92 - Joan Bagaria: What Is Set Theory?

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.

Episoder(277)

197 - Martha Nussbaum: Justice for Animals

197 - Martha Nussbaum: Justice for Animals

Patreon: https://bit.ly/3v8OhY7 Martha Nussbaum is the Ernst Freund Distinguished Service Professor of Law and Ethics at the University of Chicago, with appointments in the Department of Philosophy a...

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196 - Stephen Wolfram: The Fundamental Theory of the Universe

196 - Stephen Wolfram: The Fundamental Theory of the Universe

Patreon: https://bit.ly/3v8OhY7 Stephen Wolfram is the founder and CEO of Wolfram Research, and the creator of Mathematica, Wolfram|Alpha, and the Wolfram Language. He received his PhD in theoretical...

26 Feb 20241h 52min

195 - Brian Keating: Cosmological Inflation and the Universe’s First Light

195 - Brian Keating: Cosmological Inflation and the Universe’s First Light

Patreon: https://bit.ly/3v8OhY7 Brian Keating is the Chancellor’s Distinguished Professor of Physics at the Center for Astrophysics & Space Sciences at UC San Diego, host of the Into the Impossible Po...

19 Feb 20241h 39min

194 - Daniel Dennett: Consciousness, Free Will, and the Evolution of Minds

194 - Daniel Dennett: Consciousness, Free Will, and the Evolution of Minds

Patreon: https://bit.ly/3v8OhY7 Daniel Dennett is Professor Emeritus of Philosophy at Tufts University, where he was co-director of the Center for Cognitive Studies and the Austin B. Fletcher Profess...

12 Feb 20241h 50min

193 - Robert Sapolsky: Determinism, Free Will, & The End of Moral Responsibility

193 - Robert Sapolsky: Determinism, Free Will, & The End of Moral Responsibility

Patreon: https://bit.ly/3v8OhY7 Robert Sapolsky is John A. and Cynthia Fry Gunn Professor and Professor of Biology, Neurology, and Neurosurgery at Stanford University. He’s also a best-selling author...

7 Feb 20241h 53min

192 - Norman Finkelstein: Hamas, Hezbollah, and Justice in the Israel-Palestine Conflict

192 - Norman Finkelstein: Hamas, Hezbollah, and Justice in the Israel-Palestine Conflict

Patreon: https://bit.ly/3v8OhY7 Norman Finkelstein received his PhD from the Princeton University Politics Department, and is best known for his indefatigable research on Israel and Palestine, which ...

28 Jan 20241h 25min

191 - Victor Davis Hanson: An American’s Case For Israel

191 - Victor Davis Hanson: An American’s Case For Israel

Patreon: https://bit.ly/3v8OhY7 Victor Davis Hanson is a renowned classicist, military historian, and political commentator. He is the Martin and Illie Anderson Senior Fellow in Residence in Classics...

21 Jan 20241h 2min

190 - Richard Wolff: A Marxist’s Case For Palestine

190 - Richard Wolff: A Marxist’s Case For Palestine

Patreon: https://bit.ly/3v8OhY7 Richard Wolff is Professor Emeritus of Economics at the University of Massachusetts Amherst and a visiting professor at The New School, where he works on economics in ...

17 Jan 20241h 38min

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