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140 - John Burgess: Realism in the Philosophy of Mathematics

140 - John Burgess: Realism in the Philosophy of Mathematics

Robinson's Podcast vor 2 Jahren

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1:34:20

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.