Hellman’s second line of argument against absolutely general quantification rests — according to the title of Section 4 of his paper — on the multiplicity of ‘factually equivalent ontologies’.
The claim is that ‘The same underlying factual situation [can be] described accurately and adequately in ontologically diverse ways. It would be arbitrary and unwarranted to say that just one is “really correct”.’ What sorts of case does Hellman have in mind? ‘Familiar examples cited long ago by Goodman … and others come from geometry (pure or applied), e.g. a framework with points and lines (say, in the two-dimensional case) vs. a framework with just lines, points being definable as (suitably selected) pairs of intersecting lines.’ But hold on, both frameworks agree that there are points and lines. Either way, then, in promiscuously quantifying over absolutely everything, I’ll be quantifying over both points and lines. So what’s the problem?
Ah, says Hellman, the absolutist must claim that there is one correct answer to the question ‘Are there sui generis points, i.e. points which are distinct from pairs of lines or nested volumes, etc., not constructed out of anything else? … We may not ever know [the answer], but it shows up one way or another in the range of “absolutely everything”.’ Eh? Why is someone who claims that we can sensibly quantify over everything committed to the quite different claim that issues about what is ontological basic or sui generis have determinate answers? When I say that everything is self-identical (for example), I commit myself inter alia to agreeing that points, whatever they ultimately are, are self-identical and lines, whatever they are, are self-identical. But I just can’t see why it is supposed to follow that I’m thereby committing myself to supposing that the ontology game (in the form of raising the question what’s really, really fundamental?) is even a game with determinate rules let alone delivers determinate answers.
Hellman offers variants on the points/lines case. He asks us to consider an ontology of space-time regions that doesn’t recognize the existence of ordinary objects like books; strictly, instead of saying that there are books over there, we should say that a certain region is “booked”, etc. And Hellman’s thought is that in this sort of case, ‘no entity recognized in the ontology of this theory is literally a book’ (contrast the points/lines case, where there are entities available to be identified as points in either ontology). But so what? What has this to do with the question of the possibility of absolutely general quantification over everything?
It has turned out that there are no gods (which was a bit of a surprise in some quarters); so those who thought — in quantifying over everything that there is — that they were including gods along with the books and the points and lines would have been mistaken. But the possibility of being mistaken about what exists doesn’t in itself undermine the possibility of quantifying over every that exists! Similarly, suppose it turns out that there are wonderfully conclusive arguments for an ontology of space-time regions that makes it false that there are books. That would be more than a bit of surprise! But, playing along with that fantasy, then it would have just turned out that we are as mistaken in thinking — when we quantify over everything — that books are included as our ancestors were in thinking that gods were included. That still doesn’t undermine the possibility of quantifying over everything.
So, in short, I can’t see that Hellman’s arguments in Section 4 of his paper have any force as they stand. He just seems to be running together issues about quantifying over ‘what exists absolutely, “in Reality”‘ (his phrase) with the question about whether we can quantify over absolutely everything that exists.