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 fin the trace of the
competition between infinities of universal machines.
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.
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, ...).
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)
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.
Consciousness is very near consistency. You can read Dt as "my
consciousness", if only for the fun, with B being the usual
communicable belief.
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.))
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.
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
Brent
even in the materialist framework. The only thing not effective is
the notion of substance, and eventually (globally), of physics
(that is highly counter-intuitive, but can be understood in the big
'non physical' picture, where we cannot 'add physics" and have to
retrieve it from arithmetic and/or computer science.
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