Re: Flying rabbits and dragons

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Tue, 16 Nov 1999 18:36:17 -0000

Russell,

There seems to me to be an underlying inconsistency in what you have been
saying in this thread, or else there is some kind of misunderstanding
between us. So, if I may, I will pursue matters a little further, but try to
focus just on this main point.

> > (1) Role of TM solely as an inference engine (implementing the specific
> > transition rules of Modus Ponens, substitutivity and so on) - this
creates
> > at least two problems if it is applied to your scheme:
> > (a) An inference engine can do nothing with a non-wff (it is outside the
> > context of its application).
> > (b) Why do we have this specific TM - why not others? So we have to go
to
>
> This is indeed the role of the TM. As far as problem a) is concerned,
> all bitstrings are interpretable as valid programs. However, the
> output couble be rubbish, and may correspond to a non-wff, an
> illogical universe, or even "nothing at all" - complete
> randomness.

The picture I am getting here, in simple terms, is of one program (the
inference engine) operating as best it can on all possible sequences of
bits - some of these sequences will be 'lucky' enough to be converted to
bitstrings corresponding to theories (consistent theorem sets), but most
will be gobble-de-gook (there will also be inconsistent theories - this is
where your 'illogical universes' come in, I presume).

However, previously you have said:

>>[AM:] 3) Whether bitstrings could be immediately interpreted as anything
other
>> than symbol strings.
>
>You could interpret them as anything you like - UTM programs, axioms
>of a mathematical theory, the works of Shakespeare.

So, apparently, if the inference engine generates bitstrings corresponding
to theories, they could just as easily be interpreted as rubbish. Conversely
gobble-de-gook strings could be interpreted as consistent theories - again
we descend to unanalysable anarchy.

I think this is the main problem I have with your scheme. Less important
ones are the ontological credentials of rubbish and inconsistent-theory
bitstrings/universes, and the subjective information theory problem which I
mention in my comments on your paper.

Alastair
Received on Tue Nov 16 1999 - 10:40:36 PST