I reply to Prof. Pruss:
BH: I have the vague suspicion here that by using words like
physical/matter/concrete/chunk, you're skirting the issue of how worlds are
specified in the general case, by narrowing the scope to worlds whose only
constituents are material -- literally, having mass and occupying space.
What about worlds consisting of a single point of space, populated by
(soul-like?) entities whose (of course non-spatial) internal specifications
and external relationships change over time? I fear you're taking a
short-cut that relies on our intuition that ordinary baryonic matter has a
privileged and obvious and natural way to be specified.
AP: The question of whether two chunks of matter are the same surely has
little to do with specifications.
You just did it again. Would you still say "surely" if in your statement you
replace "chunks of matter" with "souls" or "spirits" or "logically possible
entities"?
AP: just as a world should be able to contain s-t-disconnected regions,
there is nothing impossible about it containing causally disconnected
regions, unless God necessarily exists (which Lewis doesn't think, but I
do).
If two spacetime-disconnected regions are causally disconnected (such that
none of the events in each has any possibility of influence on any events in
the other), then it seems pure artifice to say the regions are in the same
world. You could as easily say that all possible events in all possible
worlds are in fact in the same world.
AP: But what, then, ARE the worlds? Are they IDENTICAL with their
specifications? Or are they concrete entities? If they are identical with
their specifications, then I do not see how to meaningfully formulate
Lewis's extreme modal realism: We would have to say something like that the
specifications are all true or something like that, and we can't do that
without contradiction since the specifications contradict one another.
I'm not sure how Lewis's extreme modal realism is inconsistent with a world
being identical with the class of specifications that do an equally good job
of specifying it. If two specifications contradict each other, they surely
specify different worlds, right?
What are the worlds? I would say they are of the same ontological category
as numbers. If our universe can be fully specified by a (possibly infinite)
bit string, then there is a sense in which it is irrelevant whether or not
ours is a "concrete" world that "really" exists. Here's something
<
http://groups.google.com/groups?hl=en&lr=&selm=3A5F7AF9.A306AAE%40eng.sun.c
om> I wrote a few years ago that gives a flavor of what I mean:
Consider gliders in Conway's game of Life. Even if nobody ever wrote down
the rules of Life, gliders would still be a logical consequent of certain
possible configurations of the logically possible game of Life. It has been
proven that Life is rich enough to instantiate a Turing machine, which are
of course known to be able to compute anything computable. So if mind is
computable, consider a configuration of Life that instantiates a Turing
machine that instantiates some mind.
Consider the particular Life configuration in which that mind eventually
comes to ask itself "why is there something instead of nothing?". Even if
in our universe no such Life configuration is ever instantiated, that
particular configuration would still be logically possible, and the asking
of the Big Why would still be a virtual event in the logically possible
universe of that Life configuration. The epiphenomenal quality of that
event for that logically possible mind would surely be the same, regardless
of whether our universe ever actually ran that Life configuration. So the
answer to that mind's Big Why would be: because your existence is logically
possible.
So pop up a level, and consider that you are that mind, and that your
universe too is just a (highly complex) logically possible state machine.
In that case, the answer to your Big Why would be the same.
Note that, while the Life thought experiment depends on mind being
computable, the logically possible universe (LPU) thought experiment only
assumes that our universe could be considered as a logically possible
sequence of (not necessarily finitely describable) universe-states. The LPU
hypothesis also depends on the thesis that physicalism is right and that
qualia and consciousness are epiphenomena.
So if EVERY universe "really is" something like the possible universe
described above, then what you talk of as "concreta" isn't fundamentally
very concrete after all, and talk of concreteness and tangibility and
materiality isn't very helpful in deciding whether two similar universes are
identical. Instead, identity becomes more a question of whether there is a
certain sort of equivalence between the specifications of the two universes.
There may be lots of ways to specify the number seven, but that doesn't mean
there are multiple copies of it.
AP: Is a world which consists of a particle of type A one meter apart from a
particle of type B, neither of which ever moves, distinct from a world which
consists of a particle of type B one meter apart from a particle of type A,
neither of which ever moves?
No.
AP: What I am getting at is that if one thinks in terms of descriptions, it
would make more sense to identify worlds with equivalence classes of
descriptions than with individual descriptions.
Precisely! What I've meant all along by a "specification" of a universe has
to do with a certain sort of equivalence class among possible descriptions,
abstracting over differences like the font size in which the description is
written. I don't know enough about Kolmogorov-complexity to know whether
what I would consider the same universe can have multiple minimal
K-specifications.
AP: Lewis is wrong to suppose the numbers are equal. To get that, he needs
to assume that there is an upper bound on the cardinality of things in a
world, but his reasons for supposing such an upper bound are wrong. He
neglects the possibility that there may be multiple things, even infinitely
many, at one point in s-t.
I agree it would be wrong to assume that there can only be one thing at one
point in spacetime.
I clearly need to learn more about infinite measures, but my intuition is
still that apparently regular worlds should predominate over apparently
irregular worlds, even if apparently irregular worlds predominate over
worlds that in fact contain neither apparent nor non-apparent
irregularities. I've yet to hear (or at least understand) anything that
contradicts this intuition.
Brian Holtz
blog:
http://knowinghumans.net <
http://knowinghumans.net/>
book:
http://humanknowledge.net <
http://humanknowledge.net/>
Received on Mon Jun 27 2005 - 11:16:58 PDT