The Winged Horse

Pegasus, the winged horse, does not exist.... But didn't I just refer to it?

Russell came to think of symbolic logic as an "ideal language" which could be purified of awkward philosophical problems- which, Russell suspected, arose from loose and sloppy language in the first place (especially that of Hegel and the idealists). Russell and his student, Ludwig Wittgenstein, believed at one point that the whole of reality could be completely represented by means of symbolic logic.

The basic building blocks of the world, they said, are atomic facts, which correspond to atomic statements. Any meaningful statement, however complex, can be reduced to, analyzed into, its constituent atomic statements--all of which are simple reports of sense-data such as "This is red," in which a quality (or relation) is attributed to a thing (or things).

This philosophy, called "logical atomism," is therefore a form of empiricism in the tradition of Locke, Berkeley and Hume. It is therefore open to the same problems that arose from that point of view. For instance, since ethical and religious statements involve no reference to any sense-data, how can they be meaningful?

Ethics and religion have never fared well with the empiricists. But Russell proved adept at handling certain other problems that arose within his philosophy. For example, he had once believed that any object that can be referred to must somehow exist. But this belief gives rise to contradiction.

Suppose I say: "Pegasus, the winged horse, does not exist." Such a claim contradicts itself, because if I can refer to Pegasus, it must exist--and yet I am claiming that it does not! Russell solved this puzzle by translating the statement into "There is no x such that x is Pegasus." In this ingenious way we can say what we wanted to say, without referring to any non-existent winged horse.

Or suppose I say "Nobody is faster than Achilles." Doesn't this commit me to the existence of a person called "Nobody" who can outrun Achilles? Not at all, Russell said, We simply translate this sentence into "There is no x such that x is faster than Achilles." Russell and his followers, who were numerous, were convinced by such small successes that all philosophical problems would yield to such logical techniques. This belief proved overoptimistic.

What about this statement: "There are no square circles." How would you translate this so as to avoid a commitment to square circles?

Bibliography

Edwards, Paul and William P. Alston and A.N. Prior. "Bertrand Russell," Encyclopedia of Philosophy, Vol. 7, p. 235-258.

Russell, Bertrand, Our Knowledge of the External World, Chicago, 1914 .

Weitz, Morris, "Analysis, Philosophical," Encyclopedia of Philosophy, Vol. 1, p. 97-104.