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.

Predicates that do not designate and terms that do not refer

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.