Semantics: a coursebook, second edition
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82 (2) A B Which of the two pictures would more informatively be captioned: ‘part of the extension of the word cat’? A / B (3) Might the other picture appropriately be captioned: ‘the referent of “Jaime Lass’ present eldest cat”, uttered on January 1st 1983’? (Assume that there is someone named Jaime Lass who owned cats at that time.) Yes / No (4) Could the expression her cat, uttered on di fferent occasions with di fferent topics of conversation, have a number of di fferent referents? Yes / No (5) Would each object (each separate animal, that is) referred to by the expression her cat on separate occasions belong to the extension of the word cat? Yes / No (6) Could both pictures actually be labelled: ‘part of the extension of the word cat’ (though to do so might not immediately clarify the notions involved)? Yes / No Feedback (1) (2) B (3) Yes (4) Yes (5) Yes (6) Yes, since any individual cat belongs to the set of all cats. Comment The notions of reference and extension are clearly related, and are jointly opposed to the notion of sense. The relationship usually envisaged between sense, extension, and reference can be summarized thus: (1) A speaker’s knowledge of the sense of a predicate provides him with an idea of its extension. For example, the ‘dictionary de finition’ which the speaker accepts for cat can be used to decide what is a cat, and what is not, thus de fining implicitly the set of all cats. Some semanticists describe this relationship between sense and extension by saying that the sense of a predicate ‘ fixes’ the extension of that predicate. (2) The referent of a referring expression used in a particular utterance is an individual member of the extension of the predicate used in the expression; the context of the utterance usually helps the hearer to identify which particular member it is. For example, if any English speaker, in any U N I T 8 Words and things: extensions and prototypes 83 situation, hears the utterance ‘The cat’s stolen your pork chop’, he will think that some member of the set of cats has stolen his pork chop, and if, furthermore, the context of the utterance is his own household, which has just one cat, named Atkins, he will identify Atkins as the referent of ‘the cat’. Now we will consider further the idea that a speaker of a language in some sense knows the extensions of the predicates in that language, and uses this knowledge to refer correctly to things in the world. Practice (1) The cat I had as a child is long since dead and cremated, so that that particular cat now no longer exists. Is it possible to refer in conversation to the cat I had as a child? Yes / No (2) Does it follow that the extension of the predicate cat includes the cat I had as a child, which now no longer exists? Yes / No (3) New cats are coming into existence all the time. Does it seem reasonable to say that a speaker is continually updating his idea of the set of all cats, to include the newcomers? Yes / No (4) Or does it seem more reasonable to de fine extensions in such a way as to include objects in the future, as well as in the present and the past? Yes / No (5) Is it possible to refer to the cat which you may own one day in the distant future, a cat which does not yet exist? Yes / No Feedback (1) Yes (2) Yes (3) No (4) Yes (5) Yes Comment Since clearly one can refer to things which no longer exist and to things which do not yet exist, and since the notion of the extension of a predicate is de fined as a set of potential referents, we are forced to postulate that extensions are relative to all times, past, present, and future. Thus, the extension of window, for example, includes all past windows, all present windows, and all future windows. Similarly, the extension of dead includes all things which have been dead in the past (and presumably still are, if they still exist), which are dead now, and which will be dead in the future. Predicates are tenseless, i.e. unspeci fied for past, present, or future. In actual use, predicates are almost always accompanied in sentences by a marker of tense (past or present) or a future marker, such as will. These have the e ffect of restricting the extensions of the predicates they modify, so that, for example, the extension of the phrase is dead could be said to be the set of all things which are dead at the time of utterance. Correspondingly, the extension of the phrase is alive could be said to be the set of all things alive at the time of utterance. Thus the extensions of is dead and is alive are di fferent in the appropriate way at any particular time of utterance. This restricting of the extensions of predicates is an example of a more general fact. The extension of |