If “If-Then” Then What?
Geoffrey Paul Hellman · Cambridge University Press eBooks · 2021
The roots of the view of mathematics known as “if-thenism” or “deductivism,” like its near cousins, logicism and formalism, are to be found in the nineteenth and early twentieth centuries’ “new birth” of mathematics. As summarized nicely by Maddy [to appear], this period witnessed a multifaceted transformation from mathematics as investigating formal properties of aspects of material reality, such as space, time, and motion, to its being an exploration of abstract concepts and structures in their own right quite apart from any material applications that they might have.