Pluralism in mathematics: the multiverse view

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.

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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.

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Webpage: http://www.timothynguyen.org