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