75 - Jody Azzouni: Formal Languages, Proof, and the Foundations of Mathematics

Jody Azzouni is Professor of Philosophy at Tufts University. While Jody is best known for his nominalist stance in the philosophy of mathematics, he is also an author of fiction, non-fiction, and poetry. Robinson and Jody discuss one of Jody’s poems in detail before moving on to the philosophy of mathematics and logic. They go over the distinction between natural and formal languages, the roles and varieties of proof in mathematics, and whether mathematics can have foundations. This is Jody’s second appearance on Robinson’s podcast. On his first appearance, episode #45, he and Robinson spoke about the debate between nominalists and platonists in the philosophy of mathematics, Jody’s own deflationary stance, and some adjacent concerns about ontological commitment in both formal and informal languages. His latest book is Attributing Knowledge: What it Means to Know Something (Oxford, 2020).

Jody’s Website: https://jodyazzouni.com

OUTLINE:

00:00 In This Episode…

00:40 Introduction

4:48 “Colored Themes” by Jody Azzouni

36:59 The Difference Between Formal and Natural Languages 

1:02:37 The Nature of Mathematical Proof

1:20:36 Can Mathematics Still Have Foundations?

1:26:36 Jody’s Course on Philosophy of Math

1:31:01 Mathematics as a Social Practice

1:37:23 Revolutions in Mathematics 

1:40:35 “February” by Giles Goodland

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.