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The Cartesian CafeAuthor: Timothy Nguyen
The Cartesian Cafe is the podcast where an expert guest and Timothy Nguyen map out scientific and mathematical subjects in detail. This collaborative journey with other experts will have us writing down formulas, drawing pictures, and reasoning about them together on a whiteboard. If youve been longing for a deeper dive into the intricacies of scientific subjects, then this is the podcast for you. Topics covered include mathematics, physics, computer science, machine learning, and artificial intelligence. Content also viewable on YouTube: www.youtube.com/timothynguyen and Spotify. Timothy Nguyen is a mathematician and AI researcher working in industry. Homepage: www.timothynguyen.com, Twitter: @IAmTimNguyen Patreon: www.patreon.com/timothynguyen Language: en Genres: Mathematics, Physics, Science Contact email: Get it Feed URL: Get it iTunes ID: Get it Trailer: |
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Justin Clarke-Doane | Mathematics, Reality, and Morality
Episode 20
Friday, 6 December, 2024
Justin Clarke-Doane is a professor of philosophy at Columbia University, whose interests span metaethics, epistemology, and the philosophy of logic & mathematics. In this thought provoking-discussion, Justin and I go deep into topics that are typically neglected by most mathematicians and scientists, namely the philosophy of mathematics and morality. Justin has contributed to both these areas via his book Morality and Mathematics, which takes the view that the standard position of being both a mathematical realist and moral antirealist is incoherent. Perhaps the most novel aspect of Justin's work is the treatment of the philosophy of mathematics and morality side-by-side, showing how these two topics, which are usually thought of as being unrelated, in fact have strong analogies. Along the way, we discuss many other foundational topics in epistemology and ethics, with elements of set theory, metaphysics, and logic sprinkled in. Patreon (bonus materials + video chat): https://www.patreon.com/timothynguyen Part I. Introduction 00:00 : Preview 01:56 : Naturalism & Mathematical vs Moral Realism 05:34 : Outline of the Discussion Part II. Philosophy of Mathematics 13:25 : Mathematical Realism 18:36 : The Reality of Numbers 27:58 : Anti-Realist Positions in Mathematics 41:49 : Fictionalism in Mathematics 44:06 : Distinguishing Metaphysics from Epistemology 45:39 : The Role of Naturalism and Fictionalism Part III. Philosophy of Morality (vs Mathematics) 50:24 : Moral Realism and Anti-Realism 58:31 : Analogies Between Mathematical and Moral Realism 01:05:30 : Kant's Constructivism and Ethical Contextualism 01:10:40 : Error Theory in Ethics 01:16:02 : Mathematical Realism and Moral Anti-Realism 01:17:22 : Contextualism and Moral Realism Part IV. Select Topics from Justin's Book 01:19:11 : Justification and Self-Evidence 01:21:24 : The Practice of Axiomatization: Mathematics vs Ethics 01:24:51 : Pushback: Is there really controversy in math? 01:30:24 : Justification and Belief: Quinean Empiricism and Harman's Thesis 01:41:44 : Observations, Explanations, and Moral Facts 01:48:41 : Supervenience and High-Level Descriptions 02:00:43 : Justification vs Truth: Reliability Challenge in Mathematics and Morality 02:03:53 : 2+2 not equaling 4: Accidental Truth vs Truth per se 02:13:10 : Pluralism in Mathematics and Ethics 02:31:27 : Concluding Thoughts 02:32:49 : Correction: "relativism" should be "realism" Further reading: Justin Clarke-Doane. Morality and Mathematics. X: @iamtimnguyen Webpage: http://www.timothynguyen.org
