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

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