Truth and grounding

Say that a proposition p is "grounded" provided that it has its truth value solely in virtue of reality being a certain way, i.e., of some fact about the existence/non-existence of entities and the possession/non-possession of properties/relations by entities, and the proposition is about reality being in this way.

Say that a proposition p is "extrinsically truthvalued" if and only if either p has truth as an extrinsic property or p has falsehood as an extrinsic property.

The following claims seem to me to be true:

1. A non-self-referential proposition is necessarily grounded iff it is necessarily extrinsically truthvalued.
2. Some non-self-referential propositions are necessarily grounded.
3. Some non-self-referential propositions are necessarily extrinsically truthvalued if and only if all non-self-referential propositions are necessarily extrinsically truthvalued.

It follows from the above claims that all non-self-referential propositions are necessarily grounded. Claim (2) seems the least controversial. Singular existential propositions are, clearly, necessarily grounded. Claim (3) is a claim that the truthvalue of a proposition is ontologically homogeneous across non-self-referential (nsr) propositions—either truth/falsity is always an extrinsic property of a nsr proposition, or it never is. This seems plausible to me.

Claim (1) seems the most controversial to me, but one direction is pretty plausible. If a nsr proposition p is grounded, then it holds or fails to hold in virtue of reality being a certain way, and is about reality being that way. Moreover "reality being that way" does not involve an intrinsic property of p, since if it did, then p would be self-referential. So, if a nsr proposition p is grounded, its truth/falsity is a matter of something extrinsic to p. What is most controversial, I think, is the claim that if truth is extrinsic to p, then p is true in virtue of some reality being a certain way. But even this claim seems to have signfiicant plausibility. If truth is extrinsic to p, then p is true in virtue of being related or not related to aspects of reality beyond p in some way. And it is rather plausible, then, to suppose that those aspects of reality are ones in virtue of which p is true and about which p is.