The Metamathematics of Putnam’s Model-Theoretic Arguments
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Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges.
KeywordsCompleteness Theorem Transitive Model Metaphysical Realist Correspondence Relation Constructivisation Argument
I wish to thank Timothy Bays, Michael Potter and Peter Smith for patient suggestions, advice, and comments. I particularly want to thank Gerald Sacks, who taught me model theory, with whom I had many engaging discussions, and without whom I would probably have no proof of the Submodel Skolem Theorem.
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