| Course Description |
Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In
this seminar, we will see that they are not. Whether a physical theory is deterministic—whether
it fixes a unique future given the present—can depend on one’s stance on axioms of set theory
about which there is intractable disagreement. This is not a quirk of exotic toy models. It reaches
into the heat equation, quantum mechanics, statistical mechanics, and general relativity. The
seminar builds from the ground up. We begin with the philosophy of determinism: what it
means, why it matters, and how it has traditionally been formalized. We then develop enough set
theory and descriptive set theory to state the key results precisely. In the second half, we work
through the sensitivity results in detail, showing how the content of fundamental physical
theories shifts with the set-theoretic background. We conclude by asking what this means for
debates about mathematical pluralism, scientific realism, and the boundary between mathematics
and physics.
No prior knowledge of set theory or mathematical physics is assumed. The seminar is open to
graduate students in philosophy and, with permission, to advanced graduate students in
mathematics, physics, and related fields.
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