On 8/15/2014 11:40 AM, Bruno Marchal wrote:
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".
But neither does physics is what wins the measure competition. And I can point to the
physics I mean. You can't point to the measure competition.
Then the MGA shows that you will need magic (non Turing emulable, and non FPI
recoverable) infinities to define what is that "primitive matter",
I've said repeatedly that I don't postulate "primitive matter" only "necessary matter". I
agree with you that primitive matter (like truth) is indefinable.
and it has to have some magic to do the selection, and zombify all other
computations.
All other besides what? Those that support human-like consciousness? I have no problem
with those existing and applying anthropic selection. If there's a multiverse as implied
by the UDA then some universes may not have any physics or at least none that supports
conscious beings.
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?
I haven't argued that it missed something. I argued that it had to include more for step
8 to work - it had to include so much that it amounted to creating another world in which
the consciousness could occur.
The only things I see, is a possible inflation of histories, but then the intensional
variants illustrates why that does not necessarily happen,
??
Brent
like in QM, there is a rich structure, so that UDA does not refute comp, yet.
Bruno
Brent
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