Hi everyone (in this world and all relevantly similar ones :-),
I like the solution to the Induction / Dragon / Exploding Cow problem that I
see in work by Malcolm, Standish, Tegmark, and Schmidhuber. So I forwarded
references to Alexander Pruss, whose dissertation raises the Induction
Objection to modal realism. The full context is on my blog at
http://blog.360.yahoo.com/knowinghumans?p=8. I'm interested in how the
folks on this list would respond to Pruss's most recent comment, below. Can
anyone recommend a primer on probability in transfinite contexts like ours?
--------------------------------
Remember that I am working in David Lewis's framework. Each world is
a physical object: a bunch of matter, connected together
spatiotemporally. So I do not need to work with specifications, but
with concrete chunks of stuff. There is nothing further illuminating
to be said in a lewisian context, really, about what makes two
concrete chunks of stuff the same chunk, is there?
That said, I am making an assumption that there is only one copy of
each world. I suppose one could recover the "measure" the authors
you cite have if you suppose that there is a copy of each world for
every arrangement-description of it. But I do not see why one would
suppose that.
In the Lewisian setting, it is intuitively plausible that the
probability that I exist in w1 should equal the probability that I
exist in w2, as long as w1 and w2 contain intelligent observers in
equal numbers. The "measures" from the authors you cite do not
satisfy this criterion IF there is one world for a class of
equivalent descriptions, as is going to be the case under the
assumptions I am making.
Most observers are going to be in worlds with a much higher
cardinality of stuff than our world contains. Our world probably
only has a finite number of particles. The cardinality of worlds
just like ours until tomorrow but where \aleph_8 neutrons appear in
San Francisco down-town, causing everything in the universe to
collapse is much greater than the cardinality of regular worlds. In
fact, I think what I am saying here will apply even on information-
theoretic measures. (The one or two papers you linked to that I
looked at made the assumption that there was a fixed maximum
cardinality of things. But why assume that?)
---------------------------
For one thing, Pruss seems mistaken to assume that a possible world consists
necessarily of matter in a connected spacetime. (I think he inherits this
mistake from Lewis, who uses spatiotemporal connectedness rather than causal
connectedness to define worlds, because Lewis wants to explain/define
causality instead of making it a primitive.) It seems better to define a
possible world as a causal closure than as a spatiotemporal closure.
But the main problem perhaps is that Pruss misses (or disagrees with?) the
point that in the information-theoretic paradigm for specifying possible
worlds, the number of worlds with unobserved/unobservable irregularities
will vastly outnumber the ones with the observed irregularities like his
example, even if those irregular worlds vastly outnumber the lucky few
worlds that are like ours and have no irregularities whatsoever, even
unobserved/unobservable ones.
Received on Tue Jun 14 2005 - 12:32:05 PDT