6 - Logic as a representation of meaning

Summary

CHAPTER PREVIEW

Logic is the study of the nature of valid inferences and reasoning. The logical tradition constitutes one of the major strands in the study of meaning, and some knowledge of its background is indispensable in linguistic semantics. In this chapter we will study some basic logical tools and concepts. Our aim is twofold:

• first, to understand the ways in which some types of meaning can be represented in logical symbolism

• second, to appreciate the advantages and disadvantages of this type of representation.

We begin by introducing the ideas of validity, soundness and logical form (6.1): these define the context and aims of a logical approach to language. In 6.2 we present an exposition of the basic principles of propositional logic, the logic of basic sentences, including a treatment of the principal logical operators: and, not, or and if… then In 6.3 we discuss the extent to which these logical concepts overlap with the meanings of their ordinary language equivalents. Section 6.4 introduces predicate logic, the logic of expressions like some and all In 6.5 we discuss the ways in which the concept of a model allows us to describe reference using logical techniques. Section 6.6 contains a discussion of the sentence relations of entailment, presupposition and contradiction This leads to a discussion of meaning postulates in Section 6.7, which use the sentence relations introduced in 6.6 as part of a non-decompositional approach to meaning. In 6.8 Russell's theory of descriptions is discussed.