RE: possible solution to modal realism's problem of induction

From: Brian Holtz <>
Date: Wed, 15 Jun 2005 22:02:19 -0700

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

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

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.

That depends on what you mean by "regular" worlds. If you mean worlds just
like ours with no deviation from our laws, you may be right. But if you mean
worlds apparently just like ours due to having no observed deviation from
our laws, my intuition is to disagree.
Alastair Malcolm points out
( that Lewis
addressed this subject in On The Plurality Of Worlds, p. 118:

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;

My suspicion/hope is that the work I cited by Malcolm/Standish/Schmidhuber
suggests an approach to defining such a linear order, by which we can judge
that apparently regular worlds predominate over apparently irregular worlds.
(Alastair, Russell -- am I reading you correctly?)

(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

Best wishes,

(For earlier context and links, see

Brian Holtz
Received on Thu Jun 16 2005 - 01:05:24 PDT

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:10 PST