Abstract
We revisit Putnam’s constructivization argument from his Models and Reality, part of his model-theoretic argument against metaphysical realism. We set out how it was initially put, the commentary and criticisms, and how it can be specifically seen and cast, respecting its underlying logic and in light of Putnam’s contributions to mathematical logic.
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Notes
- 1.
The permutation argument is another model-theoretic argument from Putnam (1980); any theory with a model has multiple distinct yet isomorphic models given by permuting elements, and so there is a fundamental semantic indeterminacy.
- 2.
Sets of integers are routinely identifiable with, and called, reals, but we stick with the thematic trajectory here for a while.
- 3.
In fact, this holds, by a straightforward modification of his argument, for any \(\gamma < \omega _1^L\).
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Kanamori, A. (2018). Putnam’s Constructivization Argument. In: Hellman, G., Cook, R. (eds) Hilary Putnam on Logic and Mathematics. Outstanding Contributions to Logic, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-96274-0_13
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