In CSLDI I attempt to develop six arguments against philosophical naturalism. These arguments are
1) The argument from intentionality
2) The argument from truth
3) The argument from mental causation
4) The argument from the psychological relevance of logical laws
5) The argument from the unity of consciousness in rational inference
6) The argument from the reliability of our rational faculties
In a post found in October's archives at Maverick Philosopher, we find a response to my argument from truth. Is there a Place for Truth in the Naturalist's World. I wrote a response to Vallicella which I would like to include here:
You present an argument that a "sophisticated naturalist" ought to opt for the idea that truths are abstract states rather than mental states, something like Fregean Gedanken. Otherwise, the truth that P would fail to exist unless there were someone thinking P. If this argument goes through, then it severely cuts down the naturalist's options. Carrier, for example, will not be pleased; he really does think of truth as a correspondence between the brain and objects in the world. In Hasker's reply to me he claims that the naturalist should not be too worried about the AFT because of a Tarskian reply "P is true if and only if P" seems to be naturalistically acceptable. Perhaps Drange's argument on pp. 40-1 of the issue of Philosophia Christi is along the lines you are suggesting. He says
a) Only propositions can be true or false.
b) No propositions are states of a person.
c) Hence no states of a person can be true or false.
If this is true, then truth can exist in a naturalistic world, but, how those naturalistically conceived "truths" can possibly be relevant to the production of, say, states of the brain is going to be a serious problem for the naturalist. As I put it on p. 81 of my reply
"However, what this means is that whether or not those mental acts occur has nothing to do with the propositional content of the acts themselves, since those acts are governed by natural law, and what the laws of nature dictate has nothing to do with the propostional content of mental states (I should have added, especially if those propositional contents are conceived of as abstract states with no particular spatial location). so even if this is a possible reconciliation of propositional attitudes with naturalism, it has the disadvantage of making those mental states (I should have said the contents of those mental states) epiphenomenal, that is, without causal influence."
Hence the Drange-Vallicella response to the argument from truth, even if it works, is a poisoned pawn. It brings truth into a naturalistic universe, but makes it irrelevant to the actual occurrence of belief. This is going to be a serious problem if you are trying to argue, as naturalists are going to have to argue, that a creature's having true beliefs makes it more likely to survive and pass on its genes than those who believe falsehoods. Truth becomes irrelevant to the actual production of brain states, and hence invisible to evolutionary selection pressures.
Naturalists, therefore, may try to resist this analysis of truth-bearer in such a way as to make brain-states primary truth-bearers. Or come up with reductionist or redundancy analyses of truth that are not so ontologically expensive.