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# Philosophical Trials

Author: Tedy Nenu

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© 2021 Philosophical Trials

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My name is Tedy Nenu and I am the host of the 'Philosophical Trials' podcast. This is a place where philosophers, mathematicians, linguists and other bright individuals share with us fascinating aspects of their work. Whether you are interested in the nature of mathematical reality or how language works, there will be an episode here that caters to your interests.

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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 Introduction01:05 Vicky’s mathematical background04:13 Motivations for writing a book on reasons to study mathematics07:11 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 Mathematics25:00 Is Number Theory more beautiful than other mathematical subfields? 25:52 A mathematician’s view of the metaphysics of numbers27:58 Fermat’s Last Theorem, Andrew Wiles and finding meaning in Mathematics29:26 FLT and the Twin Prime Conjecture32:27 Should graduate students tackle famous open problems?33:41 Closing the Gap: significant progress towards solving the Twin Prime Conjecture35:10 Polymath: an example of collaborative Mathematics39:40 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/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

Professor Peter Koellner is a leading Logician and Philosopher based at Harvard University. He has made very important contributions to areas surrounding Mathematical Logic and today he was kind enough to join me for a discussion on Penrose's arguments against the prospects of mechanizing the mind (given Kurt Gödel's work on Incompleteness). Note: I am sorry for the occasional internet connection problems. I hope the relevant parts can still be understood! Conversation Outline: 00:00 What are the Incompleteness Theorems?01:59 Why are Gödel’s results relevant for discussions concerning the mind?03:28 Connections between Turing Machines and Formal Systems04:20 When we talk about whether the mind can be mechanized or not, what do we mean? 06:56 Should Cognitive Scientists (or Philosophers of Mind) be interested in this discussion?09:45 The First Generation of Arguments against The Prospects of Mechanizing the Mind19:52 Three Versions of The Mechanistic Thesis21:55 What makes Penrose’s New Argument harder to evaluate in theory EA+T?22:56 Penrose’s Formulation of The Argument (Quote from his Book)27:49 What are the explicit assumptions behind Penrose’s New Argument?32:14 What are the indeterminate statements that Penrose uses in the argument? 36:10 Do you think we’ll ever have an adequate formal theory of type-free truth which settles Gödel’s First Disjunct (the one targeted by Penrose)? 37:18 Do you think your opponent would accept bringing the key notions of relative provability, absolute provability and truth in the setting of effectively formalized theories? 42:25 Why do you think Penrose does not abandon his New Argument, despite resistance from mathematical logicians?44:35 Unlike Lucas or Penrose, some authors such as Hofstadter use Gödel’s results to illuminate the workings of the mind. Do you think the Incompleteness Theorems have anything worthwhile to say here?Enjoy!Apple Podcasts:https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

Dr Sara L. Uckelman is an Assistant Professor of Philosophy at the University of Durham. She earned her PhD in Logic at the University of Amsterdam and her research interests cover many interesting areas including Medieval Logic, Onomastics, Philosophy of Fiction (among others). Today she kindly joined me for a fun discussion on many logic-related topics: I hope you’ll enjoy it!Conversation Outline: 00:00 Introduction01:43 University teaching during the pandemic04:15 “What is Logic?” YouTube series06:00 So, what is Logic?09:18 Should all University undergraduates have some logical training?13:50 Some History of Logic16:35 What was missing from Aristotle’s Logic?20:32 How was Logic being taught back then? 24:16 Research in Medieval Logic27:10 Women in the History of Logic32:03 Onomastics37:34 Does studying Logic improve one’s life?45:35 Book recommendationsEnjoy!

Professor Timothy Williamson is one of the most important philosophers alive. He is the Wykeham Professor of Logic at the University of Oxford, a position that he has been holding since 2000. His groundbreaking work in the areas of philosophical logic, philosophy of language, epistemology and metaphysics has shaped many of the contemporary debates. Today I’m joined by him to discuss Relativism about Truth and the Epistemic account of Vagueness. Enjoy!Conversation outline: 00:00 Introduction: What is Philosophy? 03:11 Can Philosophy help you have a better life?06:47 What’s the story behind your book “Tetralogue”? A discussion on relativism about truth12:44 Relativism about matters of taste20:21 Moral relativism29:47 Tips for finding out the truth about various issues35:34 Vagueness and Classical Logic48:20 Sharp cut-offs52:40 Epistemicism says that you cannot know these cut-offs: why is that? 56:59 Baldness is not really a function of the number of hairs. Does your account apply to situations which are “non-discrete” situations?01:01:47 How can a colour predicate (e.g. “_ is red”) latch on to an objective property out there in the world when people may have different perceptions?01:05:37 If the properties expressed by predicates are person independent, wouldn’t this change the ramifications and implications of the epistemic view?Enjoy!Apple Podcasts:https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

Thomas Cormen is a world-renowned Computer Scientist, famous for co-writing the indispensable 'Introduction to Algorithms' textbook. He is currently a professor at Dartmouth College and former Chairman of the Dartmouth College Department of Computer Science. In 2013 he wrote a wonderful algorithmic book aimed at nonexperts which is entitled 'Algorithms Unlocked'. Professor Cormen also is well-known online for being Top Writer on Quora on numerous years, most recently in 2018. He is a great communicator of Computer Science and I hope you will enjoy the following conversation!00:00 Intro00:16 The story of CLRS plus remarks on the 4th edition11:39 Relationships between Competitive Programming, Software Engineering and academic Computer Science13:16 What makes an algorithm beautiful? 16:33 Thoughts on P=NP19:32 Algorithmic efficiency and Artificial General Intelligence24:12 Will progress in fields such as Deep Learning make the study of classical algorithms obsolete? 27:37 Algorithms Unlocked 33:07 What should the average lay person know about algorithms?37:46 Advice for students, both graduates and undergraduates Enjoy! TwitterApple PodcastsSpotifyGoogle PodcastsYouTubeInstagram

Scott Aaronson is a world-renowned expert in the fields of Quantum Computing and Computational Complexity Theory. He is a David J. Bruton Centennial Professor of Computer Science at The University of Texas at Austin. Every Computer Science enthusiast knows who Prof. Aaronson is because of his extremely clear and engaging way of communicating difficult theoretical ideas. His book Quantum Computing since Democritus is a wonderful resource of dipping into the topics that we are discussing today. Conversation outline: 00:00 Introduction01:04 What draws you to Philosophy?04:36 The importance of focusing of subproblems of the big questions: insights into space, time and thinking machines09:19 The Turing Test and the chinese room argument15:37 What other philosophical areas would benefit from looking at Complexity Theory?21:35 What is Computational Complexity after all?30:03 NP, complexity classes and the P=NP problem45:27 Complexity Theory in light of time and memory limitations52:24 Why do we believe in Quantum Theory?55:36 What is Quantum Computing?01:05:45 How are qubits physically implemented?01:11:14 Quantum Supremacy01:13:26 Would the construction of a quantum computer which could run Shor’s algorithm confirm the many-worlds interpretation? Remarks on David Deutsch’s quantum views. Enjoy!Twitter: https://twitter.com/tedynenuApple Podcasts:https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

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 Introduction00:18 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 sentences33:43 What are possible worlds? Are they the same as the many-worlds of quantum theory? 39:52 Differences between ‘school’ grammar, syntax and formal logic49:07 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 languageTwitter: https://twitter.com/tedynenuApple Podcasts:https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10Google Podcasts:https://podcasts.google.com/?q=philosophical%20trialsInstagram: https://www.instagram.com/tedynenu/

Ed Cooke is a Grandmaster of Memory and the CEO and co-founder of Memrise, one of the most used Language Learning apps in the world. He was also a main character in the international bestseller “Moonwalking with Einstein”. He graduated with a first-class degree in Psychology and Philosophy from the University of Oxford and today we are discussing various memory related issues, briefly described in the following timestamps:00:00 Memrise introduction00:39 Grandmaster of Memory and memory feats01:40 How long have you been into the art of memory?02:48 Did your memory skills benefit your life outside competition?04:16 Is there anything you have trouble remembering?05:32 The scope of memory techniques and remembering your autobiography08:30 How do you actually memorise a pack of cards in 45 seconds?12:07 The functional role of memory and forgetting17:22 Myths about memory19:23 Relationship between memory and attention23:39 False memories27:41 Can memory give insights into consciousness?33:07 Tell us about the work that takes place at MemriseEnjoy!

Tim Crane is a world leading philosopher whose areas of research gravitate towards the study of the mind. His book, The Mechanical Mind, has introduced thousands of people to the central ideas which unite Artificial Intelligence, Philosophy of Mind and Cognitive Science. He is currently the Head of Department at the Central European University, having previously been the Knightbridge Professor of Philosophy at the University of Cambridge.Conversation outline: 00:00 The problem of mental representation10:38 Can a computer think? Is the Turing Test satisfactory?14:15 Can a robot think?18:32 What is the Computational Theory of Mind?20:20 The Language of Thought Hypothesis26:33 Do neural networks implement our language of thought?31:32 Can deep neural networks achieve a complexity which brings about awareness or AGI?33:03 What is general intelligence?34:29 Are there necessary conditions for intelligence?38:00 What is the mechanical view of the human mind?42:35 Consciousness46:32 Can we have free will on the mechanical picture?50:58 Can God account for the explanatory gap between science and consciousness?54:40 Comments on aspects of religionhttps://www.twitter.com/tedynenu

Simon Blackburn is a Fellow of the British Academy. He is a Professor of Philosophy at Trinity College, University of Cambridge who is well known for his contribution to meta-ethics (where he defends quasi-realism) and for his excellent introductory books (such as 'Think' or 'Being Good'). Outline of the conversation:00:10 What motivated you to write 'Think'?02:00 What is the role of Philosophy?04:10 Progress in Philosophy07:18 Remarks on the notion of Truth09:27 Deflationism about Truth14:15 The Correspondence Theory of Truth and problems with Facts17:40 Is there anything wrong with abstract objects?19:44 The Liar's Paradox28:37 The relationship between religion and morality33:55 Free Will47:18 Which philosophers influenced you the most?48:50 What contributions did Hume make to modern thought?Twitter: https://twitter.com/tedynenu

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 Introduction00:50 MathOverflow and books in progress04:08 Mathphobia05:58 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 Mathematics16:58 Cantor's Theorem: the real numbers cannot be enumerated24:22 Russell's Paradox and the Cumulative Hierarchy of Sets29:20 Hilbert's Program and Godel's Results35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs40:50 Computer Assisted Proofs and mathematical insight44:11 Do automated proofs kill the artistic side of Mathematics?48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousnessTwitter: https://twitter.com/tedynenu