Peter van Inwagen is an example of the first kind of Meinongian, but not the second. He argues* (p. 237 ff) that the correct way, and the only way, to understand the use of variables and quantifiers is to show how they can be translated into expressions of ordinary English that we already understand. He gives a few examples to show how it is clear that the formal predicate calculus is simply a regimentation of the ‘all’ and ‘there are’ of ordinary English. He concludes (p.239) “The existental quantifier therefore expresses the sense of ‘there is’ in ordinary English. (As an opponent of any form of Meinongianism, I would say that the existential quantifier is appopriately named – for the reason that, in expressing the sense of ‘there is’ in English, it thereby expresses the sense of ‘exists’ in English).” To the objection (p.242) that this account of the meaning of a sentence containing quantifiers does not tell us the conditions under which it would be true, he neatly replies that “the conditions under which a sentence would be true, are not the first thing about the meaning of a sentence. The first thing about the meaning of a sentence is what the sentence means” – which is just what his account tells us about sentences containing quantifiers, he says.
This has an important consequence for fictional discourse (meaning not the discourse you find in works of fiction, but rather what is spoken or written about works of fiction, such as found in literary criticism). Such discourse can potentially include complex quantification. Inwagen’s example is
(1) There is a fictional character who, for every novel, either appears in that novel or is a model for a character who does.
This involves apparent existential quantification and a complex quantificational structure, as well as the ability to generate all the inferences licensed by quantifier logic. For example, we can deduce
(2) If no character appears in every novel, then some character is modelled on another character.
If the quantification is real, and given Inwagen’s rejection of the second kind of Meinongianism (i.e. the kind that accepts existential quantification but not existential commitment) then we must accept the reality, indeed the real existence, of fictional characters. If the quantification is not real, we must explain (p.244) how to paraphrase the two sentences above, show whether the second sentence follows from the first, and if not, why it does not. In summary:
*The existential quantifier expresses the sense of ‘there is’ and ‘there exists’ in English.
* ‘For some x, x is a fictional character’ is true.
* There are fictional characters, i.e. fictional characters exist.
Thus Inwagen is a Meinongian in the first sense. He affirms the reality of fictional characters in the most direct way, claiming that they exist. But he is not a Meinongian in the second sense. For he upholds the Brentano thesis - ‘For some x, x is a fictional character’ = ‘There are fictional characters’ = ‘Fictional characters exist’.
Van Inwagen recognises he must explain the apparent truth of sentences like ‘Sherlock Holmes does not exist’. I will discuss his explanation tomorrow.
* "Quantification in fictional discourse", in Empty Names, Fiction and the Puzzles of Non-existence, Stanford 2000, pp. 235-247.