Abstract:
At the very end of his life (1924-25),
Frege came to the conclusion that our knowledge of mathematics has a
geometrical source. In this paper, I propose a theory of how it is that
Frege was lead to this conclusion, and argue that it is more in keeping
with his earlier logicist views on the nature of numbers than usually
supposed. I begin by giving an interpretation of what Frege meant early
in his career in claiming that a statement about number contains an
assertion about a concept, and how this core idea is realized
differently in his works at different periods owing to changes to his
views about language. I lastly consider another possibility, besides an
appeal to geometry, a neo-Fregean might pursue in order to preserve a
broadly Fregean view about the nature of numbers and our knowledge of
them, and some problems that remain for this approach.