Reference

7. Other terms

Many terms that we have not discussed – like adjectives, adverbs and verbs – are naturally taken to refer. It is certainly no easier to explain reference for these terms than for the terms discussed, but we may hope that doing so will not pose sharply different problems (see Adverbs; Predication).

We must also consider sentential operators like ‘and’ and ‘not’, and quantifiers like ‘every pen’, ‘some stones’, ‘most dogs’ and ‘few bachelors’. Perhaps these should be seen as largely syncategorematic (see Logical constants; Quantifiers). If we are prepared to accept the existence of certain abstract entities, however, we can take these expressions as referential also. Thus we can take ‘and’ as denoting a ‘truth function’ conjunction which is such that the sentence ‘p and q’ is true if and only if ‘p’ is true and ‘q’ is true. The quantifiers involve a ‘determiner’ and a general term, and can be taken as applying to sets. Thus ‘most dogs’ involves the determiner ‘most’ and the general term ‘dogs’ and can be taken as applying to any set that contains more than half the dogs; and the sentence ‘most dogs bark’ is true if and only if there is such a set and ‘bark’ applies to all its members.

In virtue of what do these expressions have these referents? The most promising answer for the sentential operators has two stages. We start by describing the ‘conceptual role’ of the operator in deductive, inductive and practical inferences. For a token to denote ‘conjunction’ it must have the appropriate conceptual role. But in virtue of what should we assign to a token with that role the denotation ‘conjunction’ rather than, say, ‘disjunction’? Because, under that assignment, deductive inferences are truth-preserving, inductive inferences are reliable, and so on. A similar line is presumably part of the answer for the quantifiers: ‘most dogs’ applies to any set containing most dogs (rather than, say, to any set containing a few cats) partly because of the reference of ‘dogs’ and partly because of the conceptual role of the determiner ‘most’ and the reliability of inferences. A worrying feature of both these answers is that they seem to make widespread irrationality impossible (see Semantics, conceptual role).

Finally, we must consider anaphoric terms. Pronouns, and even definite descriptions, often depend for their reference on other expressions in their verbal context. Thus ‘one’ in ‘John owns a car and Alice owns one too’ is (using Geach’s term) a ‘pronoun of laziness’, going proxy for the noun phrase ‘a car’ in the preceding conjunct. And consider ‘he’ in ‘John is happiest when he is alone’ and in ‘Every man knows a woman that he admires’. In the former sentence ‘he’ is naturally seen as coreferential with ‘John’, in the latter as ‘bound by’ the quantifier ‘every man’ and so functioning like a bound variable in logic.

Geach (1962) has argued that all anaphoric pronouns are either pronouns of laziness or bound by quantifier antecedents. Against this Evans (1985) has argued that some pronouns with quantifier antecedents are unbound. He calls these ‘E-type’. (a) Consider:

If ‘they’ were bound by ‘few congressmen’, (9) should mean that few congressmen both admire the president and are very junior. But it does not. The first clause of (9) entails that few congressmen admire the president; the second that all of those who do admire him are very junior. (b) If ‘they’ were bound in (9), then we should be able to substitute any quantifier for ‘few congressmen’ and still make sense. But ‘No congressmen admire the president, and they are very junior’ does not make sense. (c) Last, consider:

The quantifier ‘many men’ could bind ‘them’ only if (10) meant ‘Many men are such that if they come to the ball Mary will dance with them’, which is not the natural reading. As a result of these considerations and others – particularly pronouns in one person’s sentence that are anaphoric on quantifiers in another person’s – it is generally agreed that Evans has identified a distinct type of pronoun.

However, Evans’ view of this type has been challenged. He thinks that the reference of such a pronoun is determined in a Russellian way by a definite description that can be derived from its quantified antecedent; thus, the reference of ‘they’ in (9) is determined by ‘the few congressmen who admire the president’, and that of ‘them’ in (10) by ‘the many men who come to the ball’. Because these are definite descriptions, for (9) to be true all the Kennedy admirers must be junior, and for (10) to be true Mary must dance with all the men who come. This consequence does not seem to generalize. ‘Some congressmen admire the president, and they are very junior’ seems to be compatible with some other congressmen admiring him and not being very junior. The problem is more acute in singular cases: ‘Socrates owned a dog and it bit him’ seems to be compatible with Socrates owning another dog which did not bite him. Finally, there are the formidably difficult ‘donkey sentences’: ‘Every man that owns a donkey beats it’ and ‘If John owns a donkey, he beats it’. On one reading, these sentences concern not simply the unique donkey of each donkey owner but all the owner’s donkeys (see Anaphora).