Logical Dependence of Physical Determinism on Set-theoretic Metatheory
Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. I argue that this is doubtful once determinism is read the way it is used in physics. At the analytic layer, determinism verdicts for possible systems can differ between canonical extensions of ZFC -- Goedel's Axiom of Constructibility (V=L) and large cardinal assumptions sufficient for Projective Determinacy (LC/PD) -- through coherence, uniqueness, and the identity of a definable initial datum. The main claim concerns a second, regularity layer. Determinism claims are meant to withstand admissible changes of gauge, mesh, coarse graining, and readout, and they are stated as claims about generic or almost sure behavior. Robust profiles of this kind land at the Sigma^1_2 level, the first level of the projective hierarchy at which regularity can fail in V=L while holding under LC/PD. Two unconditional theorems are proved. First, a fixed computable nearest neighbor Ising Hamiltonian on Z^3 with a fixed zero temperature Glauber schedule yields a Sigma^1_2-complete tail-readout profile in which only the initial microstate varies. Second, at the Kerr Cauchy horizon, canonicalizing continuous extension germs in a fixed collar contains E_0, so no universally measurable rule solves it in ZFC, while V=L supplies a projectively definable rule and PD forbids any projective one. I call the systematic study of such dependence reverse physics, on analogy with Friedman's and Simpson's reverse mathematics. One upshot is a dilemma: either physical theories must be relativized to foundational frameworks, as Carnap held for mathematics, or, with Quine, the search for new axioms is continuous with the search for new physical laws.