Chalmers on Ontological Anti-Realism

Today I read Carrie Jenkin's interesting post and David Chalmers' equally interesting paper -- very quickly on a very bumpy flight. But let me try to summarize Chalmers' paper (leaving out a whole bunch of important details). The paper begins with a discussion of ontological disputes. Here is one: there is a table with two cups. Is there in addition to the two cups also a cup-cup -- the fusion of the two cups? Here is another: there are some atoms arranged chair-wise. Is there in addition to the atoms also a chair? Realists in the relevant disputes would tend to say 'yes'. Chalmers is an anti-realist. His new position -- as I understand it on a quick read -- is this. There are worlds with micro-physical facts. But worlds do not come equipped with domains of quantification. Instead when we utter a sentence such as 'this is a chair' or 'this is a cup-cup' the context of utterance supplies a funishing function -- a function from worlds to domains. In ordinary contexts the furnishing functions may yield domains with chairs and cups but no cup-cups, and in the ontology room the furnishing functions may yield domains with cup-cups or alternatively no cups and no chairs. There are various admissibility constraints on the furnishing functions. 'There are unicorns' is inconsistent with a semantically neutral description of the micro-physical level of reality. So, it is not correct in any (actual) context to say that there are unicorns.

Some questions:
(1) Chalmers assimilates his quantifier domain restriction approach to other more well-known forms of quantifier domain restriction. But it is well-known that different occurrences of quantified noun phrases in one and the same sentence can be restricted in different ways. Stanley and Williamson offer this example: "every sailor waived to every sailor', which may be used to make a true assertion if the sailors on one ship waived to the sailors on another ship. I wonder whether there could also be different furnishing functions relative to different elements of a sentence or discourse fragment. Suppose I say "There are just two objects on the table unless we include the fusion of the cups". What I said may well be correct. But 'there are just two objects on the table' must then be associated with one furnishing function and 'the fusion of the cups' with another. Furnishing functions would then be specific to the occurrences of quantified noun phrases and not to the conversational context as such.

(2) This takes us to my second question. Are the furnishing functions values of function variables which are represented syntactically? Or do they enter into the analysis at a different level? On Stanley and Szabo's quantifier domain restriction strategy, the domain and function variables are represented syntactically. Since Chalmers assimilates his approach to other more well-known forms of quantifier domain restriction, one might suspect that the function variables are represented syntactically.

(3) If the function variables are represented syntactically, how do we deal with cases of the following sort? 'Each journal editor told each referee to reject each paper' (See Schlenker 2005, Mind & Language for similar examples)

(4) On a different note: are there in fact two kinds of quantifiers? Those ranging over the micro-physical domain (that is, those occurring in a semantically neutral description of a world) and those ranging over domains yielded by the furnishing functions? If so, then why isn't this a form of ontological realism?

I have a number of additional questions. But I will save them for later. I still need to read the paper more carefully.