On Wed, 25 May 2005, Russell Standish wrote:

On Tue, May 24, 2005 at 10:10:19PM +0100, Patrick Leahy wrote:

Lewis also distinguishes between inductive failure and rubbish universes as two different objections to his model. I notice that in your articles both you and Russell Standish more or less run these together.

I'm interested in this. Could you elaborate please? I haven't had the advantage of reading Lewis.

If what you mean by by the first is why rubbish universes are not
selected for, it is because properties of the selected universe follow
a distribution with well defined probability, the universal prior like
measure. This is dealt in section 2 of my paper.

If you mean by failure of induction, why an observer (under TIME)
continues to experience non-rubbish, then that is the white rabbit
problem I deal with in section 3. It comes down to a "robustness"
property of an observer, which is hypothesised for evolutionary
reasons (it is not, evolutionarily speaking, a good idea to be
confused by hunters wearing camouflage!)

In that case, how am I conflating the two issues? If I'm barking up
the wrong tree, I'd like to know.

It's the second point where I think you conflate two problems.

My distinction is a little different from Lewis' anyway. From my pov, it's a matter of degree, but one which makes a qualitative difference:

* Failure of induction: the past fails to predict the future. This occurs in universes a la Hume where physical laws only appear to have been followed by some massive fluke. Also in universes which always had no, or very little, regularity. I claim that as soon as regularity breaks down to this extent, SAS cease to exist, so no matter how common these cases are, we never observe them. No problem. (Lewis' defence is different).

* White Rabbit: cognizable universes require a high degree of regularity for the survival of SAS (not to mention evolution), as above. Hence induction in any cognizable universe will work most of the time (which is all it does anyway), for a sufficient set of properties of the world. The key point is that this is not *every* property, and not all of the time. Hence there should be universes in which SAS can survive pretty well, but contain a wide variety of phenomena which cannot be unified into a simple theory. An extreme case is the "rubbish" universe proposed against Lewis, in which the extra phenomena are completely undetectable. Lewis takes this as a serious objection and counters by arguing that it is not possible to say that such universes are "more likely". As scientists, I guess we would only take seriously detectable rubbish. NB: whatever the measure you use, unless extremely artificial, the rubbish almost certainly would have much higher entropy than talking White Rabbits. Think of reality has having "snow", like a badly-tuned TV.

Of course on objective state-reduction models of QM, our universe does have "snow" in the form of random quantum jumps. But this is a very regular form of snow, which does "unify" into the basic physical laws. The argument is that for some plausible measures (not yours, obviously), even
macro-scale snow is much more likely than not.

Paddy Leahy

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