In this dissertation I offer my objections to three famous arguments concerning the mindbody problem.

The first argument is Saul Kripke’s (1980) modal argument against psychophysical identity theory. Kripke argues that if pain is identical to C-fibre firing then this identity must be necessary. However he points out that the identity is, if true, also a posteriori, and he argues that this alleged a posteriori identity cannot be accounted for in the way that scientific a posteriori identities are accounted for. He concludes on this basis that pain cannot be identical to C-fibre firing, and, more generally, that alleged psychophysical identities are false.

The second argument is David Chalmers’ (1996) ‘zombie’ argument against materialism. Chalmers argues that zombies are conceivable, that the conceivability of zombies entails the possibility of zombies, and that the possibility of zombies is inconsistent with the truth of materialism. He concludes that materialism is false.

I show that these arguments both share the same logical form—a form distinctive of what I call a ‘conceivability argument’. I show that for any such conceivability argument, C, there is a corresponding ‘mirror argument’ that is deductively valid and has a conclusion contradicting C’s conclusion. I show that a proponent of C can challenge the premises of the mirror argument only at the cost of undermining C’s premises. I conclude on this basis that conceivability arguments are fallacious in general, and, more particularly, that both Kripke’s modal argument and Chalmers’ zombie argument are unsound. This critique of these two arguments constitutes the first part of the dissertation.

The second part is devoted to Hillary Putnam’s (1967) multiple realisability argument against identity theory. Putnam argues that if human pain is a neural firing pattern in the brain, then octopus pain will likewise be identical to some physical state of the octopus— say, an excitation pattern in the jelly-ish tissue of the octopus brain. But while human pain and octopus pain feel alike, neural firing and jelly excitation are not alike. It follows from standard logic that human pain is not identical to neural firing patterns.

In reply, I attempt to reconcile identity theory with multiple realisability by advocating a semantics in which identity statements involving vague terms such as ‘pain’ are indeterminate. I develop a non-classical axiomatic theory of indeterminate identity relations, which implies that indeterminate identities are non-transitive. I also show that the principle of the transitivity of identity is a vital inference rule in Putnam’s argument. If my analysis is correct then Putnam’s argument is invalid.