I’ve been rereading John Bigelow and Robert Pargetter’s “Science and Necessity”, which is full of good stuff. (Sadly, it isn’t in the Rutgers library, so it was a bit harder to read than it should have been.) They open with a defence of the correspondence theory of truth against various rivals. Much like I think the JTB theory of knowledge, and the “UnGettierized” JTB theory (as discussed “here”:http://twitter.com/AidanMcGlynn/status/5994795696) fail because of the paradoxes, I think the correspondence theory of truth fails for the same reason. I assume this isn’t a new point. (It is at least implicit in several arguments Roy Sorensen has made, for instance.) The problem is that (Co) is obviously true.

(Co) (Co) does not correspond to reality.

Assume (Co) corresponds to reality. Then it is true, assuming at least the correspondence theory. So it does not correspond to reality, assuming only the weaker version of the T-schema (that if p is true, then p). That contradicts our original assumption. So (Co) does not correspond to reality. And that’s what it says, so presumably it is true. (Though this step does require a p, therefore p is true inference, which some might find problematic.) So something that does not correspond to reality is true, contradicting the correspondence theory.

Bigelow and Pargetter, like many defenders of correspondence, focus primarily on various kinds of ‘anti-realist’ alternatives to the correspondence theory, such as coherentist and pragmatist theories. But I don’t think those are the major problems for the correspondence theory, or truthmaker like alternatives to correspondence. Rather, the paradoxes are the real problem.