On 05 Jun 2017, at 21:48, Brent Meeker wrote:
Here Scott Aaronson addresses the "pretty-hard problem of
consciousness"
http://www.scottaaronson.com/blog/?p=1951
Not much time to read it all, but very interesting. But they miss the
point. They still don't listen to the machine.
I would say they (still) miss the "third incompleteness theorem of
Gödel-1931", like Penrose (and this despite I think Aaronson is aware
of the main mistake made by Penrose).
The "third theorem" of Gödel is at the end of the 1931 paper where he
explains that the proof of the second theorem (no consistent theory/
machine can prove its own consistency) can be carried out in (I prefer
to say by) the theory/machine itself.
If the machine/theory is PA, or a PA theorem prover, the second
theorem says that if PA is consistent then consistent(PA) is not
provable by PA.
The "third theorem" says that PA already knew it. It says that PA
proves (consistent(PA) -> Non(provable(consistent(PA)).
Gödel was quite quick on this, and that will be proved with all the
precision required by Hilbert and Bernays in 1939, and generalized and
embellished in an utter strange way by Löb, in 1955.
That changes everything. Consciousness becomes almost easy, but matter
needs revision.
His idea of "participation in the Arrow of Time"
I will have to look at that.
is a narrower and more technical version of my idea that
consciousness only exists in the context of an environment in which
it can both perceive and act.
Absolutely. We have already discuss this. But you don't to reify it.
I have to explain you that for the (Löbian) machine or number Gödel's
COMpleteness theorem (1930), a machine/theory/number is consistent if
and only if there is a reality satisfying its beliefs. Logicians uses
"model" for reality, but physicists uses model for theory. So I will
use reality. A reality is "modelled" by a structured collection. The
(standard) model of PA is the structure (N, 0, +, *) with their usual
intepretation.
You ask for an environment. Translated in arithmetic, this is asking
for a reality, and thus (by completeness) for consistency, which ~Bf =
Dt (D = ~B~).
When you ask, for consciousness, that we add the reality to the
machine, so that things are contextualized, your argument, in a
language that PA can understand, is to replace the simple *belief of
p* by *belief of p and consistency (of p)*. You motivate for the
passage of []p to the passage of []p & <>t.
(Note that we have Bp & Dp equivalent with Bp & Dt)
Gödel makes <>p unavailable by logic, so that indeed it makes sense,
and changes the logic, to add such a requirement. <>p means (for us,
the machine can miss this, or misapplies this, ...) the existence of a
structure (environment) which satisfies p. It is also the necessary
requirement to make sense of a probability or any measure on
uncertainty.
We get it by the passage from []p to []p & p, or Bp to Bp & p. The
idea of Theaetetus. This entails Dp. Truth and correctness implies
consistency, but consistency
does not imply correctness/truth.
You are right we must take the environment, but as we cannot justify
it, that requirement can be used to define that (type) of consciousness.
Consciousness is (first person self)-knowledge, provided more aptly by
Bp & p (than the mere representational belief Bp), so your requirement
for consciousness is more given by Bp & p & Dt. Amazingly perhaps,
incompleteness differentiates again the logics, and it corresponds
more to immediate perception, sensibility. Bp & p & Dt is less
solipsistic than the "pure" Bp & p.
The universal machine gives us already a "theory of consciousness"
which is S4Grz, and X, X*, X1, X1*, and all nuances imposed by self-
referential correctness. It is also empirically testable, as physics
should be obtained with S4Grz1, Z1*, X1*.
They should listen to the machine, or to those listening to the machine.
The physicists have the good motivations, but the bad strategy. The
logicians have the good strategy, but the bad motivation.
The book by Cohen(*) shed a lot of light on the recent origin of this
situation, and why logicians are anxious with the possibility that
logic could be applied in philosophy, theology, biology (and when I
was young, even in computer science!).
Thanks for the link, I will surely come back to it, and comment.
Bruno
(*) Cohen J. Daniel, 2007. Equations from God, Pure Mathematics and
Victorian Faith, John Hopkins Press, Baltimore.
A lot of good comments too.
Brent
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