Language is a very complex system. In earlier chapters we have studied a variety of factors that affect how hearers will interpret the meanings of sentences: lexical ambiguity, vagueness, figurative and other coerced senses, implicatures and other pragmatic inferences, knowledge about the world, etc. In order to make progress in understanding how compositionality works, the Model Theory approach attempts to isolate the rules for combining word meanings from these other complicating factors. This same basic strategy is adopted in many other fields of research as well. For example, if medical researchers are investigating genetic factors which may contribute to heart disease or diabetes, they will do everything possible to control for other contributing factors such as diet, age, exercise, lifestyle, environmental factors, etc. The specification of a test situation in terms of an explicit model, as illustrated below, within which the rule system can be tested, is a way of controlling for lexical ambiguity, vagueness, incomplete knowledge about the world, etc.
A model must specify two things: first, the set of all individual entities in the situation; and second, the denotations of the basic vocabulary items of the language, at least those that occur in the expressions being analyzed. This would include words which function as predicates (verbs, adjectives, and common nouns), and proper names, but not non-denoting words like not, and, if, etc. Our semantic analysis can then be stated in terms of rules of interpretation, which will specify the denotation of complex expressions formed by combining these vocabulary items according to the syntactic rules of the language.
As a preliminary example, imagine a very simple situation which contains just three individuals: King Henry VIII, Anne Boleyn, and Thomas More. Our model of this situation would include the listing of these individuals, plus the denotation sets for the content words available for use. Let us begin with a limited vocabulary consisting of just three proper names (Henry, Anne, and Thomas) plus three predicate words: snore, man, and woman. The denotation set for man would include Henry VIII and Thomas More. The denotation set for woman would include just Anne Boleyn. Let’s assume that King Henry VIII is the only person in this situation who snores; then he would be the only member of the denotation set for snore. The denotation of the proper name Thomas would be the individual Thomas More, etc.
In Chapter 12 we stated a rule of interpretation for simple sentences: the proposition expressed by a (declarative) sentence will be true if and only if the referent of the subject NP is a member of the denotation set of the VP. We can use this rule to evaluate sentence (1a) relative to the situation described by the model we have just constructed. The rule says that the sentence will be true if and only if the individual named Henry (i.e., King Henry VIII) is a member of the denotation set of snore. Since this is true in our model, the sentence is true relative to this model. The same rule of interpretation allows us to determine that sentence (1b) is false relative to this model. In Chapter 14 we will discuss additional rules that will allow us to evaluate (1c), which is false relative to this model, and (1d), which is true relative to this model.
(1) a. Henry snores.
b. Anne snores.
c. All men snore.
d. No women snore.
Notice that this approach seeks to provide an account for compositional meaning, but not for the meanings (i.e., senses) of individual content words. In other words, Model Theory does not try to represent the process by which speakers of English determine that King Henry VIII would be referred to as a man and Anne Boleyn would be referred to as a woman, etc. We simply start with a model which specifies the denotation sets for content words. In adopting this approach, we are not denying the important role that word senses play in our use of language, or treating word meanings as a trivial issue that can be taken for granted. In fact, accounting for word meanings is a very complex and difficult undertaking, as our earlier discussions of the issue have demonstrated. Rather, the Model Theory approach assumes that it is possible to make progress in understanding compositionality without solving all of the difficult questions surrounding word meanings; and this strategy has proven to be extremely successful and productive.
As we have already hinted, the rules of interpretation which we formulate will be stated in terms of set membership and relations between sets. For that reason, before we proceed with our discussion of compositionality, we need to introduce some of the basic terminology and notation used for speaking about sets.
