In Chapter 6, we introduced the idea that the extension of a noun, adjective or verb is the set of all entities to which it can be applied truthfully. For example, the extension of tree is the set of all entities of which we can truthfully say ‘x is a tree’, the extension of dead is the set of all entities of which we can truthfully say ‘x is dead’ and the extension of fell is the set of all entities of which we can truthfully say ‘x fells y’. We also introduced the idea that the intension of an expression is a set of semantic features associated with an expression, and that this set of features allows us to determine whether we can truthfully apply an expression to an entity or situation.

This idea can be extended to sentences: the meaning of a sentence is the set of situations to which we can apply it truthfully. Look at the sentence in (1):

We can apply this sentence to any situation where the following statements are true: ‘x fells y’, ‘x is called Zoe’ (remember the special nature of names), ‘y is a tree’ and ‘y is dead’. In this chapter, we will discuss how this idea can be used to investigate various aspects of sentence meaning.

In Section 8.2, we will introduce some terminology and a particular type of notation for comparing the truth values of different sentences in relation to each other. We will then use this notation to discuss a range of logical relations that can hold between sentences. For example, the sentence in (2), is true under exactly the same conditions as that in (1), while the sentence in (3) is true whenever (1) is false, and vice versa:

In Section 8.3, we will take a brief look at what happens to truth values if we connect sentences with conjunctions like and or or.

In Section 8.4, we will discuss the following phenomenon: even when we are using sentences in the simplest, most straightforward, direct way imaginable, we usually communicate much more than we actually say. For example, (1) says that a person named Zoe felled a dead tree, but in addition, it communicates the following:

Again, we will use truth tables to work out the relationship between what is said and what is communicated.

In Section 8.5, we will connect our discussion to the previous chapter and look at the way in which the meaning of sentences is built up from the meaning of individual words in parallel with the way in which the form of sentences is built up from individual words using phrase structure rules. For example, the NP dead tree is constructed using the phrase-structure rule [_NP [_AP [_A ]] [_N ]], which combines an adjective and a noun into a larger constituent. In a similar way, the meaning of the NP dead tree combines the meanings of the adjective and the noun into a larger unit of meaning — ‘x is a dead tree’ is true if both ‘x is a tree’ and ‘x is dead’ are true.

In Section 8.6, we will discuss cases where the meaning of a constituent or clause does not seem to be a combination of the meanings of the words occurring in it. Look at (5):

The meaning of this sentence is ‘Zoe keeps talking about something that has already been discussed to everybody else’s satisfaction’. Thus it is not true if the following are true: ‘x beats y’, ‘x is an entity called Zoe’, ‘y is a horse’ and ‘y is dead’. Such so-called idioms are a common feature of human languages and must be accounted for by a semantic theory.

 

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CC-BY-NC-SA 4.0, Written by Anatol Stefanowitsch