David Brightly asks whether there is really any problem with Van Inwagen’s position that Sherlock Holmes ‘holds’ the property of being a detective rather than ‘having’ such a property. Surely there is. Inwagen’s position is inconsistent with the three main theses he puts forward in the paper. First, he holds that certain kinds of statements about fiction are true. For example, ‘There is a fictional character who, for every novel, either appears in that novel or is a model for a character who does’, or just ‘there are fictional characters’. Second, he holds that ‘there is’ is equivalent to ‘there exists’. Thus, it is true that fictional characters exist. Finally, there is a simple correspondence between the predicate calculus and ordinary language. For example, ‘There are fictional characters’ translates to ‘for some x, fictional_character(x)’ and back.
This is inconsistent with his position that ‘Sherlock Holmes does not exist’ is true, and that he holds, but does not have, the property of being a detective. If it is possible to translate between ordinary language and predicate calculus and back, it follows that any valid inference in predicate calculus is also valid for the corresponding ordinary language statements, and conversely, and that anything true we can say about the predicate calculus statements, is true of the ordinary language ones. So take ‘Some fictional characters are detectives’, which Inwagen (presumably) holds to be true. Thus at least one fictional character is a detective, and thus has, rather than holds that property. Furthermore, if the corresponding predicate calculus statement ‘Ex, fictional_character(x) & detective(x)’ is true, there must be at least one object a in the domain such that fictional_character(a) & detective(a). For example a = sherlock Holmes. But the predicate detective() expresses the property of having, not holding the property of being a detective, so Inwagen’s claim that Holmes (or whatever x satisfies the predicate) does not have that property, is false.
Furthermore, Inwagen holds that 'All fictional characters exist’ is true, and clearly holds that Sherlock Holmes is a fictional character. And he holds that these can be simply translated into predicate calculus, so – according to him - the following are true.
(x) fictional_character(x) implies exist(x)
But these together imply exist(Holmes). This translates back into ‘Holmes exists’, and so his claim that ‘Holmes exists’ is false is contradictory.