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 Episode links, show notes and bonus content here: https://www.matthewgeleta.com/ Make a one-off donation here: https://bit.ly/donate-to-paradigm 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-book-of-infinity - Panorama of logic: https://www.infinitelymore.xyz/s/panorama-of-logic - Other books: https://amzn.to/4dhMh14 - Referenced papers: Paul Benacerraf "What Numbers Could Not Be" - https://www.jstor.org/stable/2183530