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Joel David Hamkins: Philosophy of Set Theory, Mathematics and Infinity #3
- 2024/06/07
- 再生時間: 2 時間 38 分
- ポッドキャスト
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サマリー
あらすじ・解説
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