Tom Graham at the TLS:
That some things – unicorns, the largest number, Sherlock Holmes – do not exist seems so obvious, and is so frequently taken for granted in our everyday discourse, that denying it would be ridiculous in any ordinary context. And so it may come as some surprise that since the beginning of the twentieth century this view has been among the least popular and most berated in anglophone philosophy. Many even claim that the position, so widely held by non-philosophers, is unintelligible, and the British philosopher Gilbert Ryle even went so far as to say that if it were not a dead view in philosophy, nothing was. To revive the view that some things don’t exist (known these days as “noneism”) and situate it as a plausible contender in current debates on existence is the aim of Graham Priest’s formidable 2005 book Towards Non-Being, which has now appeared in a significantly expanded second edition.
A fundamental motivation for the dominant view is that to lack existence, it seems, is to be nothing at all. Things, by contrast, are not “nothing” – they are things! If so, then “being a thing” and “existing” go hand in hand, and there cannot be “things” that do not exist. Adherents of this view thus read the noneist’s claim “some things don’t exist” as entailing the self-refuting “some things are not things” and therefore to be self-contradictory.