I had several exchanges with Leslie on this a year or two back and came up
against a brick wall. He is faithfully opposed to MWI on the same kinds of
daft grounds as Henry Stapp: I suspect his real objection is that it is
extravagant to have all these unused universes! Clearly Stapp refuses to
apply his intelligence to the issue. As if a 'used' universe is somehow more
'valuable' or something than the other ones! As if 'this one' is more
important than 'another one' that 'we're not in'. The most childish,
anthropocentric thing I have ever heard.
Anyway, induction does fail, water does turn into wine, etc. - even in the
Newtonian scheme of things. It just doesn't happen very often. As I
mentioned in my own scheme, this current thought includes the thought that
there are no flying rabbits being peceived. So what?
> -----Original Message-----
> From: Alastair Malcolm [SMTP:amalcolm.domain.name.hidden]
> Sent: Friday, 12 May, 2000 12:47 PM
> To: everything-list.domain.name.hidden
> Subject: WR/Induction failure problem
>
> Everythingers might just be interested in an extract from an email forming
> part of a recent brief discussion with John Leslie, who in his book
> 'Universes' (sect 4.69), dismisses the idea of all logically possible
> universes because it seems to entail the failure of induction (ie failure
> of some known physical laws).
>
> This is the extract:
>
> A defence against the induction failure challenge to the all logically
> possible universes hypothesis (ALPUH):
>
> 1. The aim is to obtain a general idea of how numbers of indistinguishable
> universes vary under any reasonable ALPUH. This general idea only needs a
> level of precision and plausibility that is sufficient to cast serious
> doubt
> on the induction failure challenge to that ALPUH. [Names used elsewhere
> for
> this challenge: white rabbit problem, dragon universes problem.] (Note
> that
> there can in principle be different ALPUH's according to how many copies
> of
> indistinguishable universes that they predict.)
>
> 2. We only need to consider the failure or otherwise of induction in those
> universes which contain thinking entities of our general kind ('self-aware
> structures' in Tegmark's terminology).
>
> 3. There are at least two general categories of ways to represent our
> universe. The first category is directly related to how we perceive it:
> this
> can be in terms, say, of percepts, or of objects embedded in space-time.
> (It
> is this way that is at the basis of the induction failure challenge.) The
> second category entails directly incorporating the physical laws that
> govern
> some or all of our universe. An example of such a way is a mathematical
> model of our universe (incorporating initial or boundary conditions). Such
> a
> formal system would be expected to be ultimately grounded in axioms, from
> which the theorems (specifying everything in the universe governed by the
> laws) would be derivable by simple rules of inference. Any events/entities
> in the universe not entirely governed by the laws (or, if one is a strict
> physicalist: any events/entities in a similar kind of universe that are
> not
> entirely governed by physical laws) would have to be incorporated in the
> mathematical representation by additional axioms (perhaps comprising in
> some
> way a simple list of its properties), and/or by adding new rules of
> inference, and/or (most likely) including adjustments to the existing
> axioms/inference rules. Note however, that all of these increase the
> complexity of the representation.
>
> 4. In any naturally occuring all logical possible universes scenario, one
> would expect the distribution of unverses to be more likely to be closer
> to,
> or actually reflect, the second category of representations than the
> first,
> partly because the second explicitly makes allowance for the physical
> laws,
> and partly because the direct view of human beings of the world (the first
> category) is governed by how we happen to have evolved to perceive it,
> which
> in turn is governed by the requirements of how to survive in our
> environment, and what features of the environment biological creatures are
> physically able to perceive. It is likely to be 'anthropically biassed'.
>
> 5. We will pursue the idea of 'all possible axiomatic formal systems' as
> an
> example of the second category, but bearing in mind that this may only be
> one possibility for this category.
>
> 6. Formal systems are expressible in terms of fundamental units - usually
> the symbol (we can add a delimiter symbol to separate axioms). So a symbol
> string of axioms, plus standard rules of inference, if well-formed and
> providing consistent theorems, will comprise a theory, which may specify
> one
> (or more than one) universe. We can have as many axioms (and inference
> rules - though it is simplest to keep these fixed if possible) as we like.
> Now all possible universes that are expressible by any formal system must
> be
> found within all possible combinations of symbols (or all possible axioms
> -
> this is easier to imagine).
>
> 7. Let us suppose that our universe (A) is minimally specifiable by m
> axioms; and another universe (B), which is identical to ours except that
> induction apparently fails at some future moment by the physical laws
> suddenly changing, is minimally specifiable by m+p axioms. (Strictly
> speaking this is misleading because we can't just specify a change in a
> law
> by adding some axioms, but the point is that B would need more axioms than
> for A.)
>
> 8. Now if we consider all possible combinations of axioms up to n, where n
> is any number greater than m+p, we find that universes indistinguishable
> from A must greatly outnumber those indistinguishable from B by the
> following reasoning. Between m+p and n we have many combinations of
> axioms available - these will not (for the most part) be able to include
> variables already functionally involved in A or B (because as theories
> they
> are already consistent), but they can include axioms involving entirely
> new
> variables - effectively specifying a different universe, or entity. For
> this
> range (m+p to n), the effect is to multiply up the number of examples of A
> and B by roughly the same amount - so this effect more or less cancels
> through. However for the range m to m+p we have a multiplier for A, but
> not
> for B (because B already requires axioms in this range to be of a certain
> type). So in total there are more examples of A than of B.
>
> 9. Bearing in mind [similar] results from other approaches falling within
> the second
> category, it seems plausible to suppose that for whatever logical unit
> (axioms/bits/symbols etc) is most applicable to the actual provision of
> all
> logically possible universes, the same underlying method will still hold
> good: simpler universes will predominate. The result explains why Ockham's
> Razor is applicable to our physical world and also why we don't find
> unambiguous cases of paranormal events: our world is the simplest possible
> consistent with the existence of self-aware structures, if the hypothesis
> is
> correct. Induction will not fail in general, because such failures would
> entail a more complex universe, which is less frequently represented (and
> so
> we are unlikely to be in it).
>
> Alastair Malcolm
> (More details: see web pages starting at
> <http://www.physica.freeserve.co.uk/p105.htm>)
>
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Received on Fri May 12 2000 - 07:28:39 PDT