Being Explained Away?
Oh dear.
Returning to philosophy, here is a remark by John Burgess about the possibility of translating ordinary sentences into sentences with seemingly less ontological commitment, as described in Prior's "Egocentric Logic" and Quine's "Variables Explained Away":
Thus whether one speaks of abstract objects or concrete objects, of simple objects or compound objects, or indeed of any objects at all, is optional. Or at least, this is so as regards "surface grammar". My claim is that if children who grew up speaking and arguing in Monist or Nihilist or some Benthemite hybrid between one or the other of these and English, it would be gratuitous to assume that the "depth grammar" of their language would nonetheless be just like that of English, with a full range of nouns and verbs denoting a full range of sorts of objects and connoting a corresponding range of kinds of properties. And any assumption that the divine logos has a grammar more like ours and less like theirs would be equally unfounded, I submit. It is in this sense that I claim any assumption as to whether ultimate metaphysical reality "as it is in itself" contains abstract objects or concrete objects, of simple objects or compound objects, or again any objects at all, would be gratuitous and unfounded. (p.18 of "Being Explained Away" -- Microsoft Word format, use Neevia to convert)
I'm not sure to what extent I agree with that. I do agree that there is something strange about asking whether numbers really exist. Burgess takes this to be the core question dividing nominalism and platonism about numbers. Thus he argues e.g. in "Nominalism Reconsidered" (MS Word again, coauthored with Gideon Rosen) that if nominalists agree that "there are numbers" is true -- while offering a nominalistically acceptable interpretation --, they have actually given up nominalism.
I don't think this is a helpful way of looking at the debate. No doubt there are nominalists who claim that there are no numbers. These nominalists reject mathematical truths and try to show how science can be done without. But they are usually not the nominalists who propose novel interpretations of mathematical truths. The larger class of nominalists who do that don't want to reject mathematical truths. They don't deny that there are numbers. But they want to solve the philosophical puzzles associated with such truths by somehow reducing them to more familiar truths, e.g. to counterfactual conditionals about material objects. So here, the question dividing nominalists and platonists is not whether there are numbers, but whether talk about numbers can be analyzed (philosophically, not linguistically) as talk about less troubling matters.
What's more, the trouble nominalists have with mathematical truths is, I think, not mainly about 'ontological commitment'. In this respect, I agree with Burgess: Ontological commitment is a vastly overrated methodological virtue (see this posting from last year.) What I find attractive about nominalism isn't that it promises to eschew ontological commitment. The puzzling thing about numbers is not their existence. Rather, it's their nature, their whereabouts, their relation to us, their modal status, etc.
If, as I believe, the dispute between nominalism and platonism is not about about what there is -- and if generally philosophical disputes are hardly ever about ontological commitment --, the possibility of speaking a language without quantifiers is not as interesting as Burgess seems to think. My worries about numbers don't go away by adopting a Monist or Nihilist language. I'm puzzled about the nature and whereabouts of numbers, and I'm equally puzzled about the qualitative and spatiotemporal ways in which the Absolute numeralizes.
Finally, something about which I'm uncertain. Suppose, contrary to what I've just argued, that whether numbers exist is in itself a substantial philosophical question. In the language of the Monists, "numbers exist" gets translated as "the Absolute numeralizes". In a sense, these two sentences mean exactly the same (in their respective languages). That's what makes Prior's proposal much more interesting than the proposal to 'translate' every English sentence into the French "il pleut". But if the "the Absolute numeralizes" in some language means just the same as "there are numbers" in our language, then how could it be 'optional' to say that there are numbers? What's 'optional', it seems, is using the string "there are numbers", rather than "the Absolute numeralizes", or "les nombres existent". But nobody would have thought otherwise.
Of course, if we acquiesced in Monist, we couldn't use Quines criterion -- "to be is to be a value of a bound variable" -- as a criterion of ontological commitment. For there wouldn't be any quantifiers in our language (not even hidden in its 'deep structure'). What we call questions about ontological commitment wouldn't disappear, though. They would turn into questions about the features of the Absolute.
But what if we spoke a hybrid language, doing away only with some existential statements, perhaps about numbers or possible worlds or the future, in favour of certain primitive numerical or modal or temporal operators? Would we then mean the same as we actually mean by our quantificational idiom? Does "everything is actual" mean the same in this language as in ours? Or should it be translated as "everything actual is actual"? If so, there is again no substantial disagreement between us, only a disagreement in wording.
But I'm not sure if I want to accept that conclusion. For one, it seems odd to say that actualists and presentists mean something special by "exists". It rather seems that we all mean exactly the same, but disagree about what there is. Moreover, I would like to think that there is a substantial difference between plural quantification and first-order quantification about collections, even in areas where the latter provided a full replacement for the former.