Joel David Hamkins: Philosophy of Mathematics and Truth

Joel David Hamkins is a renowned mathematician and philosopher whose work covers logic, computability, game theory, the philosophy of infinity, and more. He’s also the top rated user by reputation on the MathOverflow network.

Find episode details, video and more at: https://www.matthewgeleta.com/

Topics:

the concept of truth in maths and elsewhere

the nature of proof in mathematics

the acclaimed completeness and incompleteness theorems

the relationship between mathematical thinking and the human mind ...

and other topics

Joel's links:

Substack: https://www.infinitelymore.xyz/

Book of infinity: https://www.infinitelymore.xyz/s/the-book-of-infinity

Panorama of logic: https://www.infinitelymore.xyz/s/panorama-of-logic

Other books: https://www.infinitelymore.xyz/p/books

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LinkedIn: https://www.linkedin.com/in/matthewgeleta/

Twitter: https://twitter.com/MatthewGeleta

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PODCAST INFO:

Spotify: https://spoti.fi/3IVDF2W

Apple Podcasts: https://apple.co/3oEZYmJ

Google Podcasts: https://bit.ly/paradigm-on-google

YouTube: https://bit.ly/paradigm-on-youtube

RSS: https://api.substack.com/feed/podcast/1656558/s/65176.rss

Timestamps:

0:00 Intro

1:17: Truth

8:38 Intuition vs objective truth

13:15 Proof

20:39 Completeness

30:18 Incompleteness

37:20 Is completeness a 'problem'?

43:07 Hierarchies of logical systems

48:44 Axioms and where they come from

1:03:50 Motivations for studying pure mathematics

1:19:57 Joel's books

1:22:58 Who should represent humanity to an AI superintelligence?