Re: this very moment

From: Brent Meeker <meekerdb.domain.name.hidden>
Date: Fri, 12 May 2000 12:53:17 -0700

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.

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.

Brent Meeker
Received on Fri May 12 2000 - 14:00:18 PDT