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From: Brian Holtz <brian.domain.name.hidden>

Date: Tue, 14 Jun 2005 09:26:54 -0700

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

Date: Tue, 14 Jun 2005 09:26:54 -0700

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

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