There are good reasons to introduce facts as truth-makers for contingently true atomic sentences. (Some supporting reasoning here.) But if there are facts, and they make-true contingent atomic sentences, then what is the semantic relation between these declarative sentences and their truth-makers? It seems we should say that such sentences name facts. But some remarks of Leo Mollica suggest that this will lead to trouble. Consider this aporetic triad:
1. 'Al is fat' is the name of the fact of Al's being fat.
2. 'Al is fat' has a referent only if it is true.
3. Names are essentially names: a name names whether or not it has a referent.
Each limb of the triad is very plausible, but they can't all be true. The conjunction of (1) and (3) entails the negation of (2). Which limb should we abandon? It cannot be (1) given the cogency of the Truth Maker Argument and the plausible assumption that the only semantic relation between a sentence and the corresponding fact is one of naming.
(2) also seems 'ungiveupable.' There are false sentences, and there may be false (Fregean) propositions: but a fact is not a truth-bearer but a truth-maker. It is very hard to swallow the notion that there are 'false' or nonobtaining facts. If 'Al is fat' is false it is because Al and fatness do not form a fact. The existence of a fact is the unity of its constituents. Where there is the unity of the right sort of constituents you have a fact; where there is not, you don't.
As for (3), suppose that names are only accidentally names, than a name names only on condition that it have a referent. We would then have to conclude that if the bearer of a name ceases to exist, that the name ceases to be a name. And that seems wrong. When Le Verrier put forth the hypothesis of an intra-Mercurial planent that came to be called 'Vulcan,' he did not know whether there was indeed such a planet, but he thought he had good evidence of its existence. When it was later decided that there was no good evidence of the planet in question, 'Vulcan' did not cease to be a name. If we now say, truly, that Vlucan does not exist we employ a name whose naming is not exhausted by its having a referent.
So it seems that names name essentially. This is the linguistic analog of intentionality: one cannot just think; if one thinks, then necessarily one thinks of something, something that may or may not exist. If I am thinking of something, and it ceases to exist, my thinking does not cease to be object-directed. Thinking is essentially object-directed. Analogously, names are essentially names.
So far, then, today's triad looks to be another addition the list of insolubilia. The limbs of the triad are more reasonably accepted than rejected, but they cannot all be true. A pretty pickle.
By the way, I insist on the primacy of the intentional over the linguistic.