Joel David Hamkins: Mathematics, Philosophy of Set Theory and Infinity | Back to the Stone Age #5

Journey to the edge of reason with Professor Hamkins! Joel is a Professor of Philosophy and Mathematics at the University of Notre Dame. His research work spans Mathematical Logic and Set Theory. You can find him here: - Personal website: https://jdh.hamkins.org - Twitter: https://twitter.com/JDHamkins - Google Scholar: https://scholar.google.com/citations?user=MHLQDYQAAAAJ&hl=en&oi=ao Back to the Stone Age is on: - YouTube: https://youtube.com/playlist?list=PLZrhMJ5eusE_ACw6Ec3TqCbvDVZ6HP809&si=EHUZow_K4nlcWw8M - Spotify: https://open.spotify.com/show/3pT8MUeR8bskcsuu8gmUGK?si=7f6f32052e9a4587 - Apple Podcasts: https://podcasts.apple.com/it/podcast/back-to-the-stone-age/id1741219288 Outline 00:00 - Introduction 00:55 - Mathematician or philosopher? 05:05 - Set Theory 09:52 - Is mathematics invented or discovered? 15:42 - Godel Incompleteness Theorem 24:14 - Infinity: potential and actual infinity 46:51 - Paradoxes on infinity 55:56 - Penrose three world model: mathematical, physical, and platonic world 01:00:21 - Mathematical reality 01:08:34 - Transfinite numbers, cardinals and ordinals 01:18:44 - The Absolute Infinity 01:25:08 - Infinity and time 01:30:57 - Irrational numbers, Alan Turing and computability 01:40:00 - Cantor’s definition of Set 01:43:40 - Cantor’s theorem 01:54:00 - Continuum Hypothesis 02:05:46 - Hostility of mathematician towards infinity 02:11:39 - Law of excluded middle and infinity 02:17:38 - Not finding answers to questions 02:19:58 - Is there more than maths permeating reality? 02:25:20 - AI and maths/physics 02:31:51 - AI and consciousness 02:36:36 - Most beautiful idea in mathematics and conclusion