Justin Clarke-Doane | Mathematics, Reality, and Morality

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Dec 6, 2024

Justin Clarke-Doane, Columbia philosophy professor and author of Morality and Mathematics, explores parallels between mathematical and moral realism. He discusses whether math realism forces moral realism, compares anti-realist options, and examines justification, indispensability to science, and evolutionary reliability. Short, sharp conversations about foundations, pluralism, and how values guide action.

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ANECDOTE

Most Civilizations Didn't Axiomatize Geometry

Historical math practice rarely relied on axiomatization; Greek axiomatization was atypical and modern foundational concerns rose only in the 19th century.
Clarke-Doane notes many civilizations did advanced mathematics without Euclidean-style formal proof, so axioms are historically contingent.

ANECDOTE

Field Tried to Expunge Mathematical Entities

Hartry Field and Quine attempted a fictionalist program to remove mathematical entities, treating math as representational machinery replaceable within naturalism.
Field pursued a research program to reformulate science without Plato's beard, but Quine later reluctantly accepted Platonism as unavoidable.

INSIGHT

Moral Realism Mirrors Math Realism

Moral realism parallels mathematical realism: it claims independent moral facts (rightness, wrongness) exist that we can discover, not invent.
Normative topics (ethics, epistemology, logic) share the same structure: categorical facts versus context-sensitive or hypothetical norms.

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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