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92 - Joan Bagaria: What Is Set Theory?

92 - Joan Bagaria: What Is Set Theory?

Robinson's Podcast vor 3 Jahren

0:00

2:05:53

Joan Bagaria is ICREA Research Professor in the Department of
Experimental Sciences and Mathematics at the University of
Barcelona. He is a mathematical logician who works in set theory,
which is the branch of mathematics that not only specializes in
the investigation of infinity but serves as the foundation for
the rest of mathematics—what this means, and its implications,
are explored in the episode. Joan and Robinson discuss all things
set theory, beginning with its origins in the mind of Georg
Cantor, its development in the 20th century, some philosophical
questions, and some current outstanding problems. They also
briefly touch on Catalan independence, a topic dear to Joan’s
heart. Joan’s Twitter: ⁠https://twitter.com/BagariaJoan⁠ Set
Theory: https://plato.stanford.edu/entries/set-theory/ The Early
Development of Set Theory:
https://plato.stanford.edu/cgi-bin/encyclopedia/archinfo.cgi?entry=settheory-early
OUTLINE 00:00 In This Episode… 01:01 Introduction 06:18 Joan and
Set Theory 09:11 The Development of Set Theory 21:08 Naive Set
Theory and Axiomatic Set Theory 30:52 Zermelo-Fraenkel Set Theory
with Choice 46:35 Metaphysics and Epistemology 01:03:06 Set
Theory as the Foundation of Mathematics 01:09:48 The Continuum
Problem 01:16:13 Settling the Continuum Problem 01:35:21
Alternative Set Theories 01:43:37 Alternative Foundations
01:47:53 Catalan Independence Robinson’s Website:
⁠http://robinsonerhardt.com⁠ Robinson Erhardt researches symbolic
logic and the foundations of mathematics at Stanford University.
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