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(276)

84 - Chris Potts: Semantics, Pragmatics, and ChatGPT

84 - Chris Potts: Semantics, Pragmatics, and ChatGPT

Chris Potts is Professor and Chair of the Department of Linguistics at Stanford University, and also Professor by courtesy in the Department of Computer Science at the same. Chris has worked on a wide...

2 Mai 20231h 20min

83 - Barry Loewer: Probability, Laws of Nature, and Statistical Mechanics

83 - Barry Loewer: Probability, Laws of Nature, and Statistical Mechanics

Barry Loewer is Distinguished Professor of Philosophy at Rutgers. Before that he did his PhD in philosophy at Stanford (!). Barry works largely in the philosophy of physics, the philosophy of science,...

30 Apr 20231h 27min

82 - Jonathan Wolff: Cities, States, and Political Philosophy

82 - Jonathan Wolff: Cities, States, and Political Philosophy

Jonathan Wolff is Alfred Landecker Professor of Values and Public Policy at the University of Oxford. He works in numerous areas of political philosophy. Some topics he has researched include equality...

27 Apr 20231h 53min

81 - Anubav Vasudevan: Mathematics, Physics, and History of Logic

81 - Anubav Vasudevan: Mathematics, Physics, and History of Logic

Anubav Vasudevan is Associate Professor in the Department of Philosophy at the University of Chicago, where he works in formal epistemology and the history of logic, though he has published in a numbe...

25 Apr 20231h 57min

80 - Pamela Hieronymi: Free Will and Moral Responsibility

80 - Pamela Hieronymi: Free Will and Moral Responsibility

Pamela Hieronymi is Professor of Philosophy at UCLA. Before that, she did her undergraduate studies at Princeton and received her PhD from Harvard. Her work extends in a variety of directions, but som...

23 Apr 20231h 16min

79 - Rachel Barney: Ancient Philosophy and the Sophists

79 - Rachel Barney: Ancient Philosophy and the Sophists

Rachel Barney is Professor of Classics and Professor of Philosophy at the University of Toronto. She received her PhD at Princeton and has taught at the University of Ottawa, Harvard, and the Universi...

22 Apr 20231h 33min

78 - Paul Horwich: Truth, Realism, and Moral Facts

78 - Paul Horwich: Truth, Realism, and Moral Facts

Paul Horwich is Professor Philosophy at NYU. He has worked in a number of areas of philosophy, but is especially well-known for his writing on the philosophy of language, particularly with regard to t...

20 Apr 20231h 16min

77 - Stephen Yablo: Non-Existence Claims, Jokes, and Defining Philosophy

77 - Stephen Yablo: Non-Existence Claims, Jokes, and Defining Philosophy

Stephen Yablo is David W. Skinner Professor of Philosophy at MIT. Before MIT, he taught at the University of Michigan, Ann Arbor. Steve works in metaphysics, philosophy of mathematics, and the philoso...

18 Apr 20231h 55min

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