The Hole Argument and Putnam’s Paradox

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 (The Reality of Spacetime, University of Oxford, 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 (Philosophical Perspectives 11:17–42, 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 (Philosophy of Science 89(5): 1223–1232, 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.