Thanks to the link that Peter van Inwagen sent, I was able to look at his paper “Creatures of Fiction”* which has a much clearer explanation and justification of his thesis that fictional characters can be such and such without having the property of being such and such. Caution: the paper was written in 1977, 34 years ago, and I don’t know if van Inwagen still holds the views expressed there.
The distinction is motivated by the problem of sentences such as “Some fictional characters are witches”. Van Inwagen holds that such sentences are true, and because he is an anti-Meinongian (or rather, as I have argued, because he holds Brentano’s Thesis), he holds that it is equivalent to ‘Fictional characters that are witches exist’, and so implies ‘Witches exist’. But witches don’t exist. Inwagen gets round the difficulty by asserting that predication has different senses. “Witches don’t exist’ has the conventional sense, meaning that nothing has the property of being a witch. But “Some fictional characters are witches” has a non-standard sense, and does not imply that anything does have the property of being a witch, and so is consistent with "witches don’t exist".
He justifies this by an argument from analogy. His example is a Cartesian who holds that people are immaterial substances. Hence Jake, who is a person, is an immaterial substance. But the sentence “Jake is 6 feet tall” can’t be literally true, for an immaterial substance is unextended, and can’t be 6 feet tall. The Cartesian can get round this by claiming that in ordinary speech we often say "is" when strictly speaking we should say "animates a body that is": the predicate ‘is F’, when predicated of a person, really and strictly means "animates a body that is F". Thus what looks like predication in ordinary speech is not always predication. And so “Alexandra Medford is a witch”, said of the witch played by Cher in The Witches of Eastwick, does not imply that anyone has the property of being a witch. Thus (as I interpret Inwagen) there is no inconsistency between his view that Alexandra Medford exists, but that witches do not, for the following syllogism is invalid:
No one is a witch
Alexandra Medford is a witch
No one is Alexandra Medford
It is invalid because ‘is’ is equivocal in the major and the minor. In the major, it means ‘nothing has the property of being a witch’. In the minor, it is not the ‘is’ of predication, and thus is not equivalent to “Alexandra Medford has the property of being a witch”. Fallacy of equivocation. Thus we can consistently claim that Alexandra Medford exists, i.e. that someone is Alexandra Medford, that she is a witch, although she does not have the property of being a witch, and that no one has the property of being a witch.
My only reply to this (although I am sure there will be more to say), is to invoke Ockham’s other razor, which I discussed some time ago. To one who claims that the verb 'to be' is ambiguous in certain arguments, he objects that this is completely irrational, he says "for it amounts to destroying every argument form. For whenever it pleases me, I will say that 'to be' is equivocal in the premisses, and I will ascribe at will a fallacy of equivocation to every syllogism".
* American Philosophical Quarterly, Volume 14, Number 4, October 1977