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?)
---------------------------
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.
