Abstract

Chapter 1 distinguishes between the Cartesian intellectualist and Lockean sensationalist versions of the presentational-phenomenological model. It discusses Descartes’s and Locke’s treatments of intuitive and demonstrative knowledge, and argues that there are significant remnants of Cartesianism in Locke. It provides a new interpretation of the Cartesian conception of clear and distinct ideas, and of Leibniz’s transformation of ideas into concepts. Unlike in Leibniz’s logical-conceptual model, the ostensive apprehension of particulars, independently of a priori rules, constitutes ultimate evidence for both Descartes and Locke: there is a possible sceptical gap between intuitive and demonstrative knowledge. Descartes develops a skeptical challenge concerning demonstrative reasoning based on the need for memory. Locke’s discussion of memory in demonstrations is also considered in detail. In the end, neither Descartes nor Locke can provide a satisfactory account of the necessity and universality of mathematics—as shown by Leibniz’s criticisms of both versions of the presentational-phenomenological model.