Title: Message
Quite often, when several of us talk about 'descriptions' and 'specifications' in relation to measure (or relative measure) of worlds, we are also implicitly or explicitly referring to a corresponding underlying ontology (so the world would not 'really' be made of 'concrete chunks of stuff') - and it is *this* underlying ontology that determines the relative frequency or measure of worlds.
Even if it is just a matter of comparing cardinalities, I can't see why that of all possible invisible combinations would be less than that of the total possible number of combinations (even assuming the unit of comparison is a s-t whole, which I don't in my paper). Lewis says something not too dissimilar here in 'On the Plurality of Worlds':
"We might ask how the inductively deceptive worlds compare in abundance to the undeceptive worlds. If this is meant as a comparison of cardinalities, it seems clear that the numbers will be equal. For the deceptive and undeceptive worlds alike, it is easy to set a lower bound of beth-two, the number of distributions of a two-valued magnitude over a continuum of spacetime points; and hard to make a firm case for any higher cardinality." [p118]
(An upcoming holiday will probably prevent any further contribution to this discussion unfortunately)
----- Original Message -----
Sent: 14 June 2005 17:26
Subject: Re: possible solution to modal realism's problem of induction

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.

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