Alex Pruss wrote:
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?
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.
By the way, I think I disagree even with the the spatiotemporal stipulation of Lewis. It makes more sense to me to define a world as a causal closure rather than a spatiotemporal closure, but perhaps that would give up on an ambition of Lewis to analyze causality rather than consider it a primitive. For example, what if a world consists of two disconnected regions of space, between which there can still be causal relations? Would Lewis just say that the events are temporally related even though not spatially related? (Hopefully he wouldn't try to introduce some extra spatial "dimension" by which to allow a coordinate specifying which region, as such an effort could I think be confounded.) If so, then maybe my disagreement with Lewis is that I would define time in terms of causation, where he would define causation in terms of time....
That said, I am making an assumption that there is only one copy of each world.
As I understand it, a virtue of the information-theoretic perspective is that if we define worlds as one-to-one with their minimal K-specifications, we don't have to bother with questions like whether there can be copies of worlds.
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.
I'm a novice when it comes to the concept of measure, but my sense is that these many-worlds theorists restrict themselves to methods of world-specification in which different specifications map by definition to different worlds.
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.
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 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. However, there might be a sense in which one or the other class of worlds predominates even without a difference in cardinality. There is a good sense, for instance, in which the primes are an infinitesimal minority among the natural numbers, even without any difference in cardinality: their limiting relative frequency is zero. We cannot take a limiting relative frequency among the worlds, for lack of any salient linear order;
(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?)
I'm not sure which assumption you mean. Can you point it out in e.g. Malcolm or Standish? (I'm cc'ing them by virtue of firstname.lastname@example.org.)
(For earlier context and links, see http://blog.360.yahoo.com/knowinghumans?p=8.)