On 07 Apr 2010, at 10:32, Skeletori wrote:

I would define intelligence by an amount of self-introspection
ability. In that case the singularity belongs to the past, with the
discovery of "Löbian machine", that is universal machine knowing that
their are universal.
This makes all humans intelligent, as far as they have the courage and
motivation to introspect themselves enough, and be aware of the
unnameability of truth and correctness. As far as you are (luckily)
'correct', Löbian machine like PA or ZF are as intelligent than you
and me, despite having different knowledge (even different
arithmetical knowledge).

Hi! I have a couple questions. If you say that a human is Löbian, does
it only apply to the special machinery that is able to process this
logic, or the whole human, whatever that is?

It applies to all self-referentially correct "state", or relative "beliefs system".
The boundary depends on what you are ready to identify with.

I may be way off but ISTM that if there was a Löbian machine in the
real world it would have to prove its own incorruptibility (from
itself and the environment) before it could use its logic to derive
any facts about the world.

On the contrary Löbian machine, when "incorruptible", are able to prove (believe), and know (when true) that they cannot prove theor own incorruptibility. Actually they cannot even express that "correctness" concept, but they can define it for simpler löbian machine, and abot themselves, they can prey, hope, bet, and evaluate plausibility. Like 'ideal scientists" they know that they cannot *prove* anything about *reality*. We can't even prove there is a reality. They can just build theories, and hope that *reality* refutes them, or tolerate them, for awhile.

Would this in practice reduce Löbianity to
an approximation, an imprecise model that can be "merely" useful?

On the contrary. Löbianity is the real thing. *we* are the approximations. I would say. Assuming digital mechanism, of course (see my papers for the reasoning, check my url, or the archive, if interested).

"real matter" is a product of our "soul" itself being the Knower, (Bp & p) corresponding to the Löbian machine (G + p -> Bp). So the whole point, in a nutshell, is that IF we are machine, THEN the laws of physics are given by an intensional variant of the mathematics of self-reference, and this makes digital mechanism experimentally testable. Up to now, quantum physics (especially) confirms that theory/ belief/idea/hypothesis.

The advantage of this theory (digital mechanism), is that it leads to double theories, taking into account the difference between provable and true (and sometimes non provable yet still accessible). At the physical intensional variants (arithmetical hypostases) it gives an homogenous theory of both quanta and qualia, which does not depend on our (unknowable) mechanist substitution level, nor even of the existence of oracle, random or not. If mechanism is true, the couplings 'consciousness/realities' emerge from inside from the positive integers laws of addition and multiplication (I argue!).



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