I emphasised earlier that the nominalist must at all cost pre-empt the Intentionalist’s driving a wedge between ‘some thing’ and ‘some existing thing’. This appears to be just what Peter Lupu has done here. Peter agrees that the consequence ‘Tom is thinking of a mermaid, so there are mermaids’ is invalid, but (apparently) for the reason that in the antecedent sentence the term ‘mermaid’ ranges over mermaids thought-of, i.e. intentional mermaids, and so is true. In the consequent, the same term ranges over ‘ordinary objects’, and so is false, and so the consequence is invalid.
There are many reasons against this. Some I have already given. I will repeat them, together with some more.
1. If Peter’s reason is correct, then the consequent of ‘Tom is thinking of an intentional object, therefore there are intentional objects’ is false, as the term ‘intentional objects’ ranges over ordinary objects (intentional objects being weird, not ordinary). But as I argued here and here, it would not be possible for the intentionalist and the nominalist to disagree at all unless they agreed on the meaning of categorical statements like 'no A is B' or 'some A is not B'. When the nominalist says that there aren't any intentional objects, he is denying exactly what the intentionalist asserts when he asserts that there are such things. They both agree that the scope of ‘intentional objects’ includes potentially any kind of objects, queer and straight, and the nominalist is denying there are any queer ones.
2. In ‘Tom is thinking of a mermaid, but there are no such things as mermaids’, the second ‘mermaid’ clearly picks up the scope of the first. So if the first ranges over queer objects, so does the second. But the second denies there are any such things. Indeed, we could leave out the second ‘mermaids’ and just say ‘Tom is thinking of a mermaid, but there is no such thing’, where it is clear that what the second sentence denies the existence of precisely what Tom is thinking of.
3. The sentence ‘Tom wants a cigarette’ does not assert that Tom wants some weird object that ‘a cigarette’ ranges over. No: Tom wants a real cigarette, and the only reason he wants one is because none is there. Intentional cigarettes are so unsatisfying.
4. Similarly in ‘this house lacks a bathroom’, the scope of term ‘bathroom’ does not include a non-existing bathroom. The statement is merely equivalent to the negative statement ‘this house does-not-have a bathroom’.