It can be doubted whether the idea of formal semantics arising from
Gottlob Frege's work makes any sense at all. Meaning, as it is ordinarily
understood, is clearly distinct from abstract representations of
meaningful utterances. To clarify some basic points these constructions
may, however, serve as a useful starting point. What is a sign? We already
characterized it as something pointing to, or standing for, or
representing, something else in an orderly fashion. It seems natural to
assume that such relations can be described systematically. ,,Model
theory''
is a completely abstract way of doing this, building up an increasingly
complex structure starting with interpretations of signs that are not
considered to be complex (elementary things) and moving on to
configurations of signs, presenting configurations of things in a formally
suitable way.
It is not necessary to go into the details of this approach
in order to discuss several presuppositions exhibited by this approach.
Let me explain some implications of the underlying picture.
Perhaps the most fundamental assumption is this: something serving as a sign is not regarded simply by itself, as an element of syntax. It is incorporated into a semantical relation that can be understood as directing attention away from the given inscription, drawing it to something else, its semantical value. Such values (entities, relations, truth) are readily defined in formal semantics and as a consequence little emphasis is normally put on the fact that they are constructs of a special kind, not on the same level with syntactic marks. Nevertheless it is commonly conceded that a qualitative jump separates concatenations of inscriptions from the ,,meanings'' they represent ,,under an interpretation.'' Theoretical ideality marks the realm of the signified in any semantical theory worth its name.
Now, if we follow our intuition that words have meaning we seem committed to an explanation of where they get it from. There is considerable theoretical disagreement about how to proceed at this point, but one fundamental move cannot be in dispute, since it establishes the semantical enterprise itself, namely starting from a split, introducing two different kinds of entities before proceeding to interrelate them systematically. Formally speaking, variables, constants and terms refer to something; well formed formulae are satisfied by sets, and sentences characterize models. This structural pattern should not distract attention away from the fact that a certain tension between presence (of the signifier) and absence (of the signified) lies at the heart of this analytical account. Can such a gap be allowed to stand at the beginning of a discipline? Mustn't it be retracted immediately because it would be impossible to explain the interrelation of the components of the scheme? Consider formal languages designed to refer to mathematical structures that are supposed to have a certain existence of their own. On the one hand, they are conceptually separated from their reference, on the other hand, exactly the same language of set theory is used to introduce the elements of both the system of signification and of the signified. It is in fact by assuming a common logical structure that the split is made to work as an inducement to bridging the gap. This can be generalized.
A sign enacts an essential distinction of realms, but it cannot function without the possibility of their fusion either. If semantics does not simply occupy itself with empirical investigations it has to reflect on this apparent contradiction. The essentials of this situation are a double perspective and a unifying overview, the relata of the procedure of interpretation on the one hand and its underlying logic on the other. In model theory the interchange between presence and absence that constitutes a signifying unit is couched in prescriptive mathematical meta-language. Thus the difficulty of having to explain how two domains, per definition separate, can function as a whole is avoided. From this perspective they are not at all unrelated to each other, since they form part of a more inclusive pattern, held together by the rigor of a formal discipline. But this explanation obviously fails when metaphysical, epistemological and deconstructionist questions are raised.