Sider on quantifier variance and equivocation

In "Ontological Realism", Ted Sider imagines a dispute between David Lewis (DKL) and Peter van Inwagen (PVI) about whether there are tables.

DKL: "Tables exist"

PVI: "Tables don't exist"

According to Sider, one type of ontological deflationist (D1 in the paper) diagnoses the disagreement thus: "PVI and DKL express different propositions with 'Tables exist'; each makes claims that are true given what he means; so the debate is merely verbal". Such disagreement presumably arises from some equivocation. And the question Sider considers next is: 'Where is the equivocation located?'. The only possibilities are 'table' and 'exist'. He argues that the equivocations on the former are of no help to the deflationist account, so he must hold that it is 'exist' that is equivocal.

I don't follow him here. I think that the deflationist has a third option: the words 'table' and 'exist' are univocal; however, the disputants are allowing their quantifiers to vary over different domains. And it is this that accounts for the different meanings each attaches to the sentence "Tables exist".

Perhaps what I have in mind will come out more clearly in light of another sample sentence that Sider discusses. "Consider a world in which there exist exactly 2 material simples, which are not arranged in the form of a living thing. Of that world, DKL would accept, while PVI would reject: [Sider writes this out in logical notation] "there are at least three things"." In the logical expression of this sentence, there are: quantifiers and variables, truth-functional connectives, and the identity predicate. But, says Sider, the connectives and identity are univocal, so it must be the quantifier that is equivocal.

I don't follow this. Why not say that the quantifiers have a univocal meaning and that the disputants recognize different domains? DKL recognizes a domain that includes tables and PVI recognizes a domain that does not. This sort of difference will provide the deflationist with a means of accounting for how DKL and PVI are "talking past each other". But, notice, there is no equivocation in the quantifier 'exists', only a disagreement about the range of entities over which 'exists' ranges.

Here's an example of what I have in mind. Consider the universal quantifier and two models, M1 and M2. The domain of M1 contains both of my feet and nothing else. The domain of M2 contains both my feet and the Eifel Tower. If I say "everything is a foot", what I have said is true in M1 and false in M2. I may get in an argument with someone. My disputant says, "What Ed says is wrong, something (the Eifel Tower) is not a foot; so not everything is a foot". This disagreement, like the one Sider discusses, is not substantive. But the reason for its lack of substance is not a disagreement about the meaning of "everything" but rather that we are talking about different models with different domains. As I understand the domain of quantification, everything is a foot, and as my disputant understands the domain of quantification, something is not a foot.

Ed