Cheng, Bryan and Read, James
(2024)
The Hole Argument and Putnam's Paradox.
[Preprint]
Abstract
We discuss connections and differences between the hole argument in general relativity on the one hand, and Putnam's model-theoretic argument against metaphysical realism (`Putnam's paradox') on the other. Both arguments identify means by which objects in theories fail to correspond uniquely to metaphysical content in the world, and thereby motivate anti-realism about certain structure. We object to claims that the hole argument is a specific case of Putnam's paradox, because (following Pooley (2002)) the latter underwrites a more pervasive failure of correspondence than the former. Both of these arguments have been responded to through meta-linguistic means---while van Fraassen (1997) claims that Putnam’s paradox dissolves due to our inability to identify a function mapping our theories to objects in the world independent of our total language, Bradley and Weatherall (2022) maintain that the language of general relativity does not allow for the hole argument to be formulated. In the latter sections of this article, we compare these responses and assess the extent to which either is successful.
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