Re: Bruno's argument

From: Bruno Marchal <>
Date: Sun, 23 Jul 2006 17:06:52 +0200

Le 22-juil.-06, à 22:02, Brent Meeker a écrit :

>> No bigger than the "assumption" that "other" minds exists (a key
>> assumption in comp if only through the trust to the doctor).
> Aren't those two propositions independent - that there are other minds
> and that we cannot possibly
> know what their experiences are like?

Not with comp. Other minds have personal experiences, and if they are
vehiculated by a software having a complexity comparable to your's,
those personal experience are knowable only by empathy, for you. Not
3-describable knowledge.

>> And then it is a theorem that for any correct machine there are true
>> propositions about them that the machine cannot prove.
> And there are true propositions about itself that the machine cannot
> prove - but are they
> "experiences"? Certainly there are myriad true propositions about
> what my brain is doing that I am
> not, and cannot be aware of, but they aren't experiences.

I don't try to use a sophisticated theory of knowledge. You mention
yourself "knowing" can be given by true justified opinion (Theaetetus).
I take "provability of p" as a form of justified opinion of p: Bp.
Then I get knowledge by adding that p is true, under the form "& p".
Limiting ourself to correct machine, we know that Bp and Bp & p are
equivalent, but the key (godelian) point is that the machine itself
cannot know that for its own provability predicate, making the logic of
Bp & p different. It can be proved that Bp & p acts as a knowledge
operator(*) (S4 modal logic), even a "temporal one" (S4Grz logic), and
even a quasi quantum one with comp: S4GRz1 proves LASE p -> BDp
necessary to get an arithmetical interpretation of some quantum logic.
So "non provability" is not the way I "model" experience in the lobian
interview. I model experiences and experiments with *variant* of G and
G*, the logics of provable and true provability respectively.
The variants are obtain by adding "& p" or "& Dp". This could sound
technical, it is, sorry.


(*) Which I should have recall to Russell (it is the best justification
for the "& p"). Artemov has shown that it is the only one possible(*)
if we decide to restrict ourself (as I have done) to what Russell call
"mathematical knowledge", but if Russell agrees with the UDA, this
should not cause a problem (especially knowing that S4Grz describes
mathematically a form of knowledge which cannot be put (knowingly) in a
mathematical form. That's admittedly counter-intuitive and subtle and
explains why I need to get people familiar with many similar
counter-intuitive propositions which all are obtained directly or
indirectly from diagonalizations.


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Received on Sun Jul 23 2006 - 11:09:06 PDT

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