Indispensability and Platonic knowledge

pp. 156-171

in: Colin Cheyne, Knowledge, cause, and abstract objects, Berlin, Springer, 2001

Abstract

Willard Quine and Hilary Putnam argue that the methods by which we confirm scientific theories are the means by which we acquire knowledge of platonic objects. In outline, they argue as follows.¹ Our best theories about the world postulate entities that we cannot observe (for example, electrons) in order to make sense of our experiences. But those same theories postulate platonic objects (for example, numbers and sets). Mathematical objects are just as indispensable to science as theoretical entities like electrons. Electron theory quantifies over numbers and other platonic entities, just as it quantifies over electrons. So we have the same reason for thinking that numbers exist as we do electrons. Our knowledge of platonic objects is obtained in the same way as our knowledge of physical objects, from sense experience. The process by which we obtain platonic knowledge is the same as the process by which we obtain non-platonic scientific knowledge. Indeed, platonic knowledge is an indispensable part of scientific knowledge.