Philosophical Intuitions, Scientific Naturalism, and The Mathematico-Centric Predicament

Abstract

[H]ow does mathematical language function? Does it relate the world in the same ways as the language of natural science? What happens when human beings come to understand mathematical theories? How does mathematics work in various kinds of applications? And so on. To answer these questions, [the scientific- naturalist philosopher of mathematics] must face many of the metaphysician’s concerns: do mathematical entities exist, and if so, what is the nature of that existence? Are mathematical claims true, and if so, how do humans come to know this? These are not detached, extra-scientific pseudo-questions, but straightforward components of our scientific study of human mathematical activity, itself part of our scientific investigation of the world around us.