John Burgess is John N. Woodhull Professor of Philosophy at Princeton University, where he works in mathematical and philosophical logic and the philosophy of mathematics. In this episode, Robinson and John discuss realism in the philosophy of mathematics, and while the nature of this question is itself disputed, it can be roughly described as concerning the extent to which we should be committed to the mind-independent truth of mathematical theorems, or to the existence of the objects they apparently describe. Robinson and John begin by addressing the nuances of this question, and they then turn to various developments in mathematics that have been historically associated with realism—set theory, in particular—as well as specific philosophical positions associated with realism (such as Platonism) and anti-realism (such as conventionalism). John’s most recent book is Set Theory (Cambridge, 2022).

Set Theory: https://a.co/d/cF305wf

OUTLINE

00:00 In This Episode…

00:22 Introduction

03:17 Mathematics or Philosophy?

08:06 What is Realism in the Philosophy of Mathematics?

14:11 Objectivity and Mathematics

24:34 What Is Set Theory?

47:29 Platonism and the Continuum Problem

01:15:42 Conventionalism

01:22:06 Finitism

01:31:17 A Cap on Infinity?

Robinson’s Website: http://robinsonerhardt.com

Robinson Erhardt researches symbolic logic and the foundations of mathematics at Stanford University. Join him in conversations with philosophers, scientists, weightlifters, artists, and everyone in-between.