Reverse Physics: Set Theory, Determinism

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.