92 - Joan Bagaria: What Is Set Theory?
Robinson's Podcast21 Touko 2023

92 - Joan Bagaria: What Is Set Theory?

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.

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36 - Justin Clarke-Doane: What is Mathematics?

36 - Justin Clarke-Doane: What is Mathematics?

Justin Clarke-Doane is a professor of philosophy at Columbia University, where he works on the philosophy of mathematics, physics, and metaethics. After a long-anticipated catch-up on recent ice cream...

19 Joulu 20222h 10min

35 - Barry Lam: Philosophical Zombies, Resurrecting Cannibals, & Dating Vampires

35 - Barry Lam: Philosophical Zombies, Resurrecting Cannibals, & Dating Vampires

Barry Lam is the host of Hi-Phi Nation, which is a much better podcast than this one, and which is devoted to exploring pressing philosophical questions through narrative. He did his graduate work at ...

15 Joulu 20221h 11min

34 - C Thi Nguyen: Agency, Aesthetics, & The Philosophy of Games

34 - C Thi Nguyen: Agency, Aesthetics, & The Philosophy of Games

C Thi Nguyen is a professor in the philosophy department at the University of Utah. Before that, he did his graduate work at UCLA, where he was also a food writer with the LA Times. Robinson and Thi t...

12 Joulu 20221h 14min

33 - Quayshawn Spencer: The Biology of Race, Natural Kinds, & Craniometry

33 - Quayshawn Spencer: The Biology of Race, Natural Kinds, & Craniometry

Quayshawn Spencer is the Robert S. Blank Presidential Associate Professor of Philosophy at the University of Pennsylvania. Before taking up his post in Philadelphia, he studied chemistry and philosoph...

8 Joulu 20221h 20min

32 - Ray Briggs: Transfeminism, Philosophy of Sex, & Queer Science Fiction

32 - Ray Briggs: Transfeminism, Philosophy of Sex, & Queer Science Fiction

Ray Briggs is a professor in the philosophy department at Stanford University. They did their doctoral work at MIT, and have since been working primarily in decision theory, epistemology, and metaphys...

5 Joulu 20221h 4min

31 - Haim Gaifman: Richard’s Paradox, Infinity, & Set Theory

31 - Haim Gaifman: Richard’s Paradox, Infinity, & Set Theory

Haim Gaifman is a professor of philosophy at Columbia university in New York City. He is also a mathematician and probability theorist. In this episode (Haim’s fourth appearance), Robinson and Haim di...

28 Marras 20221h 9min

30 - David Albert: Foundations of Physics, Time’s Arrow, & Moral Expressivism

30 - David Albert: Foundations of Physics, Time’s Arrow, & Moral Expressivism

David Albert is the Frederick E. Woodbridge Professor of Philosophy at Columbia University and one of the world’s most respected philosophers of physics. He is also the director of the Philosophical F...

21 Marras 20221h 52min

29 - Christopher Bobonich: Etymology, Classics, & Ancient Ethics

29 - Christopher Bobonich: Etymology, Classics, & Ancient Ethics

Christopher Bobonich is the Clarence Irving Lewis Professor of Philosophy at Stanford University. After studying government at Harvard, he went on to do his graduate work at Cambridge and Berkeley. He...

14 Marras 20221h 3min

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