Monday, August 06, 2007

What is logical possibility?

It is said that 1 + 1 = 2 is true in all possible worlds, that it is logically impossible for it to be false. And yet aliens might, for all we know, have made us believe that equation despite it being false. Although we might now believe that it is true by definition, and so could not possibly be false, perhaps we are wrong about that. Perhaps those terms really get their meaning in some other way, which the aliens have made us forget about. Perhaps they are preventing us from imagining how the world really is—is that not conceivable? And yet the falsity of that equation is said to be logically impossible.
......At another extreme, it is sometimes said of beings—zombies—that are physically identical to us but which do not have subjective experiences, by definition, that they are both logically possible and physically (or nomologically) impossible. It is said that they are conceivable, and hence logically possible, but that the matter of which we are composed happens to be such that our minds arise from (or supervene upon) our brains. But it seems to me that a being that was, by definition, physically identical to a being that was necessarily, by the laws of physics (of nature), conscious, would be conscious by definition, so that a zombie would be both conscious by definition, and lacking in consciousness by definition.
......That is, zombies seem to me to be logically impossible. Consider why round squares are logically impossible. If something is square then it is, by definition, geometrical, and so it must obey the laws of (Euclidean) geometry, and it is geometrically impossible for the same (Euclidean) shape to be both square and round. A round square is geometrically impossible and so, because it would be by definition geometrical if it existed, it is therefore logically impossible.
......I might imagine something that was topologically identical both to a circle and to a square, but it could not be a round square because roundness and being a square are not topological properties. And when I try to imagine a zombie I presume that just as tables are clouds of molecules so are we, and then I imagine such a cloud of molecules obeying the physical laws of nature (a bit like planets, stars and galaxies moving through the darkness), whence I am not imagining any consciousness there (in that darkness).
......But if zombies are physically (or nomologically) impossible then, insofar as what I’m imagining might be my body, there would have to be consciousness there. It is like trying to imagine both (i) that a table is a cloud of molecules and (ii) that we can have that same cloud of molecules without the table. Similarly, I have no trouble imagining a talking donkey, but were I to imagine it becoming more and more like an actual donkey, it should eventually become impossible for me to imagine it talking (assuming that actual donkeys cannot talk).


Perezoso said...

""It is said that 1 + 1 = 2 is true in all possible worlds."""

Binary works as well as base 10 number systems (better in computing contexts), so 00000010 = 2 as well (in all possible worlds?). The number-sign is NOT what the number "means." The sign refering to the "ONE-grouping" could be anything: 1, or 00000001, Ein, or P#*#$#$*(^(C, etc.

Again, that is a fairly obvious semantic--- and nominalistic--- point , but overlooked by many filosophical types.

"ONE" is a bit unusual in that it is, well, ONE, and singular. But the semantics are in a sense more important. ONE names a certain situation: one apple, one atom, one person, etc. The integers are variables, right?

I don't have the proof handy (Frege has one I think), but it's really a sort of existence claim: there exists a set x, and there is one and only individual in it, and any other assumed individuals (y, z. etc.) = x. So there is an "uniqueness." aspect, I guess. But I think the real issue is that numbers, integers (even the fancy ass ordinals and cardinals) can be in principle defined constructively, and one dares say empirically: an abacus in a sense a better guide to number theory than any platonists.

So, in a sense, 1 + 1 = 2 in all possible worlds , only if you include the little semantic story.

Anonymous said...

i don't know ... but i've been
blacked-out drunk many times.

reliable reports have me
walking, talking, and, alas,
quite often doing things
even *i* wouldn't do when sober.
but not making new memories
of *any* of it in my own mind.

anyhow, this looks like the best
description of what goes on
that i'm aware of.
and if that's not zombie-ism,
it's sure as heck close enough
for me ....

trouble with zombies (and with
philosophy of mind more generally):
it's evidently impossible
to define terms properly
(so questions of *logical*
impossibility don't really arise).