The problem of negative existentials

Russell asks us to consider sentences like:

The round square is unreal. 

The round square is nonexistent.

These sentences are called ‘negative existentials’ because they can be understood as the negation of an existence claim.

If it were the case that definite descriptions were to be understood as a kind of name, and names were understood as mere proxies for their bearers, then it may seem that we could give an account of these sentences using the elementary theory of reference sketched above: that is, the sentences would be true just in case there was some object referred to by ‘the round square’ which was, respectively, among the unreal things or the nonexistent things.

Russell does not think that this is plausible; there is, after all, no object -- the round square -- which could be the referent of the ‘the round square.’ He says:

“It is argued ...that we can speak about ‘the golden mountain,’ ‘the round square,’ and so on; we can make true propositions of which these are the subjects; hence they must have some kind of logical being, since otherwise the propositions in which they occur would be meaningless. In such theories, it seems to me, there is a failure of that feeling for reality which ought to be preserved in even the most abstract studies. Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features. To say that unicorns have an existence in heraldry, or in literature, or in imagination, is a most pitiful and paltry evasion. What exists in heraldry is not an animal, made of flesh and blood, moving and breathing of its own initiative. What exists is a picture, or description in words. Similarly, to maintain that Hamlet, for example, exists in his own world, namely in the world of Shakespeare’s imagination, just as truly as (say) Napoleon existed in the ordinary world, is to say something deliberately confusing, or else confused to a degree which is scarcely credible. There is only one world, the “real” world: Shakespeare’s imagination is part of it ...If no one had thought about Hamlet, there would be nothing left of him; if no one had thought about Napoleon, he would have soon seen to it that someone did.” (‘Descriptions,’ 169-170)

Russell’s point here is that there are no nonexistent things; there are no round squares, and there is no golden mountain. What we need is an account of how definite descriptions work which can explain the truth of some negative existentials without the ‘pitiful and paltry evasion’ of claiming that such things do exist, or at least are around to serve as the referents of definite descriptions.

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