Page 125 - Encyclopedia of Philosophy of Language

two. The formulation also assumes that the syntactic rules determine what the parts are, whereas the first formulation only assumes structures, no matter how they are given. The formulation regards the syntax as the input for meaning assignment, and the principle then describes how the meanings are projected from this input.
It is instructive to look at these assumptions in the light of a grammatical theory like generativeseman- tics. This theory distinguishes two structural levels, one called 'semantic' and the other 'surface.' The grammar or syntax consists of formation rules for the semantic structures and a gradual transformational mapping procedure between semantic and surface structures. Here the syntactic form is projected from the meanings, and the semantic structures provide the compositional framework for a calculus producing meanings. Under certain assumptions this process is in accordance with the first formulation of the prin- ciple of compositionality of meaning, but not with the formulation given in this section.
2. Interpretation of Compositionality
The interpretation of the principle of compositionality provided in Montague Grammar (and in other forms of logical grammar as well) is an application of the essential methods of formal logic to the study of natural language semantics (for a more extensive dis- cussion, see Gamut 1991; Janssen 1997). The main features are the following.
2.1 Rule-to-rule Correspondence
The syntax contains several rules and thus provides several ways to form a compound from parts. Each of these possibilities may have its own semantic effect. Therefore, for each syntactic rule there is a cor- responding semantic function expressing the semantic effect of that rule, i.e., for each syntactic rule there is a corresponding semantic rule. This is known as the rule-to-rule correspondence. This correspondence asks for a uniform method to obtain the meaning of the resulting expression. It does not, however, imply that each syntactic rule should produce a change in meaning: the semantic rule corresponding with a syn- tactic rule can be the semantic identity function. Nei- ther does it imply that every detail of a syntactic rule has a semantic counterpart. For instance, in English, the rule for yes-no question formation as well as cer- tain other constructs involves Subject-Aux inversion. This inversion occurs in some rules of syntax, yet it does not seem to have any semantic effects. One might use a terminology in which such operations are called 'subroutines' of rules.
2.2 'Part' is a Theoretical Concept
The principle of compositionality speaks about the parts of an expression, which implies that it has to be determined somehow what these parts are. As it is
the syntax which provides the rules for the formal construction of expressions we shall let the syntax determine what the parts of an expression are. Differ- ent syntactic theories may assign different structures. Consider, for example, the English sentence Mary does not cry. A grammar might distinguish the main constituents Mary and does not cry, but it may also impose a tripartite structure consisting of Mary, does not and cry. A theory might also neglect constituents, focusing on logical aspects, and have a negation rule that takes the positive sentence Mary cries as its one- part input. This means that 'part' is a technical notion, that only coincides with intuitions for certain kinds of rules, to which one may wish to restrict the theory.
Parts of sentences may have parts themselves, and so on. Usually this analysis stops at the level of words or word stems. In logical grammar, lexical words such as love or know are left unanalyzed and considered to correspond with semantic primitives. Words like all and only, on the other hand, are analyzed further in the semantics with the help of logical tools.
2.3 Parts Have Meanings
The principle presupposes that parts have meanings. This excludes approaches in which only complete sen- tences can be semantically interpreted. More to the point, the principle requires that all expressions arising as structural parts have an independently given mean- ing. For some structural parts it is easy to imagine intuitively what their meaning specification should be. A verb phrase like loves Mary, for example, is immedi- ately interpretable on an intuitive level. Not all parts, however,haveasemanticinterpretationthatisreadily supported by intuition. Constituents like only Mary, for example, in the sentence John loves only Mary, or whether John comes in Mary knows whether John comes, seem less readily interpretable on purely intuit- ive grounds. But compositionality requires that we choose a meaning. The criterion for such a choice is then whether the meaning is a suitable ingredient for building the meaning of the whole expression.
2.4 The Role of Derivational History
The meaning of an expression is determined by the way in which it is formed from parts. The derivational history of an expression is, therefore, the input to the process of determining its meaning. Since the com- positionality principle, based on such part-whole relations, is taken to give a complete characterization of how the meaning of an expression is computed, there is no other input to the process of meaning assignment than the derivational history of the sen- tence in question. No outside factors are allowed to have an effect on the meaning of a sentence. This applies for instance to contextual factors: the Mon- tagovian perspective does not allow for any kind of 'discourse' input to the compositional calculus deter- mining the meaning of an expression. The most it
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