Joel David Hamkins: Philosophy of mathematics and truth

Joel is a renowned mathematician and philosopher whose work covers a wide range of important topics, including logic, computability theory, game theory, the philosophy of infinity, and more.

Joel is the author of several books including Lectures on the Philosophy of Mathematics, and the The Book of Infinity, which he’s publishing in a serialised form on his Substack, Infinitely More.

#truth #maths #logic #philosophy #infinity

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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

Timestamps:
0:00 Intro
0:17: Truth
7:38 Intuition vs objective truth
12:15 Proof
19:39 Completeness
29:18 Incompleteness
36:20 Is completeness a 'problem'?
42:07 Hierarchies of logical systems
47:44 Axioms and where they come from
1:02:50 Motivations for studying pure mathematics
1:18:57 Joel's books
1:21:58 Who should represent humanity to an AI superintelligence?

Joel' links:
Substack: https://www.infinitelymore.xyz/
Book of infinity: https://www.infinitelymore.xyz/s/the-...
Panorama of logic: https://www.infinitelymore.xyz/s/pano...
Other books: https://amzn.to/4dhMh14
Referenced papers: Paul Benacerraf "What Numbers Could Not Be" - https://www.jstor.org/stable/2183530