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. Join him in conversations with philosophers, scientists, weightlifters, artists, and everyone in-between.