Abstract

Two topics dear to James Robert Brown are discussed, and brought together. First, the applicability of mathematics: it is claimed that applicability offers an a posteriori justification of our mathematical beliefs, on a reflective, rather holistic level in a two level hierarchy. Second, the answer to Benacerraf’s dilemma. A non-empirical mathematical property M is realized in empirical reality through realizers, concrete numerical patterns. The realizers have been interacting causally with human thinkers throughout evolution, which has, through a kind of evolutionary abstraction process, left a proto-representation as of M in human mental apparatus. The innate proto-representation, and its ontogenetic avatars, guide actual humans in recognizing instances of M in the empirical reality. But does the evolutionary production of mechanisms for M-representation track truth? Hopefully yes; the applicability and indispensability of math are a testimony to the truth-tracking.