On 22 Feb 2016, at 00:33, John Clark wrote:
On Sat, Feb 20, 2016 Bruno Marchal <[email protected]> wrote:
> no machine can correctly know which machine it is.
As would be expected given the fact that matter is generic.
I am alluding to Post understanding that incompleteness shows only
that machine cannot know which machine it is. Something rediscovered
by Benacerraf and others, but were some errors remains.
Intuitively, this is more related to the fact that two identical
computers, put in two different rooms can generate the same
consciousness, making that consciousness unable to know which room
number is written in the envelope, or put in another way, to the First
Person Indeterminacy (FPI): the fact that no machine can know
*introspectively* which computations support it among the infinitely
many emulated in any completion of any universal system.
Then we have in particular that a universal machine cannot know if
she is supported by the arithmetical reality, or by some God in the
sense of Plato (that is physical universe or something or someone else).
In the formal treatment, this is recovered by the fact that G* proves
the extensional equivalence of all intensional variants of
provability, and G* proves the non intensional equivalence of thoise
variants, by constructively ascribing them different logics
(intuitionistic/epistemological for the first person singular, quantum
logic for first person plural and matter, etc.).
> It requires a personal bet on some substitution level.
And given the fact that every time the matter in your brain
changes your first person experience changes
There are infinitely many changes in the matter which would not affect
change in the first person experience. My mind is independent of all
changes made below my substitution level, which exists by the digital
mechanist assumptions. I guess you mean some special changes in the
matter, then OK.
and every time your first person experience changes the
matter in your brain changes
That is more correct.
it seems like a very good bet indeed that matter is required for
your personal experience. But any matter will do because it's
generic.
Including the matter which only appears to be material, but is really
a projection of the first person, which makes my point that, by being
"generic", we get that matter does not need to be assumed, and
eventually, cannot even be assumed at all without endowing it with non
Turing emulable properties, making mechanism false.
> The fact that molecules needed to exist for water to be
present is irrelevalant if we need to assume primary physical objects
The irrelevant thing is that matter is primitive.
Excellent. That is part of the point. Then, as nobody as ever seen or
even been able to define primitive matter, it becomes already a sort
of phlogiston which can be eliminated by Occam razor. But step 8 shows
more, it cannot even been reintroduced at all without being magical or
non Turing emulable, and this in a testable way. The test already done
shows that digital mechanism is far more plausible than materialism.
The point is that once matter is no more primitive, it has to be
explained from some other science, like machine's theology, itself
brnach of computer science itself branch of arithmetic (or Turing
equivalent).
Primitive or not molecules are needed for water to exist
But not for being wet. With mechanism, we can conceive the complete
disparition of water on the planet or in the physical reality, still
with virtual people who can still drink, and swim in water with the
exact corresponding feelings. The point is that even "real physical
water" is of that type once we take mechanism seriously enough.
and primitive or not matter is needed for intelligence to
exist
For human intelligence, yes. The point is that for intelligence and
consciousness to be related to matter, eventually that matter can only
be recovered by a sum on all computations going through my state, or
it becomes a Matter-of-the Gap, like in bad theology or bad
philosophy. Of course this necessatitate to understand that the
prediction "W or M" is always verified by all first person view
available in the self-duplication, and is the only one.
You think mathematics alone is needed for intelligence
I think nothing, I give a proof, that primitive matter, and the mind,
need to be non Turing emulable, to attach them in a way such that the
primitiveness of that matter has any role in the mind. But then,
mechanism is contradicted, and the such primitive matter is only a
call of the god-of-the-gap to block a proof in a theory which does not
assume such god.
and I think matter is also required, but neither of us think
that intelligence is primitive, we both think it needs
something. So I don't care if matter is is
primitive and I don't see why you should either.
Once matter is not primitive, it must be recovered by the math of self-
reference, making the digital mechanist hypothesis testable, and it
works, notably intuitively, as we get a MW Internal interpretation of
arithmetic, and formally, as we get from this already a quantum logic.
>> And Harry Potter can perform magic in JK Rowling's
fictional mindscape.
> But if the teacher of your kid teach them that it exists a
natural number x such that x + 7 = 17, you will not take your kids
out of the school, which I would certainly do if they taught that
there exist a guy call harry Potter and doing all those magical
things.
Harry Potter as depicted in in Rowling's books can perform real
magic every bit as well as a Turing Machine depicted in a textbook
on computer theory can perform real calculations.
Yet, nobody complains when seeing a statement like x + 1 = 17 is
soluble, when used in applied sciences. But try to publish a paper in
a science journal invoking Harry Potter's magic ...
So, I think that you are not correct here. The fact that 17 is prime
can have physical or biological consequences, but the fact that Potter
can fly has none. The fact that 17 is prime can be proved in any
Turing complete theory, with the usual standard definition, but there
is no such thing as a standard account of magic (or if you believe
there is, then you make my point even more efficaciously, as you would
introduce magic directly in your account of science: no need to even
go farer than step 3 indeed, in that case).
> The notion of Turing machine does not assume anything in
physics.
Then how does it assume the Turing Machine's tape is moved if
the acceleration of the tape is not equal to the tape's mass
divided by the force applied to it? For that matter how does
anything move, how does anything change?
Turing's tape is not physical. See how Matiyazevitch proves that any
Turing machine can be emulated by Diophantine equation, without any
reference to anything physical.
> The physical implementation of a Turing machine needs the
laws of physics.
And Harry Potter can perform magic, he just can't do the
"physical implementation" of magic.
You reassure me a little bit. There relies the difference.
And in Catholic transubstantiation bread and wine is turned into the
body and blood of Jesus Christ, it's just not the "physical
implementation" of Jesus. And if you believe that there is a bridge
I'd like to sell you.
> The notion of implementation is definable in arithmetic.
Irrelevant. Definitions can not perform calculations, but matter
that obeys the laws of physics can.
Irrelevant. definitions can not perform calculations, right, but
numbers that obeys enough laws (notably just addition and
multiplication) can. Not physically, but arithmetically, and without
magic, no Turing machine can see the difference introspectively. But
they can do test on heir most probable computations to test the
presence of not of primitive matter, and if there is such primitive
matter, computationalisme is refuted (assuming we are not in a
perverse emulation, as I have explained).
Then thanks to both Gödel theorem, and to the quantum empirical
reality, mechanism can be said to be confirmed until now.
> 1+1=2 is true independently of the fact that one beer plus
one beer gives two beers.
Yes but the effect the numbers have is NOT independent of
what the numbers represent;
But what the number represents depends on the way this or that Turing
machine (number) interpret it, through its computations, which is
itself describable as a complex) set of number relations.
the fact that one beer plus one one beer is 2 beers will effect my
decision to have a third beer, but one rock plus one rock equals 2
rocks will not. So apparently numbers can't tell the entire physical
story alone, something more is needed, something like matter that
obeys the laws of physics.
You make my point: the Gödel number of your brain cannot bring your
state of mind without the relevant universal numbers, and those must
emerges from all the numbers getting at your state. So physics must be
reduced to a mathematical measure on the sigma_1 sentences, and this,
amazingly perhaps, do the work very well.
> Once you assume you survive trhough a digital emulation, even
physical, you survive for all digital emulation,
I agree, but there is zero evidence that anything can emulate
anything unless matter that obeys the laws of physics is involved.
You don't need evidence. It is an elementary mathematical theorem,
that arithmetic or combinatory algebra emulate everything emulable.
> Computability, computations, in the Turing-Church-Post-Kleene-
Markov sense has just nothing to do with work, forces, etc.
Then things in the Turing-Church-Post-Kleene-Markov sense
can compute no better than Harry Potter can in the JK Rowling sense.
Except that there are no congress where people talk about what Harry
Potter can compute, and as a fictional element using magic, there is
no way this can be made precise.
That is different from computer science where anyone can verify
statement like all combinators can be emulated by some diophantine
polynomial equation.
> The only difference is that you claim that we need PRIMAR
matter,
AHHHHH!! I DON'T CARE IF MATTER IS PRIMARY OR NOT! How
many times do I have to repeat that?
If you don't care, why did you invoking it so many times, even for
pretending I made an extraordinary claim, where I just explained that
mechanism is incompatible with physicalism, or materialism or the
belief in primary matter?
>>> It is the person which is conscious, not the Peano
axioms, which is more like a body.
>> And both the person and the body are made of matter that
obeys the laws of physics. So what are we arguing about?
> That the point above explains the appearance of that matter,
of which my body is made,
I'm not arguing how matter came to be, I'm arguing that
however it came to be you need it for consciousness and
intelligence.
Then you *do* agree with my point. When we say that A needs B, we mean
A -> B, or that ~A v B. There is no intelligent Turing machine without
matter, indeed, that is the base of deriving matter and its laws,
phenomenologically, from computer science.
I have always insisted that it is *primitive* matter (the second God
of Aristotle) which needs to be thrown away, once we postulated
Mechanism. It is materialism and/or physicalism which is the problem,
not physics which is the best tool to test mechanism, and indeed to
confirm it thanks to QM (without collapse).
Good, you defend the point that I was arguing for all along. You have
just recalled the main theorem of the thesis.
Note that the interest in the proof I give is that it is constructive:
it explains how to derive matter, even the appearance of primitive
matter, from the logic of self-reference of the Löbian universal
machine (that is the universal machine which can prove that she is
universal).
Bruno
http://iridia.ulb.ac.be/~marchal/
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