Semantics: a coursebook, second edition
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84 a combination of several predicates is the intersection of their respective extensions, or in other words, it is the set of things common to all of the extensions of the individual predicates. Practice Study the drawing. Imagine a very impoverished little universe of discourse containing only the objects depicted. Practice Assuming that the predicates two-legged, four-legged, striped, mammal, creature, etc. have their normal English meanings, draw circles on the drawing as follows: (1) Enclosing all four-legged things, and nothing else (i.e. the extension, in this little universe, of the predicate four-legged) (2) Enclosing the extension of the predicate creature (3) Enclosing the extension of mammal (4) Enclosing the extension of two-legged (5) Did the intersection of the first two circles you drew enclose just the set of four-legged creatures? Yes / No (6) Did the intersection of the last two circles you drew enclose just the set of two-legged mammals? Yes / No (7) In this little universe, is the extension of non-human mammal identical to that of four-legged creature? Yes / No (8) In this little universe, does the extension of the expression striped human have any members at all? Yes / No Feedback (1) The circle encloses the table, the chair, the cow, and the tiger. (2) It encloses the man, the bird, the cow, and the tiger. (3) It encloses the man, the cow, and the tiger. (4) It encloses the man and the bird. (5) Yes (6) Yes (7) Yes (8) No, the extension of striped human has no members. It is technically called ‘the null (or empty) set’. Logicians allow themselves to talk of a set with no members. U N I T 8 Words and things: extensions and prototypes 85 Comment It has tempted some philosophers to try to equate the meaning of a predicate, or combination of predicates, simply with its extension, but this suggestion will not work. Classic counterexamples include the pairs featherless biped vs rational animal, and creature with a heart vs creature with a kidney. The only featherless bipeds, so it happens apparently, are human beings, and if we assume that human beings are also the only rational animals, then the phrases featherless biped and rational animal have the same extensions, but of course these two phrases do not mean the same thing. It also happens to be the case that every creature with a heart also has a kidney, and vice versa, so that the extensions of creature with a heart and creature with a kidney are identical, but again, these two phrases do not mean the same thing. Philosophers and logicians who have developed the idea of extension have been very resourceful and ingenious in adapting the idea to meet some of the di fficulties which have been pointed out. We will not discuss such developments here, because they seem to carry to an extreme degree a basic flaw in the essential idea of extensions. This flaw can be described as the undecidability of extensions. We bring out what we mean by this in practice below. Practice We will try to solve the well-known ‘chicken-and-egg’ problem. To do so we make the following assumptions: (a) the only kind of egg that a chicken can lay is a chicken’s egg, and (b) the only thing that can hatch from a chicken’s egg is a (young) chicken. (1) Do the assumptions given allow the following as a possibility? The first chicken’s egg, from which all subsequent chickens are descended, was laid by a bird which was not itself a chicken, although an ancestor of all chickens. tải về 1.74 Mb. Chia sẻ với bạn bè của bạn:
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