Horwich's minimalist theory of truth

Horwich's theory of truth is generated by all the unparadoxical instances of:

1. <s> is true if and only if s

together with the assumption that only propositions are true, where "<s>" is the proposition that s, for a sentence s. It is important that the schema (1) be defined purely syntactically. But it is not clear that this can be done. For consider this substitution instance of (1):

2. <This sentence is short> is true if and only if This sentence is short.

The problem, of course, is that the referent of "this sentence" in (2) is liable to be (2), rather than "This sentence is short", and hence we get the wrong truth value. (There is also a minor grammaticality worry because of the capital "T" in the middle of the sentence.) Or take this substitution instance of (1):

3. <A if and only if B> is true if and only if A if and only if B.

This doesn't say what it's intended to say. Fixing up is needed. But it is not clear that one can syntactically specify how the fixing up is to be done in all cases.

The truth of propositions

Suppose propositions exist, and truth is a property that some but not other propositions have. Could truth, then, be an intrinsic property of a true proposition? Observe that the proposition that George is round has truth if and only if George has roundness. Assuming (contrary to fact, but in order to simplify the example) that roundness is an intrinsic property, we now have a strange necessary coincidence between two different entities possessing intrinsic properties: necessarily, that George is round possesses truth if and only if George possesses roundness.

But the fact that necessarily x has an intrinsic property A if and only if a distinct entity y has an intrinsic property B surely calls out for, and had better have, an explanation. I am inclined to think that such correlations between the intrinsic properties of different individuals can only have a causal explanation. If so, then I think we have three options:

1. There is some third fact or entity z that both causes George to have roundness and the proposition that George is round to have truth.
2. George's having roundness causes the proposition that George is round to have truth.
3. That-George-is-round's having truth causes George to be round.

Somehow, none of these seem all that plausible to me, but if I were to choose between them and I were an atheist, I would opt for (2). If I thought that propositions were ideas in the mind of God, and I were choosing between these options, I might choose (3), and I might even further identify a proposition's having truth with that proposition's being known—that would yield Aquinas' claim that God's knowledge causes that which God knows.