(1) that arithmetical truths are known through an examination of our arithmetical concepts;It is (1) and (3) which might not seem to initially sit well together, so I look forward to seeing how Jenkins can reconcile some of kind a priorism with some kind of empiricism.
(2) that (at least our basic) arithmetical concepts map the arithmetical structure of the independent world;
(3) that this mapping relationship obtains in virtue of the normal functioning of our sensory apparatus. (x)
Tuesday, January 13, 2009
New Book: Grounding Concepts: An Empirical Basis for Arithmetical Knowledge
C. S. Jenkins' relatively new book looks like an exciting contribution to the epistemology of mathematics that aims to relate debates in the philosophy of mathematics to some more recent work on concepts and the a priori. Based on the title and on her earlier paper, I had expected that Jenkins aimed to defend some kind of neo-Millian view of arithmetic, in line with Kitcher. But this seems to have been a mistake. Her preface lays out a clear desire to defend the a priority of arithmetic: