Physicalism in mathematics is a fruitful research program

Abstract

Especially in Japan, physicalistic/nominalistic reinterpretation of mathematics is regarded as an attempt that has relevance, if any, only to a small group of “peculiar” philosophers and hence has no general significance to philosophy itself. My aim of the paper is to show that this reputation is ill-founded. Two main strategies for nominalization of mathematics, (i. e. Hartry Field's instrumentalist program and Geoffrey Hellman's modal-structuralist program) are examined. It is shown that both of these are fruitful research programs that will have a major influence on philosophy of science and language, even if they might prove to be unsuccessful in the end.