However, the (post-linguistic-turn) philosophers would reduce explaining possible worlds to explaining the talk about possible worlds, which is nothing but the linguistic (or logicolinguistic) talk about words like necessary.
This move instantiated an undesirable ambiguity of the term meaning - we should now rather speak about meaningL, which is, in accordance with common sense, a matter of language alone, and about meaningW which is, in accordance with Frege, a matter of relating words to things5.
It follows from the considerations of Dummett (1974), that even if we consider that of the Fregean terms which is really closer to the intuitive concept of meaning, namely his Sinn (sense), we are likely to encounter a parallel ambiguity, for Fregean senses have come to be taken to play two incompatible roles: to explicate what a linguistic agent grasps when she grasps words, and to determine the corresponding Bedeutung, i.e. extension.
This seems to indicate that it is misguided to see the semantic analysis of language as a matter of pairing words and things; that it is more appropriate to see it as a matter of 'finding the position of the expression within the structure of language'.
An expression does have an inherent structure in that it consists of words and letters but this is not the structure held in mind by those who use the term structure to make sense of semantics.
What we do in explicating semantics of words and sentences via formulas and diagrams is not picturing extralinguistic things or concepts or structures purported to be the meanings of the expressions; we rather envisage the roles of the words and sentences within the structure (esp. inferential structure) of language13.
At the same time it is futile to see semantics as parasitic upon a psychology of language use. Semantics is primarily neither a matter of relating words with things, or of words with thoughts, it is a matter of displaying a certain kind of structure of language.
Frege and Wittgenstein also realized that the elements of language that are primarily significant are not words, but rather sentences, and that the discernment of the meanings of parts of a sentence is 'parasitic upon its structure' .
Hence a part-whole system can be considered as the ordered pair <U,<Oi> ∈I>where U is a set and each Oi is a (in general n partial) function from the Cartesian power U into U; in other words a part-whole system is a certain (partial) algebra.
In algebraic words, that the meaning-assignment is somehow induced by some kind of binary relations on the part-whole system of language.