Central among these concepts, according to Davidson (1999), is the concept of truth.
A concept, Frege (1892b) argued, is, as a rule, something under which a given object may or may not fall; hence it is a way of classifying objects into two groups (those falling under it and those not falling under it); and so it can be identified with a function mapping objects on the two truth values – truth and falsity.
Hence a predicate can be seen as mapping names onto sentences and, on the semantic level, referents of names, i.e. objects, on the truth values of sentences.
The central theme of semanticsL is meaning, and consequently also analytic truth (for analytic truth is "truth in virtue of meaning").
The central theme of semanticsW is (contingent) truth, and consequently reference (for reference is what is needed to compositionally yield truth).
And it must be noted that I say of our reason, and not of our imagination or of our senses: thus, for example, although we very clearly see the sun, we ought not therefore to determine that it is only of the size which our sense of sight presents; and we may very distinctly imagine the head of a lion joined to the body of a goat, without being therefore shut up to the conclusion that a chimaera exists; for it is not a dictate of reason that what we thus see or imagine is in reality existent; but it plainly tells us that all our ideas or notions contain in them some truth; for otherwise it could not be that God, who is wholly perfect and veracious, should have placed them in us. And because our reasonings are never so clear or so complete during sleep as when we are awake, although sometimes the acts of our imagination are then as lively and distinct, if not more so than in our waking moments, reason further dictates that, since all our thoughts cannot be true because of our partial imperfection, those possessing truth must infallibly be found in the experience of our waking moments rather than in that of our dreams.
If the rules which we consider are the rules of syntax (i.e. if they provide for the criterial reconstruction of well-formedness), then the resulting categories are known as syntactic categories (they express the expressions' behaviour from the viewpoint of constituting well-formed expressions and statements); if they are the rules of semantics (i.e. if they amount to truth, assertibility, or use in general), then the categories are meanings (they express the expressions' behaviour from the viewpoint of truth, or, more generally, from the viewpoint of their employability within language games).
For, in fine, whether awake or asleep, we ought never to allow ourselves to be persuaded of the truth of anything unless on the evidence of our reason.
For if it happened that an individual, even when asleep, had some very distinct idea, as, for example, if a geometer should discover some new demonstration, the circumstance of his being asleep would not militate against its truth; and as for the most ordinary error of our dreams, which consists in their representing to us various objects in the same way as our external senses, this is not prejudicial, since it leads us very properly to suspect the truth of the ideas of sense; for we are not infrequently deceived in the same manner when awake; as when persons in the jaundice see all objects yellow, or when the stars or bodies at a great distance appear to us much smaller than they are.
But after the knowledge of God and of the soul has rendered us certain of this rule, we can easily understand that the truth of the thoughts we experience when awake, ought not in the slightest degree to be called in question on account of the illusions of our dreams.