I had a brief correspondence with Van Inwagen earlier this week, but he came up with nothing that resolved some of my other puzzles about his theory. Here is one. From what he says, Inwagen seems committed to the following:
(1) 'Some x is A' is equivalent to 'some x-that-is-A exists'.
(2) 'Holmes does not exist' is equivalent to 'no one has all the properties Sherlock Holmes holds'.
(3) Someone, namely Holmes, holds all the properties held by Sherlock Holmes
(4) No one has all the properties held by Holmes.
But this leads to a contradiction, as follows.
(5) Holmes does not exist (from 2, 4).
(6) Someone, namely Holmes, who holds all the properties held by Sherlock Holmes, exists (from 1, 3).
(7) Holmes exists (from 6, elimination)
(8) Contradiction (5, 7)
Spelling it out. Van Inwagen is trying to get over the problem of 'someone' having the properties ascribed to Holmes, through his distinction between 'having' and 'holding'. No one has the properties that Holmes holds, and so Holmes does not exist. But this does not evade the problem. By the very same reasoning, someone holds the properties that Holmes does not have. And there is still 'someone', and so Holmes does exist. Van Inwagen can evade this by dropping his commitment to the equivalence of 'some thing' with 'some existing thing'. But that would commit him to the variety of Meinongianism to which he is so fundamentally opposed.