On 12/23/2012 11:19 AM, Bruno Marchal wrote:


On 26 Oct 2012, at 21:19, meekerdb wrote:

On 10/26/2012 6:19 AM, Bruno Marchal wrote:
Well, in defense of Craig, or of the devil, this has not been proved. The problem occurs, or at least is "easy" to prove only when we make the digital assumption. This entails a truncation of the subject, local and relative (its mind code) which by the MGA is incapable to distinguish the arithmetical from the real/analytical or substantial. If you introduce special (very special) infinities in both mind and matter, a non comp and materialist theory of mind an matter is not (yet) excluded.

You've mentioned this several times. Can you explain these infinities and how they function?

Sorry for answering late.


Comp and the comp indeterminacy predicts that if we look below our (sharable) comp substitution level, we should find the trace of the competition between infinities of universal machines.

Dear Bruno,

This looks like what we see in quantum field theories before the renormalization kludge is applied...

Clearly there are "little winner", as universality is cheap, and little programs can achieve it and plays some role, but this can't exclude big numbers too, as ourselves, or our local environment, which are "big" universal system, *also* emulated by arithmetic, and playing some role in the measure.

I think that the measure is defined by relations between "little winners", their common moves that leave their equilibria constant.

All programs leading to our genuine (from the 1p non communicable view) conscious state play a role in the measure, and the 1-indeterminacy bears on all those states, independently of the time-step of the UD, or the complexity of the proof of the sigma_1 sentences in elementary arithmetic, so that the global (on the UD*, or on sigma_1 arithmetical truth) indeterminacy domain is infinite, even non enumerable, as it already contains the subcomputations emulating arbitrary dovetailing of the programs on non enumerable rings (R, C, ...).

yes, the players of the game must be able to distinguish themselves from the others...

The UD does not dovetail on all programs, but also on all data, and this includes all stream, oracles, etc. So with comp we expect many infinities playing some role, and this prevents the opponents of comp to use them against comp. But some infinities are excluded, indeed comp exclude them playing a role in the working of the brain or the generalized brain, by definition, and so there is a room for imagining a possible "matter", working in some analog non Turing emulable way, and, somehow diagonalizing on the many infinities already recoverable by comp, making non-comp consistent. Those infinities introduced by the non-comp proponents have to be very *very* special, and once introduced they might make sense of singularization of identity, which is somethiong which makes no sense in comp, except in the form it is consistent.

But consistency is cheap. Comp is a bit like consistency (Dt) in Peano Arithmetic (or any Löbian machine). The second theorem of incompleteness: PA is consistent entails that PA cannot prove that PA is consistent, or equivalently PA is consistent entails that the consistency of (PA is not consistent)

Dt -> ~B Dt
Dt -> D~ Dt  (consistency entails the consistency of inconsistency)

This seems to need weakening as it implies that a sentence that is inconsistent is inconsistent for all cases. Within intuitionistic logics we can see that the inconsistency can be broken so we haev a notion of relative consistency and its inverse or dual, relative inconsistency.



So it is not so astonishing that comp can show the consistency of non-comp. But it shows also the difficulty to build an authentically non-comp theory of mind/matter.

It would be impossible, for a non-comp theory would have to be non-constructable by definition, no?


Consciousness is very near consistency. You can read Dt as "my consciousness", if only for the fun, with B being the usual communicable belief.

    Yes, it is self-consistency in this context.


Then the second incompleteness theorem, Dt -> D~Dt, says that if I am conscious then I am conscious of my own non consciousness", which might explain why self-conscious machine, as I bet the Löbian machine are, can conceive of being unconscious, with unconsciousness being an equivalent of inconsistency. But the type of inconsistency is very rich, and you can add nuance above G, so that ~Dt, i.e. Bf, can be the type of "error", "madness", "lie", or "death" (like in the Kripke model, Bf characterizes the cul-de-sac worlds, that's why we have to add Dt as a condition for probabilities on "next worlds" (but then we loss the Kripke accessibility relation, etc.))

Is this like how a sane person can constantly ask themselves if they are crazy, but a truly insane person cannot even imagine themselves as insane?


Consciousness is not consistency, to be sure, as you need the knower, which is not defined by Bp, but by Bp & p. So consciousness is closer to the trivially provable Dt v t, making consciousness "trivial" from the 1p view of the machine. But consciousness is not yet that! It is more Dt v t with an unconscious (instinctive, automated) interrogation mark. It is even more t v Dt v DDt v DDDt v ... with an interrogation mark, which can be perceptible by introspection, but never communicable. That can climb on the transfinite.


    This looks like you are working toward a monadology!




Also, the comp theory of consciousness makes it effective,

What does "it" refer to?..."comp theory" or "consciousness"?

This inspired me to say two words on consciousness above.

I think "it" refer to matter or physics, probably.

Bruno





--
Onward!

Stephen


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