On 04 Jun 2017, at 13:31, David Nyman wrote:
On 4 June 2017 at 11:47, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 02 Jun 2017, at 00:29, David Nyman wrote:
On 1 June 2017 at 18:00, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 01 Jun 2017, at 16:42, David Nyman wrote:
On 1 Jun 2017 15:20, "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 01 Jun 2017, at 15:59, David Nyman wrote:
On 1 Jun 2017 14:01, "Bruno Marchal" <marc...@ulb.ac.be> wrote:
On 01 Jun 2017, at 12:44, David Nyman wrote:
<snip>
Yes, but doesn't the comp theory itself assume the relation as if
true, in order for mechanism to make sense (which was my caveat)?
The point here is very subtle. We cannot assume Mechanism is true,
we can only assume Mechanism. We can assume it as a sort of meta-
level hypothesis. It is indeed the reason why I insist on an act of
faith, and why it is a theology.
Now, you might ask me what is the difference between assuming X,
and assuming X is true. The difference is that when we assume X,
but don't invoke the full semantic of X, and we can preserve our
consistency. By saying "mechanism is true", even in an hypothesis,
you refer to the God of mechanism at a place that is impossible.
We have something similar, but slightly simpler, for the notion of
self-consistency. Take PA. It has 6 axioms + the infinity of
induction axioms
1) Ax (0 ≠ s(x))
2) AxAy (s(x) = s(y) -> x = y)
3) Ax (x+0 = x)
4) AxAy (x+s(y) = s(x+y))
5) Ax (x*0=0)
6) AxAy (x*s(y)=(x*y)+x)
7) the infinity) (F(0) & Ax(F(x) -> F(s(x)))) -> AxF(x)
PA is consistent (I hope you are OK with this, as all
mathematicians are, except nelson)
Imagine I add to PA the axiom 8) PA is consistent. That is
8) consistent(1+2+3+4+5+6+7)
In that case there is no problem that new theory, PA+con(PA) is
consistent, and even much more powerful than PA. It proves new
theorems and it shorten many proofs.
But imagine we add the following to PA
8') consistent(1+2+3+4+5+6+7+8')
That is self-referential, but using the diagonal lemma (the D'X' =
'X'X'' trick), we can build that formula in arithmetic and add it
to PA as axiom.
In that case, we get a theory which can prove, indeed in one line
proof, its own consistency, and so, by Gödel II, that theory is
inconsistent.
The case above is more complex to describe, because it refers to
"arithmetical truth", which cannot even be defined in arithmetic.
It is almost the nuance between (Bp & p), and (Bp & V(p)). For each
partuclar p, you can write Bp & p, but you cannot define knowledge
by a general (Bx & x). It is the nuance between assuming that x +
0 = x, and using only that, and assuming True('x + 0 = x'), which
cannot be express in the arithmetical language.
Mechanism is awkward on this. Yet, this sustains your intuition
that the ultimate 3p, the outer God view, is a 0p pov.
"Out of sight, out of mind" as the proverb has it.
"Loin des yeux, loin du coeur", we say in french (which has not
exactly the same intent).
It works well with Plotinus idea that God does not exist, as it is
the ultimate reason why everything exists without mentioning ever
itself in the creation (making the idea that God can talk with us
in a direct public way nonsensical). Only the first person has
access to this, but can only stay mute.
Another example is that even if someone survives the classical
teleportation experience, he/she cannot claim that he/she knows
that mechanism is true.
OK
Still another example, even closer to what is alluded above is the
case of the notion of sigma_1 truth, or simply sigma-truth. The
notion of sigma-truth *is* definable in arithmetic, and the self-
referential sentences saying that she is sigma-true appears to be a
sigma proposition, yet it can be shown to be ... false! This is
very unlike the sigma proposition saying "I am provable", which is
always true! All this despite G* proves (sigma-true <-> sigma
provable), but again, only G* says this, the machine has to be mute.
The machine would appear to take Wittgenstein's dictum to heart.
But its guardian angel is able nonetheless to intuit a truth in
what it cannot say.
I would not use "intuit" for the guardian angel. he is not a
subject. just a machinery who knows everything about the machine(s).
At the propositional level, he knows/proves the whole truth about
the self-referential sentence. We know it is true, only because we
limit ourselves to true machine, by decision.
So the angel is not conceived as self-referential, hence cannot be
said to possess intuition. Is that it?
Yes. Only G is self-referential, and only the provability predicate
that G models can be said self-referential. The soul can be said to
refer to itself implicitly, given that it has no name. G* is entirely
devolved in talking about G, or the machine. That makes it being both
consistent and having a sort of omniscience-about-the-machine, but he
never refer to itself. In Forever Undecided, Smullyan amuses himself
in reading G* like if he was referring to itself, but that makes him
"queer". Indeed G* proves Dt and ~BDt, which really means that G*
knows that the machine is consistent and that the machine cannot prove
its consistency, but interpreted self-referentially, that would mean
that G* believes in its consistency and would believe that he does not
believes in its consistency. G* remains consistent but get queer: he
believes in some thing and believes that he does not believe in that
thing, like someone who would say both that "God exists" and say " I
don't believe that God exist"s.
I cannot say "if mechanism is true then the truth of mechanism go
without saying", but I can say at the meta-level "If mechanism then
the truth of mechanism go without saying". I think.
Perhaps "if mechanism is true" is close to what Brent calls a
reification.
Hmm... Brent does not use "reification" correctly. He accused me of
reifying arithmetic, when I said that he reified primary matter. but
arithmetic is assumes, not reified in anyway. Primary matter is
reifed, as it is an appearance only, and its assumption is uded to
avoid solving a question. It is like "God made it".
To say "mechanism is true" is more a logical mistake, although a
very subtle one, based on Tarski theorem of the undefinablity of
truth.
Well, on the basis that truth is correspondence with the facts,
there is no fact of the matter that mechanism is true.
Why? If mechanism is true, you survive teleportation when done at some
right substitution. The fact might not be verifiable, but is still
either true or false.
But nevertheless it (i.e. mechanism) can simply be assumed. I'll
continue to ponder the distinction.
Don't mind too much. I am currently writing a paper on the
"blaspheme" (and illumination), so I am right now oversensible on this
distinction, but to be franc, I get it only with the mathematical
logic and it is counter-intuitive. I am not even entirely glad on the
way I express myself on this. It is related to the fact that a
(strong) correct machine M1 can prove the theology of a simpler
correct machine M2, and that theology is true on M1 too, yet the
machine M1 cannot rationally justify that theology on itself. The
reason is simply that the machine M1 cannot know that she is correct,
nor even express it.
"If mechanism" on the other hand is a conjectural point of
departure from which we are then at liberty to reason. That
reasoning may then draw us towards an intuition of truth.
OK with this. technically, it is really the difference between
saying that 2+2=4, and saying that the sentence "2+2=4" is true. Or
between saying "Darwin is perhaps right" and saying God made "Darwin
perhaps right".
I am not sure I could have grasp those nuances without the help of
mathematical logic. They are quite counter-intuitive.
Yes, I think I'm inching (or even centimetre-ing) towards a
grasp of the nuances, at least some of the time.
OK, but be careful. Bohr and Feynman, and others often said that if
someone says "I understand QM", it means that he understood nothing of
it! With computationalism, there is something similar: the machine can
prove that she will will never understand it. The more she will think
about it, the more she will be skeptical, and the leap of faith to say
yes to the doctor can only grow with the knowledge the machine can
have about herself.
Computationalism has to seem false (and somehow is from the soul's
pov). That is part of the reason why consciousness has to seem
mysterious. With reflexion, we can perhaps develop a sort of meta-
intuition, or we can forget the mystery, and use the teleporter as a
bike, and get the habit, but that intuition is dangerous in the sense
that it can make us taking mechanism for granted, which is logically
inconsistent. We can't avoid the act of faith, and above all, we
cannot impose Mechanism to others. Mechanism is build in anti-
proselyte, and artificial brain sellers should add the mention "this
product might not work at all and damage fatally your identity" or
something.
It depends on one's theory of what could 'make something true' and
indeed, even more simply, 'make something' at all. That's why
computationalism has to be seen as a candidate Theory of Everything
not merely a theory of mind in isolation (which in fact it could
never be).
Indeed. We have to justify all the experience (including the physical
one) without committing oneself ontologically. For truth, "2+2=4" will
be enough, as it justifies the phenomenological truth of psychology,
theology physics, etc. (Assuming it works of course).
So one needs to grasp the means by which anything whatsoever could
be said in the first place to be made, to be made true, and hence to
be performed, to be perceived or intuited and so forth, exclusively
in terms of the epistemological consequences of the ontological
prerequisites of computation.
Which are "2+2=4, ...". That is the wonderful thing understood by
logicians, but virtually unknown by most non-logicians. We don't need
mechanism here: we can prove that anyone willing to accept 2+2=4 is
obliged to accept the existence of all computations. Then with
mechanism that gives all the dreams, and the question is "do the
dreams cohere enough to give stable physical realities like the one we
live right now?".
IOW, it's a principled justification of the appearance of creativity
itself on the basis of a constructive theory of origins.
Yes. especially if you use "creativity" in the sense of Post, which
has been shown equivalent with Turing universality.
Bruno
David
Bruno
(I fall myself in that trap often, but *sometimes* it is just to
avoid nuances which at some stage is a bit like a 1004 mistake with
respect to beginners ...). In our context, I told you that we are
always close to inconsistency. You seem to like the panorama we can
get from climbing a very high cliff.
Yes. Oddly enough, I'm fond of what I call "C. D. Friedrich
moments". It's dizzying sometimes.
David
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