The final section of Hellman’s paper is called ‘Making do with “less”‘, and concerns strategies that the sceptic about the coherence of absolutely general quantification can use to makes sense of (true!) assertions like ‘there are no talking donkeys’ or ‘there are no gods’ which seem on the face of it to make absolutely general claims.
I found his discussion murky. (At least as far as philosophy is concerned, I’m with Isabella Dale in The Small House at Allington [ch. xliv]: ‘I hate books I can’t understand,’ said Bell, ‘I like a book to be as clear as running water, so that the whole meaning may be seen at once.’) But the main point Hellman makes, if I’m understanding him aright, is what strikes me as the obviously right point. ‘There are no talking donkeys’ stands or falls with ‘No animal is a talking donkey’, and there are no problems about the restricted quantification involved there. Issues about indefinite extensibility are beside the point because ‘animal’ (unlike ‘ordinal’ or ‘set’) is not indefinitely extensible; and issues about relativity to alternative conceptual schemes are beside the point since, in talking about donkeys at all, we are already talking within a certain scheme that recognizes animals.
‘There are no gods’ can’t be handled quite so straightforwardly (pace Hellman): but not because of issues about absolute generality so much as because of issues about the lack of clear content of ‘gods’. (Who knows what a boojum is? Especially if boojums are described as having all sorts of daft and seemingly incompatible properties. If I then impatiently say there are no boojums, I’m not making a bold speculation about the contents of the universe but rather rejecting — though perhaps not in the most transparent way — the presupposition that there is any clear content to claim that there are boojums. It is pretty similar with gods.)