Sage advice. You might apply it to what I write.
In the next paragraph of that paper, we have
The sentence ‘D is a domain containing everything; and some domain contains an object that is not contained in D’ is a logical falsehood.
He uses this in a reductio against the possibility of quantifier variance. But there is another way to view it, as a diagonalisation, showing how the very idea of a domain containing everything is subject to the obvious Russelian paradox. What it shows is that the idea of a domain containing everything is inherently contradictory.
Sider acknowledges the situation in footnote 45 but thinks he can get around this by stipulating that he can have a domain of just “any quantifier wholly unrestricted in its application to individuals (nonsets)”. Can he? I think not; or better, even if he does so, the real problem for his account lies not in individuals vs sets but in the items he is discussing being iterative. As soon as he admits iteration he becomes subject to Cantor’s theorem; and he does so in §5.
More generally, one would replace singular quantifiers over composites with plural quantifiers over simples, and replace each predicate, F , of composites with its irreducibly plural form pl(F ) (e.g., pl(‘is a table’) is ‘are arranged table-wise’; pl(‘x is on y’) is ‘the X s are on the Y s’.)
First-level plural quantification is (arguably) safe under the individuals/nonsets restriction; the plural quantifications Sider’s own translation scheme requires are not obviously safe, and he never extends his footnote 45 defence to cover it.
Wittgenstien’s §48 in Philosophical Investigations encourages us to see that what counts as a simple is iterative in a way that debars any one domain being inherently an absolute. The entire dispute presupposes that “simple” picks out a determinate, language-independent class for the plural quantifiers to range over. Wittgenstein shows that the class is not language independent in the way required by both sides of the debate.
So two objections, the first that the notion of a domain of everything is a non starter, the second that what counts as an individual in the domain is itself a part of the language being used, and not separable in the way required.
Here’s the article, for convenience:
ontological_realism.pdf (273.6 KB)