On 14 Aug 2014, at 19:41, meekerdb wrote:
On 8/14/2014 1:09 AM, Bruno Marchal wrote:
On 13 Aug 2014, at 21:47, meekerdb wrote:
On 8/13/2014 7:01 AM, Bruno Marchal wrote:
Does Bruno actually say what he thinks consciousness is? (This
is probably somewhere beyond the MGA, which is where I tend to
get stuck...)
When I've asked directly what it would take to make a robot
conscious, he's said Lobianity. Essentially it's the ability to
do proofs by mathematical induction and prove Godel's theorem.
But "ability" seems to be just in the sense of potential, as a
Turing machine has the ability to compute anything computable.
That is what you need for your robot being able to be conscious.
OK. But to be conscious, you need not just the machine/man, but
some connection with god/truth.
To put is roughly the believer []p is never conscious, it is the
knower []p & p who is conscious. It is very different: []p can
be defined in arithmetic. []p & p cannot be defined in
arithmetic, or in the machine's language.
But that's just an abstract definition. What is the operational
meaning of "p".
It is means true in (N, +, *).
That's not operational.
Indeed. but p here is for the truth of p, and that has no operational
definition. It is not computable, unless true and sigma_1.
The only operational meaning of true derivable in (N, +, *) is
true=provable,
That will not work. You have an infinity of different bigger and
bigger notion of proofs.
RA-provable (contain the full sigma_1 truth, but a quite tiny part of
the pi_1 truth)
PA-provable (contains a *much* larger part of the pi_truth, almost all
the "interesting" mathematics, but still an infinitesimal part of the
pi_1 truth)
ZF-provable (contains a *vastly* much larger part of the pi_1 truth ,
but still not the whole pi_1 truth, indeed "ZF is consistent" is an
arithmetical pi_1 sentence)
ZF+Ex(x = kappa), with kappa a very big cardinal (so big that you can
define set theoretical truth in that theory), but you will still miss
the pi_1 truth that ZF+Ex(x = kappa) is consistent, but you do extends
the set of arithmetical propositions you can prove.
etc.
You can easily define the notion of arithmetical truth in ZF, like you
can define set-theoretical truth in ZF+j-kappa, and that asks for less
than some work in topology, not to talk on category theory. The
definition will indeed not be operational, but that is the case of
many definition, already in analysis.
Except for RA, a bit too weak, all those provability notions are all
Löbian.
but it's essential to your theory that there are true and unprovable
propositions.
Unprovable by this or that machine. yes. For all machine there are
infinitely many such unprovable proposition, some concerning them. It
is their theology.
You can believe there are such propositions and prove that there
must be one, but can you actually produce one?
"I am consistent". If true, I can't prove it. But I can hope for it.
In other words it seems you can get []p, and [][]p, and [][][]p...
but you can't get to p.
I can get to p, by proving p. I cannot assert that p is true (as I
cannot define true), but I can use a simple generic truth, like the
constant t, or like "0= 0" and proves that p is equivalent with it. I
do that implicitly in proving p. Then from that p, I can even prove
[]p -> p. By Löb, that will be the only case in which I can prove []p -
> p. In particulat I cannot prove []f -> f (if I am consistent).
This cannot be defined in PA, but you don't need to define it in
PA, to get the needed consequences.
If consciousness depends on knowing and knowing depends of my
belief being true, then I will be unconscious if my belief is
mistaken.
Not necessarily, because although your belief is false, you can
still have the true belief that you believe it.
Yes that's [][]p & []p. But people who believe the Earth is flat
are not believing that they believe the Earth is flat. Yet they are
conscious.
Well, in this case they are not conscious that they believe the earth
is flat, but they might still be conscious of something else. Then.
Yet it seems that []p & p, where p=f implies one is unconscious.
OK.
I don't think consciousness depends on knowing (as defined by
Thaetateus).
Agreed. It is too much. The "[]p" can be weakened, especially for the
raw consciousness. But to get the physics we need those rich
introspective machine. The other are conscious, but can't really talk
about all this.
Does mere belief, []p, already require consciousness.
No, it needs the reality intended in the proposition p, and it needs
it explicitly, only that make consciousness non representational.
That "& p" is a tour de force, as it requires God (truth) at the
metalevel, but not at the level of the numbers and its beliefs.
Or if you allow unconscious belief what does it add to require that
they be true?
Immortality. Wrong beliefs have finite life-time. The FPI select the
immortals, not the mortals.
Well, the technical point is that the Theaeteus works in the
arithmetical context of comp. It does provides a knower (S4Grz).
[]p can be false, yet [k][]p can be true. That would be the case in
a dream, for example. You believe that you can walk on water
(false), but you believe also that you believe that you can walk
and that belief is true, so you are conscious in the dream, even if
the belief that you can walk on water is false.
I recall that [k]x = []x & x.
That makes no sense. Consciousness obviously does not depend on
"& p". In my view consciousnees is creating an internal mode of
the world.
That is what []p does. It is related to the 1p consciousness of
that belief through [k][]p
The model includes propositions "p" which are more or less true
depending on their correspondence with the world.
Which world? The arithmetical reality, or a primitive physical world?
The physical world that is necessary for consciousness. Although
you said we agreed in the last post, you revert to assuming that
physical=primitive physical and that arithmetic=reality. I thought
what we agreed was that in order for there to be consciousness there
must be some kind or level of physical world that provides a
context. This is what I might refer to as "our reality" allowing
that there might be other kinds (although I doubt it) which is not
everything in arithmetic.
Bt the UD provides all the programs, and all the contexts, which are
other programs, usually universal, and below our substitution level,
there is the FPI selection of a competition between infinities of
universal numbers.
A solution asserting just: there is a physical reality which makes the
selection explains not better that "God made it so". Then the MGA
shows that you will need magic (non Turing emulable, and non FPI
recoverable) infinities to define what is that "primitive matter", and
it has to have some magic to do the selection, and zombify all other
computations.
It is up to you, it seems to me, to provide <something>, playing a
role in my "computation" that the UD misses systematically, even in
the infinite union of those computations defining the FPI domain?
The only things I see, is a possible inflation of histories, but then
the intensional variants illustrates why that does not necessarily
happen, like in QM, there is a rich structure, so that UDA does not
refute comp, yet.
Bruno
Brent
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