The problem of non-being (Bertrand Russell, Alexius Meinong)

Parmenides argues that we can't think or speak of that which doesn't exist, because such speech is about nothing, which is meaningless nonsense. Since we discuss myth, fiction and false scientific theories with ease, there must be something wrong with Parmenides' argument. It is surprisingly difficult to say where the mistake lies. I look at twentieth century answers to this question. Meinong's theory is considered in detail. While initially it looks promising, it turns out to be contradictory, although not in the straight-forward way that Russell thought.; Russell first offers his theory of denoting concepts in the Principles of Mathematics. Although this theory is riddled with logical and metaphysical problems, Russell seems to reject it for epistemic reasons. In its place he proposes his theory of descriptions, only to see the same logical and metaphysical problems resurface concerning the nature of variables. There is also a hard core of cases that are resistant to Russellian paraphrase, and so the theory must be rejected.; Some argue that the best solution is to interpret the "existential" quantifier substitutionally. Unfortunately, no version of substitutional quantification strong enough to solve the problem is intelligible. Others argue that we should free logic of any existential assumptions. Unfortunately, each species of so-called free logic has unacceptable consequences.; Finally I consider theories of truth in fiction. I argue that the only adequate theories are those that posit abstract objects which play the role of fictional characters. These theories should be generalized beyond fiction and applied to the problem of non-being in general. I briefly develop such a generalized theory of abstract objects which I call holders.