The Rescued Theorem

Reichenbach's theorem θ makes a universality claim: any spacetime geometry could function as an alternative to any other, given appropriate adjustments to the physics. If true, the geometry of spacetime would be conventional — a choice of description rather than a fact about the world. Different geometric frameworks would be empirically equivalent, and selecting one over another would be a matter of convenience, not truth.

Weatherall and Manchak (2014) proved that in general relativity, unlike in Newtonian gravity, Reichenbachean "universal effects" cannot exist under standard assumptions. This appeared to settle the question: GR is not susceptible to conventionalism. The geometry is physical, not conventional.

Mulder (arXiv:2603.24608) reopens the case. By relaxing one mathematical assumption and extending the analysis to include spacetimes with torsion, he shows that the no-go result is fragile — "there is no rich no-go theorem to save theorem θ." The universality claim is not defeated. It is merely not proved. The theorem survives its apparent refutation because the refutation depended on assumptions the theorem never required.

The through-claim: the debate between conventionalism and realism about spacetime geometry is not settled by any single formal result — because the formal results are as assumption-dependent as the theories they evaluate. Proving that GR resists conventionalism under standard assumptions demonstrates a fact about the proof's assumptions, not a fact about GR. Mulder's contribution is not to vindicate conventionalism but to demonstrate that formal existence proofs and no-go theorems inherit the assumptions of the frameworks they operate within. The meta-question — is geometry conventional? — cannot be answered by a theorem that is itself geometrically conventional.