From pycyn@aol.com Sun Feb 11 14:45:27 2001 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_0_3); 11 Feb 2001 22:45:16 -0000 Received: (qmail 88150 invoked from network); 11 Feb 2001 22:45:16 -0000 Received: from unknown (10.1.10.27) by l10.egroups.com with QMQP; 11 Feb 2001 22:45:16 -0000 Received: from unknown (HELO imo-r12.mx.aol.com) (152.163.225.66) by mta2 with SMTP; 11 Feb 2001 22:45:15 -0000 Received: from Pycyn@aol.com by imo-r12.mx.aol.com (mail_out_v29.5.) id r.7f.100a2066 (4325) for ; Sun, 11 Feb 2001 17:45:13 -0500 (EST) Message-ID: <7f.100a2066.27b86ff9@aol.com> Date: Sun, 11 Feb 2001 17:45:13 EST Subject: RE:Imaginary Worlds (an early piece of an exposition) To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_7f.100a2066.27b86ff9_boundary" Content-Disposition: Inline X-Mailer: 6.0 sub 10501 From: pycyn@aol.com --part1_7f.100a2066.27b86ff9_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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. [How does this one look? Off Wordpad] --part1_7f.100a2066.27b86ff9_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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.

[How does this one look?  Off Wordpad] --part1_7f.100a2066.27b86ff9_boundary--