On Wed, May 25, 2005 at 02:11:56PM +0100, Patrick Leahy wrote:
> >
> >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).

This is easy to assert, but less easy to prove. It also does not
explain away the non appearance of unlawful phenomena that do not
affect the observer's existence. There are still far more worlds of
this kind than lawful ones. The point I make in my paper is that the
vaste majority of these unlawful worlds will be indistinguishable from
lawful ones, or lawful ones + magic. The universal prior then comes
into play - the total measure of  lawless worlds indistinguishable
from lawful ones will be vastly greater than this indistinguishable
from lawful worlds + magic.

> * 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.

Indeed. Undetectable rubbish is not a problem. Only magic. And magic
has provably less measure :)

> 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

Yes - some on this list have speculated that quantum randomness is a
manifestation of this - can't remember what we concluded now though...


*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
Australia                                http://parallel.hpc.unsw.edu.au/rks
            International prefix  +612, Interstate prefix 02

Attachment: pgpppZTonR6yY.pgp
Description: PGP signature

Reply via email to