Subject: RE:Imaginary Worlds (an early piece of an exposition)

From: [email-masked]
Date: Sun, 11 Feb 2001 17:45:13 EST

Hoooooboy! I am not going to insist that possible worlds exist; they are 
convenient devices within set theory for modeling certain kinds of linguistic 
behavior and allowing the extraction of various logical principle in ways 
that can be checked, not merely intuited. It turns out in the discussion 
here that they also help clarify some pretty ordinary notions -- or so they 
seemed yesterday. 
So, a thing in possible worlds is a set-theoretic atom, a pure subject 
(in the logical, not the psychological, sense), having only the capability of 
being a member of a set (or taking on a property) but not of having members 
(being a a property of something else). If there is more than one world (as 
there needs to be for most problems that get us into this system) then we 
need a way of finding the same thing in different worlds and we cannot do 
this by its properties (sets it belongs to) for those are exactly the sorts 
of things that vary from world to world. So, outside all the worlds -- 
transcendental -- is a function which identifies in every world in which it 
occurs each thing. (This is not a soul, since souls are in the world and 
have properties in the world, are, indeed, probably things.)
Obviously, in this sense of "the same thing," the table which is and 
always has been and always will be brown and wood can be black or plastic. 
Go to the table, find the function which identifies it in this world, check 
out other worlds accessible from this one. There is one (suppose -- there 
need not be one, depedning on how the system is set up)at least where the 
thing the function picks out in that world is a wooden table but black (even 
always black), another in which in which it is plastic, though brown, and a 
third in which it is both black and plastic. There may well also be worlds 
in which it is a pink hefffalump, my aunt Maude, and the Consitution of the 
Soviet Union (provisional draft). This is the most basic sense of "the same 
thing." And it is practically useless.
We need it to get started, but it does very little to help with the 
questions that possible worlds are meant to deal with. What I can do to 
truthfully finish "If this table were the provisional draft of the 
consitution of the USSR" -- even "it would be a sheet of paper" or "it would 
be an historic dead-end" don't seem to work with any degree of condfidence. 
A world as different as the hypotheticated one may be from this world may be 
different about history and about what one writes on and about human motives. 
Or, of course, it may be just exactly like this one but with the identities 
of the players scrambled. No guidelines are available, then.
But the whole point of possible worlds is guidelines. So, we need 
another notion of "the same thing" and it seems essential to this other 
notion that some properties of the thing carry over, not just its numerical 
identity (and, indeed, it turns out that its numerical identity doesn't 
usually matter at all). It is not the thing that matters but the way the 
thing presents itself to us that matters. But how is that? Knowing Kripke's 
habits, I suppose that table T is just the table he is sitting at when 
spinning one of his monologues for his amanuensis to reconstruct into a 
lecture, article or book. So T might be presented as "the head table in 203 
Busch Hall at Washington University." Clearly, there is no problem about 
this being black instead of brown nor plastic instead of wood, indeed 
yesterday, with a different set up, it was. To say that this is impossible 
is to take a different presentation, one that presumably involves brownness 
and woodenness explicitly. But without further justification for picking 
that presentation, that is just a cheat -- it is impossible because I have 
defined what sameness means in such a way as to render it so. It tells me 
nothing about the hypothetical logic, only about my consitions for sameness.
A further justification typically comes (one does come, after all) in the 
form of a genetic criterion, as Cowan has repeatedly demonstrated. The 
object is identified by its history, not just by its present state and 
status. This leads almost automatically back to one way of structuring 
possible worlds that puts useful kinds of restraints on them: they are the 
different foreward branchings of time from each instant (or each crucial 
instant). This provides some content to the notion that things in the other 
possible worlds are pretty much like they are in this one with well regulated 
exceptions (those mentioned in the hypothesis, say). This also has the 
advantage of making sense of the fact that, in most familiar languages (to us 
Euros, anyhow) the possible world hopping is often worked out in terms tense 
patterns, various variations of future-to-the-past.
So, starting from the table here and now, we go back to the moment of its 
creation (well, period, maybe -- I don't want to get into when it is 
definitely a table) and look over the fan of alternate futures to that point. 
Certainly along some of those timelines it gets painted black, cerrtainly 
along all of them it starts out wood. Now, can we pull an Argosy on it (I 
remember it as being Jason's ship, not Theseus's, but as pi,er points out, 
the story gets around) and gradually replace it -- or suddenly, for that 
matter ("The top is terribly scarred, let's put this plastic top on the legs 
and throw the old boards in the fire" [I'm eager to prevent the extra problem 
of what happens when we save the discarded pieces and put them together again 
beside the repaired version] and then a few years later replace the now 
scarred legs with a new plastic set -- maybe one at a time)? The genetic 
rule usually says yes, but sometimes not.

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