Re: this very moment

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Sat, 13 May 2000 17:12:12 +0100

----- Original Message -----
From: Brent Meeker <meekerdb.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: 12 May 2000 20:53
Subject: Re: this very moment


> I thank Alastair Malcolm for his clear exposition of the multi-verse
> explanation of why induction is reliable. As a defense of induction
however
> I'm not sure it avoids vicious circularity. Without the technical
concepts of
> bit strings and algorithmic complexity (which I did find helpful) I think
the
> argument is as follows:
>
> 1. There is an ensemble consisting of every describable universe.
Descriptions
> must be logically consistent, since otherwise they fail to describe.
>
> 2. Some of these are described by a set of laws; by which is meant a
> mathematically consistent set of statements and inference rules from which
> everything about the universe follows.
>
> 3. Some universes will include being like ourselves, i.e. somewhat aware
of the
> world and ourselves.
>
> 4. Among those that contain sentient beings, almost all will be of the
kind
> describable by laws - this follows from what we think we know of physics,
> evolution, the brain and the mind.
>
> 5. Among those containing sentient beings and describable by laws, those
> describable by laws without exceptions, i.e. with reliable induction, will
> predominate. Note that exceptions are not logically inconsistent with the
> laws, they are just additional axioms that specify exceptions.
>
> But how does 5 follow? Malcolm claims it follows because he considers
> the desriptions as bit strings and for a fixed length (and hence a fixed
number
> of possible strings) he notes that those that contain a simple, i.e.
> short, description plus other stuff consistent with that description will
> outnumber those that contain the same short description plus other stuff
that
> describes exceptions.
>
> This is not clear to me. Is the other stuff on the bit string allowed to
be
> just noise, i.e. not describing anything? In that case I think the
conclusion
> follows. But this seems to turn on a certain interpretation of the
ensemble of
> all describable universes; namely that a description can include stuff
(bits?)
> that don't describe. If instead we say that descriptions do not contain
extra
> stuff that doesn't describe anything; then it seems that the extra bits,
over
> and above the simple law-like description, must contain either describe
things
> that are consistent with the law-like part or describe exceptions. But
then it
> is no longer clear that the possible extra stuff that is consistent is
more
> numerous than the possible extra stuff that describes exceptions. In fact
it
> seems to be the other way around.

This highlights a key part of the analysis. In any natural ordering of all
possible formal systems (conventionally: simplest first), one cannot assume
that as one randomly adds axioms (or bits encoding something equivalent or
similar), they will always (or even mostly) be relevant to the universe
described by the rest of the formal system (and they may not be visibly
relevant, even if relevant). (Strictly speaking we cannot anyway add
universe-affecting axioms to an already consistent physical theory, but
we'll ignore that technical point.) Because we have an infinity of
possibilities, new axioms/bit-segments are far more likely to specify new
entities/variables/universes than to specify adjustments to a (finitely
specified) existing universe.

> In any case our reason for supposing the world to be law like is already
> because we believe in induction; not the other way around. Hence in using
what
> we know of science and life, which is all based on induction, in step 4 we
already introduce circularity into the argument. But maybe not vicious
circularity
> - that's what makes it interesting.

I am afraid I fail to see any relevant circularity here, vicious or
otherwise. Note that the particular argument in my post takes the AUH
(plenitude) as a premise, so there cannot be circularity at that point.
Perhaps you might like to spell out exactly where you think the circularity
arises, and then I could comment further.

Alastair
Received on Sat May 13 2000 - 09:18:13 PDT