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

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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 beenproved. The problem occurs, or at least is "easy" to prove only whenwe make the digital assumption. This entails a truncation of thesubject, local and relative (its mind code) which by the MGA isincapable to distinguish the arithmetical from the real/analyticalor substantial. If you introduce special (very special) infinitiesin both mind and matter, a non comp and materialist theory of mindan matter is not (yet) excluded.You've mentioned this several times. Can you explain theseinfinities 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 thecompetition 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, andlittle programs can achieve it and plays some role, but this can'texclude big numbers too, as ourselves, or our local environment, whichare "big" universal system, *also* emulated by arithmetic, and playingsome 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 communicableview) conscious state play a role in the measure, and the1-indeterminacy bears on all those states, independently of thetime-step of the UD, or the complexity of the proof of the sigma_1sentences in elementary arithmetic, so that the global (on the UD*, oron sigma_1 arithmetical truth) indeterminacy domain is infinite, evennon enumerable, as it already contains the subcomputations emulatingarbitrary 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, andthis includes all stream, oracles, etc.So with comp we expect many infinities playing some role, and thisprevents the opponents of comp to use them against comp. But someinfinities are excluded, indeed comp exclude them playing a role inthe working of the brain or the generalized brain, by definition, andso there is a room for imagining a possible "matter", working in someanalog non Turing emulable way, and, somehow diagonalizing on the manyinfinities 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 ofsingularization of identity, which is somethiong which makes no sensein comp, except in the form it is consistent.But consistency is cheap. Comp is a bit like consistency (Dt) in PeanoArithmetic (or any Löbian machine). The second theorem ofincompleteness: PA is consistent entails that PA cannot prove that PAis consistent, or equivalently PA is consistent entails that theconsistency 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 ofnon-comp. But it shows also the difficulty to build an authenticallynon-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 "myconsciousness", if only for the fun, with B being the usualcommunicable belief.

Yes, it is self-consistency in this context.

Then the second incompleteness theorem, Dt -> D~Dt, says that if I amconscious then I am conscious of my own non consciousness", whichmight explain why self-conscious machine, as I bet the Löbian machineare, can conceive of being unconscious, with unconsciousness being anequivalent of inconsistency. But the type of inconsistency is veryrich, and you can add nuance above G, so that ~Dt, i.e. Bf, can be thetype of "error", "madness", "lie", or "death" (like in the Kripkemodel, Bf characterizes the cul-de-sac worlds, that's why we have toadd Dt as a condition for probabilities on "next worlds" (but then weloss 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 closerto the trivially provable Dt v t, making consciousness "trivial" fromthe 1p view of the machine.But consciousness is not yet that! It is more Dt v t with anunconscious (instinctive, automated) interrogation mark. It is evenmore t v Dt v DDt v DDDt v ... with an interrogation mark, which canbe perceptible by introspection, but never communicable. That canclimb 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

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