Philosophical Trials

Joel David Hamkins is an American Mathematician who is currently Professor of Logic at the University of Oxford. He is well known for his important contributions in the fields of Mathematical Logic, Set Theory and Philosophy of Mathematics. Moreover, he is very popular in the mathematical community for being the highest rated user on MathOverflow.
Outline of the conversation:
00:00 Podcast Introduction
00:50 MathOverflow and books in progress
04:08 Mathphobia
05:58 What is mathematics and what sets it apart?
08:06 Is mathematics invented or discovered (more at 54:28)
09:24 How is it the case that Mathematics can be applied so successfully to the physical world?
12:37 Infinity in Mathematics
16:58 Cantor's Theorem: the real numbers cannot be enumerated
24:22 Russell's Paradox and the Cumulative Hierarchy of Sets
29:20 Hilbert's Program and Godel's Results
35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs
40:50 Computer Assisted Proofs and mathematical insight
44:11 Do automated proofs kill the artistic side of Mathematics?
48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis
54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers
1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms
1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousness
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Professor Robert Sapolsky is a Professor of Biology, Neurology, and Surgery at Stanford University. He is the author of multiple books, including A Primate’s Memoir, Why Zebras Don’t Get Ulcers, Behave, and Determined. Professor Kevin Mitchell is a Professor of Genetics and Neuroscience at Trinity College Dublin, whose research concerns the relationship between the wiring of the brain and the human faculties. His books include Innate and Free Agents. Today’s debate was about whether the empirical literature in the biological sciences allows us to make progress on the free will debate.
Conversation Outline:
00:00 Introduction
02:28 Opening Statement: Kevin Mitchell
16:26 Opening Statement: Robert Sapolsky
27:32 First Round of Questioning
45:56 Second Round of Questioning
1:04:56 How can we make evolutionary sense of illusory agency?
1:06:13 How can we make sense of our accomplishments if we have no free will?
1:08:21 Comparisons with Dennett and Hofstadter
1:12:28 Closing thoughts
Enjoy!
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Dr Vicky Neale is the Whitehead Lecturer at the Mathematical Institute and Balliol College at the University of Oxford. She is also a Supernumerary Fellow at Balliol and the author of two great books aimed at general audiences, namely ‘Closing the Gap’ and ‘Why Study Mathematics?’.
Vicky Neale is a great communicator of Mathematics. She was given an MPLS Teaching Award in 2016 and she also won an award for being the Most Acclaimed Lecturer in MPLS in the student-led Oxford University Student Union Teaching Awards 2015.
Follow her on Twitter: @VickyMaths1729
For some clear proofs of a selection of mathematical theorems, check out her YouTube channel: https://www.youtube.com/channel/UCBGhXXBCAzbzQV65JZoGhjw and her blog https://theoremoftheweek.wordpress.com/
Conversation Outline:
00:00 Guest Introduction
01:05 Vicky’s mathematical background
04:13 Motivations for writing a book on reasons to study mathematics
07:11 Are good reasons for studying Mathematics timeless? Would this book have more or less the same contents, had it been written many years ago?
10:10 Is the job of pure mathematicians safe from AI developments?
12:13 What are the benefits (for the non-mathematician) of knowing about mathematical notions such as integrals, derivatives, matrices and so on?
15:39 Are some people more mathematically talented than others?
18:45 Does the discussion of talent change when we are talking about research-level Mathematics? Douglas Hofstadter’s experience.
22:45 Aesthetics of Mathematics
25:00 Is Number Theory more beautiful than other mathematical subfields?
25:52 A mathematician’s view of the metaphysics of numbers
27:58 Fermat’s Last Theorem, Andrew Wiles and finding meaning in Mathematics
29:26 FLT and the Twin Prime Conjecture
32:27 Should graduate students tackle famous open problems?
33:41 Closing the Gap: significant progress towards solving the Twin Prime Conjecture
35:10 Polymath: an example of collaborative Mathematics
39:40 Do we have reasons to believe that the Twin Prime Conjecture is actually true?
Enjoy!
Apple Podcasts:
https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135
Spotify:
https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10
Google Podcasts:
https://podcasts.google.com/?q=philosophical%20trials
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Professor Kai von Fintel is a world-leading linguist (Section Head at MIT) who is well known for his contributions to Semantics, an academic fields which sits at the intersection of many disciplines which is typically concerned with the meaning of linguistic expressions. He is the co-founder of the open access journal Semantics & Pragmatics. You can find more about his work on his website: https://www.kaivonfintel.org
Conversation Outline:
00:00 Introduction
00:18 What is special about language?
03:31 How did we (as a species) get linguistic abilities?
05:24 What do people who work in Semantics do?
09:19 How can babies pick up language?
15:07 What is the meaning of words? Aren’t they just dictionary entries?
19:03 On idiolects
27:00 The meanings of sentences
33:43 What are possible worlds? Are they the same as the many-worlds of quantum theory?
39:52 Differences between ‘school’ grammar, syntax and formal logic
49:07 What is the meaning of ‘if’?
01:04:54 Does the research of Semanticists impact the field of Computational Linguistics?
01:07:39 The relationship between thought and language
Twitter:
https://twitter.com/tedynenu
Apple Podcasts:
https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135
Spotify:
https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10
Google Podcasts:
https://podcasts.google.com/?q=philosophical%20trials
Instagram:
https://www.instagram.com/tedynenu/

Professor A.C. Grayling is one of the most prolific philosophers and public intellectuals. He is a Fellow of the Royal Society of Arts, the Master of the New College of the Humanities and a Supernumerary Fellow of St. Anne’s College, Oxford. He made important contributions to Analytic Philosophy, primarily in Epistemology, Metaphysics and Philosophical Logic. Prof. Grayling wrote more than 40 books, including The God Argument, The History of Philosophy and The Frontiers of Knowledge.
Conversation Outline:
00:00 Introduction
00:46 How did you get into Philosophy?
03:23 What was your PhD Thesis on? Thoughts on Skepticism and Knowledge
08:11 What are the interesting epistemological advancements (and problems) of our time?
12:27 On interdisciplinarity and higher education
15:10 Different models of education and advice for high-school students that want to go to university
19:04 STEM, Arts and public perception
21:45 Traditional epistemology and why certainty and absolute truth are not essential
27:44 Is the situation different for Mathematics? What about Theology?
35:02 Why do people take Religion to be a source of certain truths?
41:00 New Atheism
46:50 Discussing some of the main theistic arguments
59:30 God and Morality
Enjoy!
Instagram:
https://www.instagram.com/tedynenu/
Twitter:
https://twitter.com/tedynenu
Apple Podcasts:
https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135
Spotify:
https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10
Google Podcasts:
https://podcasts.google.com/search/philosophical%20trials