Everything

Quine says that the topic of ontology is "What is there?" and that the answer, everyone will agree, is "Everything." Glanzberg (and I and Kit Fine) disagree.

Most of the time, when we say "everything," we don't mean everything. I like Tim Williamson's example of his wife saying to him, "You left me to pack absolutely everything."

So, the question is, are there any contexts in which, when we use "everything" we mean that in an unrestricted, absolute sense? What is it to mean something by "everything"? The usual account says that part of the meaning must be to specify the "domain of quantification." Thus, in the Williamson example, the domain is something like all the things that needed to be packed. It can be disputed whether the domain of a quantifier is itself an object. It might, in some sense, be a plurality of objects, not a single collection or domain or set or whatever of them. The reason anyone cares is that if the domain of absolutely everything is a thing, then it must be in itself, which causes problems for the idea of absolutely unrestricted quantification. That is one case of an important dialectical tension in the debate: Those who think that we can quantify over absolutely everything think that there are fewer things than those who think we can't. Managing to quantify over "absolutely everything" while denying the existence of some things is thought by opponents of absolute quantification to be a Pyrrhic victory.

Here is the most often mentioned reason for avoiding taking quantification over absolutely everything to have a domain of quantification that is an object: Say that that object is a class, the class of absolutely everything. Then consider the class of absolutely all classes that are not members of themselves. Is it a member of itself? It is if and only if it isn't, and so, it seems, the conclusion must be that there is no such class. However, there is a different conclusion that can be drawn: Let U be a class. Let R be the subclass of U that consists of every member of U that is not a member of itself. Then R is not in U, since if it were, it would be a member of itself if and only it is not a member of itself. Conclusion: For any class whatever, there is a class not in it. It follows, not by paradox but by ordinary mathematical argument, that there can be no class of absolutely everything, since every class is "extensible."

The Russell argument seems to show that the domain of an absolute quantifier cannot be a class, set, collection, or anything like that, and so those who advocate absolute quantification deny the domain of a quantifier must be an object.

By now, you may be wondering, why not just give up on absolute quantification? I've talked about the reasons against it, what are the reasons for it? Typical restricted domains of quantification are obtained by restriction of an implicit larger domain. For example, "horses are animals" means something like "among all the living things, every one that is a horse is an animal." The implicit domain is, or at least I have taken it to be, the domain of living things, which is all the things from some larger domain that are alive. What is the larger domain? Perhaps, in this case, physical objects, but it is clear there is a vicious regress implicit in that, one that can only be stopped by the domain of absolutely everything. In addition, ontologists like to make what seem to be absolute claims like, "Each thing is identical to itself."

Glanzberg responds to the prevailing view that one can get around the problem by denying that the domain of quantification is an object. To do so, he presents Williamson's paradox: Any language has an "interpretation," which, among other things specifies the extension of each word in it. Fix a vocabulary (Williamson and Glanzberg (and all philosophers) call it a language), say English, and say there is a predicate word in it that we fasten on, call it P. Thus, for each potential extension S of a predicate, we have a new version of English, call it English-S, in which the word P is interpreted in such a way that the things to which the predicate P applies are just those in S. Say that an interpretation English-S is self-predicable if, in that interpretation, that very interpretation has P, that is if English-S is "in" S. Of course, the point is that, if we let R be the extension of non-self-predicable, then the language ("interpretation") English-R cannot include English-R in its domain. However, it does seem that ordinary English is English-R (where P is "non-self-predicable"). Thus, we cannot, in English (or any natural language) quantify over absolutely everything.

One initial response to the problem is "So what?" The problem only arises in very special circumstances talking about language or extensions. For anything we really want to say, it isn't a problem we need to confront. First of all, the argument just shows that the problem can arise, not that the Russell-like cases are the only ones in which it can arise. We would still need to assess whether it is a problem in other cases. Second, the cases where the problems arise are important for this course: They suffice to show that Quine's answer "Everything," is in trouble, and so we need a better formulation of what existence questions are. They suffice to show that we don't have an adequate account of how we get restricted domains. They show that general metaphysical claims ("each thing is self-identical") need further explanation.

Glanzberg's proposal, which is quite similar to mine, is that some statements ("each thing is self-identical") are "domain ambiguous," that is, we are not only claiming that they are true in the present domain, but that, whatever domain may be relevant, they are true in that one. It is difficult to formulate that proposal clearly, since the natural formulation would be, for example, "For every domain D, if the domain of "everything" is D, then "each thing is self-identical" is true." That won't do, since it would only work if the quantifier "every" in "every domain D" were absolute.

Pretty much everyone in this debate agrees that their reasons for their preferred answers are a result of balancing advantages and disadvantages, that is, pragmatic arguments, not conclusive arguments.

-- ShaughanLavine - 25 Nov 2008