Lecture IX

Abstract

Our knowledge of the epistemological status of the axioms of geometry suffered from a fallacy in which the given concepts of logic and of experience were surreptitiously replaced by made-up ones (and thus a synthetic judgment by an analytic one). This led to the assumption that all knowledge stems either from logic or from experience, yielding two opposing solutions to the problem of the axioms of geometry: they are either analytic (logical) or empirical. In spite of Kant’s argument that they were neither, the old logicist position was still being defended by philosophers such as Hegel in the nineteenth century.