Abstract

Gottlob Frege is a significant figure in the philosophy of mathematics and logic insofar as he is the founder of modern symbolic logic and the articulator of the key distinctions and problems that have come to define much of contemporary analytic philosophy. Frege's concept-object distinction plays a major role in underwriting his thesis that numbers must be objects of a particular kind. Fregean numbers are generally interpreted as archetypal abstract objects, demanding some explanation as to how we come to know them. Because Frege's distinction does not seem to deliver such an explanation, commentators have tended to dismiss it as a mistake. I argue that, despite its treatment by most scholars, Frege's distinction should not be read as an ontological claim, but as a methodological principle designed to prevent the errors being committed by his mathematical contemporaries. Analyzed as a norm of mathematical reasoning, Frege's concept-object distinction reveals itself as a neo-Kantian variant of Kant's distinction between a concept and an intuition. A key part of my argument involves delineating the different neo-Kantian camps that arose as a result of the clash between non-Euclidean geometries and Kant's epistemology. Frege is then shown to be aligned with the neo-Kantian camp led by Hermann Cohen and Paul Natorp. Seeing Frege as influenced by Cohen/Natorp's interpretation of Kantian epistemology not only supports my thesis that the C&O distinction is a methodological claim, but also explains why Frege defended the claim that Euclidean geometry was a body of necessary and universal truths grounded on pure intuition and continued to do so well into the 1900's