Baker’s Rocketship and the Mathematical Nominalist’s Real Problem with Physical Magnitudes

Nominalists face classic Quine-Putnam indispensability worries about how to logically regiment physical magnitude statements. Measurement-theoretic uniqueness theorems offer a popular tool for answering this challenge, by showing that the application of finitely many atomic relations between non-mathematical objects can pin down unique intended values for Platonist physical magnitude functions. However, recent discussions of Baker’s rocketship argument for absolutism about physical magnitudes raise a prima facie worry—that such nominalist paraphrases can only express comparativist friendly content, and therefore cannot capture the intuitive determinism of Newtonian mechanics. In this paper, I’ll develop that worry and argue that even nominalists who accept Baker’s premises and argument can address it by adjusting traditional nominalist paraphrases to employ absolutist physical magnitude predicates taken to be rigid designators that fix absolute scale without reference to mathematical objects.