Nathalie Sinclair

Of Polyhedra and Pyjamas: Platonism and Induction in Meaning-Finitist Mathematics

This chapter considers the epistemology of mathematical concepts through classical Edinburgh School meaning finitism, a philosophical principle from the sociology of knowledge that is now several decades old. Meaning finitism is based on the idea that communities of people adaptively derive open-ended meanings and classifications from a finite basis of experience, choosing how to interpret the world by revising their past interpretations through social interactions. Using Barry Barnes’s metaphor for classification as hospitals issuing pyjamas alongside Imre Lakatos’s famous study of Euler’s theorem about polyhedra, I analyze the implications of this school of meaning finitism for the problems of epistemic induction (inferring about the future based on past experience) and Platonism (assuming the existence of ideal objects independent of concrete experiences) in the elaboration of complex mathematical concepts from simple models and examples.