Russell’s Theory of Descriptions
Logic . . . must no more
admit a unicorn than zoology can.
The Meaning of Meaning
“Meaning” is
ambiguous. In one sense, probably the most familiar, the meaning of a term is
its “sense,” the idea or concept it signifies. In another sense,
however, the meaning of a term is the object (if any) that it picks out, thus
we say “I mean you.”
The semantic project of
classical logic, which Russell was instrumental in developing, is to account
for the meanings of expressions in the latter sense. Further, if we make the
reasonable assumption that the meaning of whole sentences is determined by the
meanings of their constituents, then the meanings of whole sentences will be
determined by what their constituents individually pick out, that is, by what
we shall call their extensions.
Names pick out individuals; predicates, on this account, designate
sets. This latter claim may seem a little peculiar but the idea is that the
extension of a one-place predicate, like “ . . . is a horse,” will
be the set of all things to which that predicate is correctly applied, that is,
the set of all horses. The extension of a relational predicate likewise will be
the set of all ordered pairs, triples, etc. of objects to which it correctly
applies, depending on whether it is a two-place predicate, a three-place
predicate or whatever. Thus, the extension of the predicate “ . . . is
married to . . . ” includes <Lucy, Desi>, <Ronald, Nancy> and
so on; the extension of “ . . . is the child of . . . and . . . ” includes
<Abel, Adam, Eve>, <Amy, Jimmy, Roselyn> and so on.
There are a number of
predicates that are not true of anything: sentences that assign them to objects
are all false as, e.g.
(1) Jean Dixon is psychic.
(2) The animal in that cage
is a unicorn.
Classical logic has no
problem with such sentences: they are simply false in virtue of the fact that
nothing is in the extensions of either psychic people or unicorns. These terms do have an extension, namely
the empty set.
Singular terms that do not
refer however do pose problems. The meaning of a name is supposed to be the
individual it picks out. Since the meaning of a whole sentence is supposed to
be determined by the meanings of its parts, it would seem to follow that
sentences which include names that do not pick out anything must be
meaningless. But they aren’t. Consider the following:
(3) The present King of
France is bald.
(4) Pegasus is a horse.
These sentences may be false
but they are not meaningless--indeed, if they are false they cannot be meaningless. So what do
we do?
Ockham’s Razor Again
One solution is to say that
they do
pick out individuals--unreal ones. On this account, things that “really
exist” are not all the things there are: there are also fictional
characters, mythical beings, creatures of the imagination and possible objects
generally, indeed, even impossible objects like round squares and odd even
numbers. “Pegasus” and “The present King of France”
pick out objects, unreal ones as it happens, so (3) and (4) are not
meaningless.
Russell rejects this account
in part because he regards it as ontologically profligate: an offense against
Ockham’s Razor.
Negative Existentials
Ockham’s Razor,
however, is not the worst of our problems. The account apears to commit us to
flat-out contradictions to the extent that it generates special problems in the
case of “negative existentials,” that is, sentences like:
(5) Pegasus doesn’t
exist.
In general, where a is a name and F is a
predicate, from a is F we should be able to infer there exists something which is
F. If, e.g. Clinton jogs we can infer that there is someone who jogs or, in the
logical argot, there exists at least one jogger. But, if we take
“Pegasus” to be a name then from (5) it would seem we can infer
that there exists at least one thing that doesn’t exist or, if you will,
there is something that isn’t. Whoops.
Russell’s Solution
Russell’s way around
this is to deny that ordinary names like “Santa Claus,”
“California” and “Bill Clinton” are names in the strict
and philosophical sense. He holds that what they really are are disguised or
abbreviated definite descriptions. And he takes care of definite descriptions,
expressions of the form “the so-and-so,” by construing them as what
he calls incomplete symbols: that is to say, they do not by themselves pick out anything but
only have meaning within the contexts in which they occur. (3) for example is
to be analyzed by something like
(3´) There is one and only one object that
is the present King of France and that object is bald.
The strategy is to get rid of
the apparent name “the present King of France” by using a
predicate, “ . . . is the present King of France” to do the job it
does in (3). And, remember, predicates that aren’t true of anything are
innocuous. Pegasus is a little harder to deal with but not impossible if we are
prepared to invent predicates as we go along. (4) and (5) can be translated as
(4´) and (5´) respectively:
(4´) There is one and only one object that
pegasizes and that object is a horse.
(5´) There is nothing that pegasizes.