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.

Avsnitt(277)

173 - Ken Olum: What Are Cosmic Strings?

173 - Ken Olum: What Are Cosmic Strings?

Ken Olum is Research Professor in the Department of Physics and Astronomy at Tufts University, where he works on exotic physics and topics in cosmology like cosmic strings, gravitational waves, anthro...

2 Dec 20231h 4min

172 - Joseph LeDoux: Neuroscience and The Four Realms of Human Existence

172 - Joseph LeDoux: Neuroscience and The Four Realms of Human Existence

Joseph LeDoux is Henry and Lucy Moses Professor of Science, University Professor, Professor of Neural Science, Professor of Psychiatry, and Professor of Child and Adolescent Psychiatry at New York Uni...

29 Nov 20231h 31min

171 - Richard Haier: What Is Human Intelligence?

171 - Richard Haier: What Is Human Intelligence?

Richard Haier is Professor Emeritus in the School of Medicine at the University of California, Irvine, where he uses brain imagining and the tools of neuroscience to study learning, memory, and intell...

26 Nov 20231h 52min

170 - Sheldon Goldstein: Pilot Wave Theory and Bohmian Mechanics

170 - Sheldon Goldstein: Pilot Wave Theory and Bohmian Mechanics

Sheldon Goldstein is Distinguished Professor of Mathematics at Rutgers University, where he researches mathematical physics, the foundations of quantum mechanics, and Bohmian Mechanics. He is also Boa...

24 Nov 20231h 31min

169 - Michael Graziano: The Attention Schema Theory of Consciousness

169 - Michael Graziano: The Attention Schema Theory of Consciousness

Michael Graziano is Professor of Psychology and Neuroscience at Princeton University, where he and his lab research the brain basis of consciousness. Naturally, this is precisely what Michael and Robi...

19 Nov 20231h 56min

168 - Una Stojnić: Slurs, Linguistic Conventions, and the Philosophy of Language

168 - Una Stojnić: Slurs, Linguistic Conventions, and the Philosophy of Language

Una Stojnić is an assistant professor in the Department of Philosophy at Princeton University, where she works in the philosophy of language, formal semantics and pragmatics of natural language, and p...

17 Nov 20231h 13min

167 - David Wallace: The Many-Worlds Interpretation of Quantum Mechanics

167 - David Wallace: The Many-Worlds Interpretation of Quantum Mechanics

David Wallace is Mellon Professor in the Department of History and Philosophy of Science at the University of Pittsburgh. Before that, he obtained PhDs in both physics and philosophy at Oxford. David ...

15 Nov 20231h 51min

166 - Robert Stickgold: Dreams and the Role of Sleep in Memory and Emotional Processing

166 - Robert Stickgold: Dreams and the Role of Sleep in Memory and Emotional Processing

Robert Stickgold is Professor of Pyschiatry at Harvard Medical School, where he researches sleep and dreams from a cognitive neuroscience perspective. In this episode, Bob and Robinson discuss the rol...

12 Nov 20232h 24min

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