This argument is a dilemma, of which I will only give the first horn today. First we need two definitions. Say that a property is "Natural" provided that it either occurs in a correct scientific account of the world or else can be constructed, in a finite number of steps, from ingredients that occur in correct scientific accounts of the world. Say that two properties A and B are "nomically coextensive" provided that in any world that has the same laws as our world, the two properties have the same extension (i.e., are had by the same particulars). Finally, "Truth" shall be the property that an utterance (a token of a sentence) has in virtue of being true.
Suppose naturalism is true. The dilemma is this: Either Truth is nomically coextensive with a Natural property or it is not.
Horn 1: Truth is not nomically coextensive with any Natural property.
There are now two kinds of problems for the naturalist. The first is the question of how we got to have the concept of Truth. A naive account of concept formation is that we observe particulars, and then from these particulars we abstract the simplest, i.e., most natural (in Lewis's sense), properties that these particulars have in common. Thus, we observe a bunch of massive objects, and the simplest property they all have in common is Mass, and so we form the concept of mass. This naive account may need to be modified in various ways. For instance, perhaps we do not need to make all the observations ourselves—our cultural or even genetic forebears might have made some of them. We might not always opt for the very simplest property that the particulars have in common, as there may be explanatory constraints on the properties beside simplicity. Thus, we might from a bunch of particulars extract not just the simplest property that they have in common, but the simplest property that they have in common which explains some common phenomenon (such as the phenomenon of being observed by us in a particular way). Furthermore, given a bunch of concepts abstracted from particulars, we can form new concepts through various combinations. Further modifications are needed to take care of determinables (like mass of x grams).
But however we modify it, I think the following will hold: If naturalism holds, we will only ever arrive at concepts of Natural properties. It is only Natural properties that enter into genuine explanations or that are causally efficacious if naturalism holds, after all. And the simplest property that a bunch of instances has in common will never be a non-Natural property, since, given naturalism, a non-Natural property is either not at all a natural property (in Lewis's sense) or is formed as an infinitely describable combination of natural properties. But if we can only ever arrive at concepts of Natural properties, and Truth is not one of those (since it's not nomically coextensive to one of those) then we do not have the concept of Truth.
The second problem is that if Truth is not nomically coextensive with a Natural property, none of our cognitive faculties could have been evolutionarily selected for truth. (Here I am sliding a bit between Truth as a property of utterances and truth as a property of belief-tokens. But just about all I say about utterances holds for belief-tokens, too.) For only Natural properties stand in causal relations if naturalism holds, and only properties that stand in causal relations occur in evolutionary explanations. But it seems to be at least partly definitory of our doxastic faculties that they are for the sake of truth. A part of what distinguishes a belief from a desire, for instance, is that a belief is something that ought only occur when it is true. If Truth is not Natural, and if naturalism holds, then our doxastic faculties do not have this normativity, and we do not have beliefs at all (including the belief in naturalism).
Moreover, if Truth is not nomically coextensive with a Natural property, not only will it fail to be the case that our doxastic faculties are selected for generating correct beliefs, but neither will there be another evolutionary explanation, say using exaptation, of any truth-tendency in our beliefs. For all scientific explanations are of the possession of Natural properties or at best (and I am sceptical of this) of the possession of properties nomically coextensive with Natural ones. But then scepticism threatens, as in Plantinga's argument.
One might hold, however, that while Truth simpliciter is not nomically coextensive with a Natural property, Truth in some limited realm, such as the truth of simple claims about mastodons and potatoes is nomically coextensive with a Natural property (the argument in the second horn of the dilemma will not contradict this). Fine. But the belief in naturalism will not fall within this limited realm. Hence the belief in naturalism still undercuts itself.
Tomorrow, we'll look at the second horn.