can only speculate about Kant's reasons for choosing some passages in Locke rather than others. Yet whatever Kant's reasons are, he gives us a useful conceptual framework which we want to apply here to Locke's view on mathematical knowledge. We hope that in that way we shall be able to show Locke's 1 am deeply grateful to Prof. Lewis White Beck for his detailed comments on earlier drafts of the paper. I also want to thank Prof. John W. Yolton for his suggestions on the penultimate draft. i Prolegomena to Any Future Metaphysics, trans, and intro, by L. W. Beck (Indianapolis: The Liberal Arts Press, 195o), paragraph 3. ' For instance, we expect Kant to say that Locke's division of propositions into trifling and instructive is analogous to his analytic-synthetic distinction. Yet Kant refers to Locke's view on identity or diversity (Kant says "identity or contradiction") as kinds of agreement and disagreement of our ideas like those in analytic judgments. Kant departs significantly from Locke's view, for obviously diverse propositions need not be contradictory. Kant isolates a subset of diverse propositions, those which are contradictory, and joins them with propositions which express identity in order to get a set of all analytic propositions. We might expect that Kant will claim that, according to Locke, our mathematical propositions are synthetic a priori. But Kant remarks that Locke's 'coexistence' propositions are synthetic, and that those of them which express necessary connections are synthetic and a priori (according to his own criteria). [511] 519 JOURNAL OF THE HISTORY OF PHILOSOPHY 28:4 OCTOBER 1990 view to be closer to modern points of view, and at the same time show how rich, interesting, and important was his account of mathematical knowledge. Let us, then, suggest a preliminary dictionary, that is, approximate translations of Locke's terminology into Kant's. According to what Wolfram a has called the "Standard Interpretation" (with which, as we shall see, she disagrees ), we have l) instructive (Locke) = synthetic (Kant), 2) trifling (Locke) = analytic (Kant). Our reasons for the propose d translation are, briefly, the following. Locke claims that trifling propositions are merely verbal and self-evident, and that they do not teach us anything new, that is, they are not instructive. Instructive propositions, on the other hand, are those which enlarge our knowledge; they need not be certain, and when they are, their certainty is not verbal. We do not get instructive propositions by the mere analysis of ("playing with") words contained in our ideas. 4 Hence, what Locke claims about trifling and instructive propositions is similar to what Kant maintains about analytic and synthetic judgments, s 9. The thesis that there is a close resemblance between Locke's view on mathematical propositions and Kant's view on mathematical judgments is not new, but it has not been much elaborated either. 6 The passage which Kant himself does not mention, but which is interpreted by some Locke commentators to demonstrate the analogy between Locke and Kant is the following one: [W]e can know the Truth and so may be certain in Propositions, which affirm something of another, which is a necessary consequence of its precise complex Idea, but not contained in it. As that the external Angle of aU Triangles, is bigger than either of the opposite internal Angles; which relation of the outward Angle, to either of the opposite internal s See Sybil Wolfram's papers, "On the Mistake of Identifying Locke'sTrifling-Instructive...