### Noneist Existence Predicate

I’d like to present an objection to noneism from a very recent van Inwagen paper, “McGinn on Existence”. (Colin McGinn is a noneist and van Inwagen is criticizing him. The objection can be extended to Priest, however.)

Non-noneists accept the following:

~upside down 'A'x~ Fx iff backwards 'E'x Fx

E!a iff backwards 'E'x (x = a)

('E!' is the existence predicate.) Noneists employ U and G quantifiers and define upside down 'A' and backwards 'E' in terms of these and E!. But notice that noneists cannot go on to define E! in terms of backwards 'E'. So noneists employ a predicate that does not make sense to non-noneists. Or if sense is made of it, sense can no longer be made of U and G.

Non-noneists accept the following:

~upside down 'A'x~ Fx iff backwards 'E'x Fx

E!a iff backwards 'E'x (x = a)

('E!' is the existence predicate.) Noneists employ U and G quantifiers and define upside down 'A' and backwards 'E' in terms of these and E!. But notice that noneists cannot go on to define E! in terms of backwards 'E'. So noneists employ a predicate that does not make sense to non-noneists. Or if sense is made of it, sense can no longer be made of U and G.

## 1 Comments:

In class Justin noted that one can understand Priest's 'E!' predicate as 'is concrete'. This seems right to me, but it raises another serious issue that we did not discuss. Given that we can understand 'E!' in this way, could we also understand crazy 'U' the way upside down 'A' is classically understood, and interpret Priest's upside down 'A' as something like 'everything concrete'? (And correspondingly for crazy 'G' and backwards 'E'?) If so, then does Priest's semantics for intentionality really commit us to noneism?

(This is a hard topic. Lewis discusses the issue explicitly in his 1990 Mind paper, "Noneism or Allism?". It is also reprinted in his _Papers in Metaphysics and Epistemology_. This issue would make a good final paper topic if anyone is interested. You can get a copy of the Lewis paper from me.)

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