Bryan Cheng

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.

What, if anything, would be wrong with replacing the light postulate in Einstein’s 1905 formulation of special relativity with a ‘sound postulate’, stating that the speed of sound is independent of the speed of the source? After reviewing the historical reasons underlying the particular focus on light in the special theory, we consider the circumstances under which such a theory of ‘sonic relativity’ would be justified on empirical grounds. We then consider the philosophical upshots of ‘sonic relativity’ for four contemporary areas of investigation in the philosophy of spacetime: global versus subsystem symmetries, dynamical versus geometrical approaches to spacetime, the possibility of a preferred frame in theories of quantum gravity, and spacetime functionalism.

We explore the significance of physical theories set in Euclidean spacetimes. In particular, we explore the use of these theories in contemporary physics at large, and the sense in which there can be a notion of temporal evolution in these theories. Having achieved these tasks, we proceed to reflect on the lessons that one can take from such theories for Knox’s ‘inertial frame’ version of spacetime functionalism, which seems to issue incorrect verdicts in the case of theories with Euclidean metrical structure.