Tuesday, May 01, 2007

Schaffer on Furnishing Functions

(X-posted from The bLOGOS.)

In a part of ‘Ontological Anti-Realism’ which I didn’t comment on (§§8-11), David Chalmers considers an objection against anti-realism based on the idea that the absolute unrestricted quantifier has an objective, determinate semantic value. I don’t want to assess his response to the objection here (see related discussion here, and references there).

In order to analyse existence assertions, however, he tentatively introduces the notion of a furnished world—an ordered pair of a world and a domain—and a furnishing function—a mapping from worlds to domains—(see the end of §8).

In his comments to the paper, Jonathan Schaffer objects:

The argument for heavyweight realism about fundamental structure: Furnishing functions are maps from a world to a domain. But a function is a map from one structure (‘the input’) to another (‘the output’). One cannot have a well-defined function without there being some articulated structure to the input. In particular we must be able to specify the arguments of the function. Any function is either complete or partial. It is either injective or not. It is either surjective or not. None of these classifications would make sense unless the input (‘the world’) already comes with some fundamental articulated structure inbuilt, to feed into the function. … I conclude that the framework that Chalmers actually supplies is at least half-realist, in the sense that it presupposes heavyweight realism about fundamental structure. (pp. 2-3)

I am probably missing something here. For I understood that a furnishing function was a map from the class of worlds to the class of domains, whose arguments were precisely just worlds. Thus I don’t see why there being such mappings requires in any sense any “articulated structure” in the items to which the function is applied. Can anyone help?

4 comments:

Brit Brogaard said...

Prior to the meeting in Arizona where Jonathan presented his comments I raised a similar question (but I formulated it differently). My questions can be found here.

I said: "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?"

Chalmers replied:

"Well, there are lots of sorts of quantifiers on this account -- various lightweight quantifiers and a heavyweight quantifier. On my view, there may be some determinately true sentences using the heavyweight quantifier, such as those stating the existing of certain fundamental entities. If so, as I say in the paper, this qualifies the extent of my anti-realism. Still, there will still be a lot of indeterminacy even with the heavyweight quantifier (e.g. sentences stating the existence of nonfundamental entities), so there's still a fair degree of anti-realism here".

I took Jonathan to be saying that if the furnishing functions are functions from worlds to domains, then there must already be worlds to begin with (to serve as inputs). So, chalmers' anti-realism is not a full-blown ontological anti-realism.

Dan López de Sa said...

Hi Brit! Many thanks for the comments.

I also have concerns about the way the notion of a heavyweight quantifier in introduced in Dave’s paper (which connects with the issues about ‘analytic’ statements discussed here). I hope to post further on this soon.

As to Jonathan’s, I thought that his worry was not as much that there must already be worlds to begin with, but maybe I'm worng (see his footnote 2). I tought that his worry was rather that there being maps from worlds to domains somehow required the imposition of an “articulated structure” in the items to which the function is applied: to wit, worlds. In any case, however, I still don’t see why Dave’s anti-realism is not a full-blown ontological anti-realism.

nick shackel said...

Surely it's significant that in the quoted remark from Schaffer --'Furnishing functions are maps from a world to a domain'-- both 'world' and 'domain' are singular. That means that Schaffer is taking the domain (sorry about potential confusion in terminology) of a furnishing function to be a single world, not a set of worlds, and so his remarks go through w.r.t. this implying the world has a structure. But if Chalmers is taking the set of worlds to be the domain of a furnishing function then Schaffer's remark is beside the point.

Dan López de Sa said...

Yes: “A furnishing function (or equivalently, a domain-determination function) is a mapping from worlds to domains. A world and a furnishing function jointly determine a furnished world. In effect, given a world, the furnishing function specifies a class of entities that are taken to exist in that world.” (p. 30 of the current version)