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.
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