Cheng, Bryan and Read, James
(2025)
The Hole Argument and Putnam's Paradox.
[Preprint]
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Abstract
We discuss affinities and differences between (i) the hole argument in general relativity and (ii) Putnam's model-theoretic argument against metaphysical realism ('Putnam's paradox'). Following Pooley (2002), we maintain that the hole argument is not a special case of Putnam's paradox. This notwithstanding, 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. We compare these responses and assess the extent to which either is successful, concluding that we find van Fraassen's argument more persuasive precisely because of the greater generality of Putnam's paradox.
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