On 1/7/2017 2:23 AM, Bruno Marchal wrote:
On 07 Jan 2017, at 02:42, John Clark wrote:
On Thu, Jan 5, 2017 at 3:18 AM, Bruno Marchal <marc...@ulb.ac.be
<mailto:marc...@ulb.ac.be>>wrote:
>>
It is insufficient to explain what a computation is, what is
needed is an explanation of how to perform a calculation. In
textbooks on arithmetic it will say something like "take this
number and place it in that set" but how do I "take" a
number and how do I "place" it in a set without matter that
obeys the laws of physics?
By using the representation of finite sequence of number by a
number, for example by using Gödel's numbering
What!? that's just passing the buck! How can anything be "used" by
anything if matter that obeys the laws of physics
is not involved somewhere along the line ?
because with the standard definition of computation, they exist and
are realized in all models of Robinson Arithmetic. The definition of
computation does not involve matter, and indeed we can eventually
understand that matter is an appearance from the points of view of
immaterial machine implemented in an non material reality.
You do the same mistake than the people who say that a (physical)
simulation of a typhoon cannot make us wet. The usual answer to this
is that a simulation of "you + the typhoon" will make a "you" feeling
being wet in a relative way. It is the same in arithmetic, where a
simulation (actually infinitely many) of "you", below your
substitution level, will make you feel the appearance of matter
relatively to you.
No universal Turing machine can distinguish the following situations:
A physical device simulating Robinson arithmetic simulating a Lisp
universal program simulating that universal Turing machine,
and
Robinson arithmetic simulating a physical device simulating Robinson
arithmetic simulating a Lisp universal program simulating that
universal Turing machine.
Is this OK for everybody?
No. What would it mean for a UTM, a logical abstraction, to
"distinguish situations"? Sounds like a category error.
And what does it mean to simulate a physical device? All the
simulations of physical devices that I'm familiar with are really just
simulations of some high-level model of the device. Given the ubiquity
of quantum entanglement, I doubt that it is possible to simulate a
physical device in an absolute sense.
If someone believes that some primary matter is needed to get
consciousness of that matter appearance, it is up to them to explain
how that primary matter can have a role in the computation. But if you
succeed, then some primary matter has a rôle in consciousness which is
no more Turing emulable, and computationalism is false.
>>
And I still don't see how you can be blithely talking about
the set that contains all true mathematical statements and no
false ones when you must know there is no way to construct
such a set even in theory.
>
That set cannot be defined in arithmetic, but admit a simple
definition in set theory or in analysis.
**
*A definition is NOT a construction!*
Yes, that is exactly the point. We can define the set of arithmetical
true statements, and so we can *talk* about it, without being able to
construct it, or to generate it mechanically.
The collection of definable set of numbers is larger than the
collection of semi-computable, or recursively enumerable sets. The set
of computable or recursive sets of numbers is not computable.
The set of solutions of a universal diophantine polynomial equation is
semi-computable, but the set of numbers which are not solutions of a
that universal diophantine equation, although easily definable, so
that we can talk about, is not semi-computable (it is pi_1 instead of
sigma_1).
**It's extraordinarily easy to define a Faster
Than Light Spaceship, it's right there in the very name of the thing,
it's a spaceship that can move faster than light, but that doesn't
mean anybody can
construct such a thing
.
The very laws of mathematics
you keep talking about
tell
us
there is NO WAY even in theory to construct a set that has all true
mathematical statements and no false ones
;
forget practicalities you can't do it even in theory, not
even if you had a
infinite amount of
time to
work on it. So using such a set to tell us something about reality is
not permissible
under the rules of logic.
>
The whole chapter of mathematical logic known as recursion theory
studies and classifies the degree of unsolvability of such set.
*A classification is NOT a construction anymore than a definition is!*
Of course. Again that is what I was saying. Nobody said that all sets
of numbers are constructible, indeed the set of definable sets is
larger than the set of recursively enumerable set, itself larger than
the set of totally computable, recursive, sets. You make my point.
The
Faster
Than Light Spaceship is in the "vehicle" class and in the "spaceship"
class but unfortunately it is also in the "fictional" class because
nobody can construct one.
By mocking the possibility of doing theology in the scientific
way, the gnostic-atheists (believers in a Primary Physical Reality
Does "
Primary Physical Reality
" mean a belief that matter is all there is?
No. It means that a Physical Reality which has to be assumed. It means
a Physical reality which would not been able to be explained without
assuming that matter.
As I said often I used "primary" in the sense: "has to be assumed", or
"the appearance of which cannot be derived from something else".
Which illustrates the flaw in your argument. Like the simulated typhoon
that can wet the simulated you, the arithmetical you can only exist
relative to an arithmetical physics. So the physics is not
dispensable. But given that it is not dispensable, it is essential to
arithmetic and consciousness and so what is primary is meaningless.
Brent
Most people agree that biological facts do not need to be assumed.
They can be derived from the laws of chemistry. That is the reason why
few scientist would assumed a primary vital principle (vitalism).
Similarly, with computationalism, the physical facts do not needed to
be assumed (and worst cannot be assumed in fact). They have to be
derived from the statistics on all computations which exist provably
when we assume Robinson Arithmetic, (or the laws of combinators, ...).
If we can explain the mind from the sigma_1 arithmetical relations,
then we have to expain the appearance of matter by the statistics on
all computations. The Universal Dovetailer Argument explains why we
have to do that, and the interview of (any) Löbian machine shows that
it works: indeed the set of computable states corresponding to
machine's yes-no type of observation inherit a precise quantum logic
derived from the logic of self-reference. It is the logic of []p & <>t
, with p sigma_1 (that is equivalent with an arithmetic formula having
the shape ExP(x, y) with P recursive.
If so then I don't believe in it. Yes nouns exist but so do
adjectives, aka information.
>
and believer in the zero personal gods theory)
maintain the field in the hands of the clericals
How long do you suppose the
Catholic Church would last if the Pope said "There is no personal
God. God exists but He's an
invisible fuzzy amoral mindless blob
.
"
?
I would estimate about .9 seconds.
That is optimist.
But who care about the opinion of someone still using argument
per-authority in the field?
A
personal
God
who might grant us immortality if we flatter Him enough
is the only type of God that 99.9% of the 1.2 Billion Catholics are
interested in.
That's why they go to Mass on Sunday, to butter Him up.
If He's not personal then God is about as useful
to them
as a screen door on a submarine
.
Who care? We know that they are wrong (methodologically wrong at the
least) since they forbid the greek way to reason on such matter (thus:
since 523, when they banished Platonism and all "pagan non
confessional religions").
You illustrate again that you want to keep the pope and the
pseudo-religious believers happy.
You illustrate again that Gnostic Atheism is a form of catholicism.
Bruno
John K Clark
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