• 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

Joel David Hamkins: Philosophy of Set Theory, Mathematics and Infinity #3

  • サマリー

  • 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

    続きを読む 一部表示

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

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