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

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

Robinson's Podcast vor 3 Jahren

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1:55:11

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.