Wednesday, July 11, 2007

Absolute Generality 2: Showing and saying

Suppose I think that there is something problematic about absolutely general quantification. So I try to say "You can't quantify over absolutely everything". But either that "everything" is absolutely general, and I've illustrated how you can quantify over absolutely everything after all. Or else my "everything" is restricted, and I fail to say what I meant to say. Either way, my attempted saying misfires.

So that disposes of the anti-absolutist? Well, no ... I just need to be a bit more dialectically supple: I shouldn't assert a position myself, but rather stand ready to reveal the tempting confusion that the absolutist has fallen into. Faced with a philosopher who stakes out an absolutist position, the enlightened opponent hits him with an extensibility argument ("Ah, take those things you are quantifying over all together as one big domain; now consider the bit of the domain which contains all the non-self-membered things you were quantifying over; then that isn't one of the things you were quantifying over, on pain of Russell's paradox"). Then -- assuming of course the cogency of such extensibility arguments -- the absolutist is in trouble. Which is something the enlightened philosopher, to coin a phrase, shows rather than says.

Kit Fine, at the end of Section 2 of his paper, floats the possibility of taking this rather Wittgensteinian line. But he doesn't endorse it -- rather there are another fifteen pages in which he tries to find the words in which one might cogently state an anti-absolutist position. The idea is to go modal, and talk in particular about "postulational modalities". This, however, all gets deeply obscure. I'm going to have to read Fine's paper for a third time and try to make more sense of it. Watch this space ...

9 comments:

Enigman said...

I don't see what's so wrong with the original anti-absolutist statement: "everything" clearly means all things, whether such a totality exists (in such a way that it could be quantified over) or not. Maybe such a totality (as something that could be quantified over) is like a round square, but even so we can say that round squares don't exist...

Enigman said...

That is, isn't it just like saying that there is no such thing as everything, which we can say without contradicting ourselves?

Peter Smith said...

Sure, we can say that there are no such things as round squares. But what is the corresponding anodyne way of saying that you can't quantify over absolutely everything? "There is no such thing as everything" will hardly do, as we can ask: what is the quantifier "everything" doing in that statement? Quantifying over everything (in which case the anti-absolutist has shot himself in the foot)? Or quantifying over some other domain (in which case the anti-absolutist hasn't said what he set out to say).

Enigman said...

Sorry and all, but I don't see why "everything" has to be doing anything in that assertion (cf. how "round square" does not have to refer to anything). (Its probably not important though. Incidentally, I'm skipping ahead to Shapiro and Wright, which is brilliantly written.) If we know what "all" and "things" mean, could we say that, given absolutely any thing, if you can quantify over its members then its members can't be all things?

Peter Smith said...

Well "everything" has to do be doing something in that assertion -- it isn't semantically inert. And if it is behaving as you'd expect, as a quantifier, then the question remains, over what is it quantifying? And if it isn't a quantifier, then what?

Anonymous said...

Enigman: could it be a quantifier that is not actually quantifying over anything, just as 'round' is an adjective that is not actually describing anything, in that use?

Enigman said...

Perhaps when absolutists analyse
R = “There is no such thing as everything,”
in the usual way, we naturally but inappropriately introduce a universal quantification. Personally I don't mind a totality of absolutely all things, but since R is clearly not intended to involve a universal quantification, surely R is implicitly involved with some lesser domain, if a suitable one is available (and if R does indeed involve quantification rather than something else).

If that lesser domain is one that would include the universe were there such a thing, then the (clearly unintended) possibility that the universe might be outside the domain is avoided. E.g. we might interpret R via the (finite) domain of all totalities specified by one ordinary English word in addition to “all,” e.g. all fish (and excluding all things, if R is true). (And surely we only need some such domain in order to analyse R appropriately, rather than all of them.)

But maybe no quantification is involved? My previous thought (in my comments above) was that, if we assume that each possibility of some thing is itself a thing, then R amounts to:
“There is not even the possibility of everything,” or:
“Everything is an impossible object,” cf.
“Round squares are impossible objects.”
And just as the latter does not necessarily imply that there are impossible objects, so although we usually analyse such claims via possible worlds, surely they might instead be analysed via the meanings of the contradicting words (R asserting that “every” and “thing” go together like “round” and “square” etc.)?

Enigman said...

That is, saying that you can’t quantify over absolutely everything might be like saying that you can’t (in principle) determine the area of a round square (because it doesn't exist) rather than saying that you can't (easily) determine the area of Red Square (because you're not authorised to), and it can't be the latter on a charitable reading of the anti-absolutist's statement, although that would be the natural way for an absolutist to read those words (?)

Enigman said...

(although as a platonist, I do think that some round squares exist, e.g. 100 :)