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It's currently fashionable to take Putnamian model theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. But I will argue that (under certain mild assumptions) merely securing determinate reference to physical possibility suffices to rule out nonstandard models of our talk of numbers. So anyone who accepts realist reference to physical possibility should not reject reference to the standard model of the natural numbers on Putnamian model theoretic grounds.
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References found in this work BETA
Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics.Tim Button & Sean Walsh - 2016 - Philosophia Mathematica 24 (3):283-307.
A Metasemantic Challenge for Mathematical Determinacy.Jared Warren & Daniel Waxman - 2020 - Synthese 197 (2):477-495.
Which Undecidable Mathematical Sentences Have Determinate Truth Values.Hartry Field - 1998 - In H. G. Dales & Gianluigi Oliveri (eds.), Truth in Mathematics. Oxford University Press, Usa. pp. 291--310.
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