Original scientific paper

Reply to Jim, aka James Robert Brown

Nenad Miščević

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.

Keywords

mathematics-applicability of; Benacerraf’s dilemma; evolutionary account

Hrčak ID:

176593

URI

https://hrcak.srce.hr/176593

Publication date:

5.5.2016.

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