Logic, Mathematics, and the Natural Sciences

Abstract

This chapter examines the relationship between logic, mathematics, and the natural sciences. A constructivist version of a mathematical theory is adequate for all the applications to be made of the theory within natural science. In the overall context of the hypothetico–deductive method in natural science, constructivist logical reasoning is adequate for the applications to be made even of classical mathematics. This chapter sets out a “minimalist” position regarding the correct logic by means of which one may pursue the hypothetico–deductivist method in natural science. It is argued that intuitionistic relevant logic (IR) is adequate. A requirement of reflexive stability is that such an argument should be conducted within the confines of the very logic whose methodological adequacy is to be established. This chapter also addresses an objection in principle that has been raised by John Burgess to the reflexive stability of the argument for IR. The question of the adequacy of constructive methods for hypothetico–deductivism in natural science is examined. The fate of strictly classical theorems of applied mathematics is also discussed in the chapter.