On 03 Oct 2015, at 04:25, John Clark wrote:
On Fri, Oct 2, 2015 at 10:21 AM, Bruno Marchal <marc...@ulb.ac.be>
wr rote
> you seem to doubt that the existence of computation in arithmetic.
Yes, I'm not dogmatic on the subject but I have grave
doubts about the existence of computation in arithmetic;
certainly nobody has ever seen even a hint of such
a thing.
You are dead wrong here, as we don't need a hint, we have a proof, and
it is in all textbook in mathematical logic. Unless you allude to a
notion of "physical computation" which has not been defined.
> your argument relies on a notion of physical computation.
Yes, I have no doubts whatsoever
about the existence of computation in physics.
I translate: ... physical existence of the physical implementation of
arithmetical computation. That is possible. But that has nothing to do
with the proven existence of computation in arithmetic. You can
emulate the (universal) computation even with only diophantine degree
four polynomial.
> When I ask what that is, your definition seems to be
"implementation of computation (in the arithmetical sense) in a
physical reality, which contradicts your statement that
computation does not exist in arithmetic.
Arithmetical objects (like numbers) can be computed
no doubt about, it but as far as we know not
by arithmetic, only by physics.
As far as you know, I would say.
> which contradicts your statement that computation does not
exist in arithmetic.
There is no contradiction, arithmetical objects can
certainly be computed but the question is what is doing the
computing,
The relative universal numbers, which exists like prime number exists.
is physics doing it or is arithmetic doing it to itself? I think
physics is more likely.
Which explains a lot. You are unaware of what is a computation in
computer science.
> you persist in confusing what is a computation in the CHurch-
Turing sense,
If "computation in the Church-Turing sense"
doesn't mean finding a particular solution to a particular
arithmetical problem then "computation in the Church-Turing
sense" INTEL would not find it interesting and neither would I.
The theory is born from reflexions in the foundation of math, if we
except the work of Babbage.
The physical implementation has come later, and although interesting,
is not reated to the theory. It needs another theory which assumes a
physical reality, or derive it from the numbers, and the notion of
physical computations is a different concept.
> none of those theories can perform calculations, no theory
can,
I agree
Actually theory are not necessarily supposed to be able to do that,
I agree.
> only machine (in the mathematical sense) can do that.
Only a machine (in the PHYSICAL sense) can
do that.
Not at all. In the arithmetical sense, they do it too, and no machine
can know from personal introspection if they are primitively run by
the arithmetical reality of by a physical reality.
> Now, it happens that if a theory is sigma_1 complete, like RA
and PA, they can do that, because such theories are universal machine
If you know how to do that then for God's sake stop talking about
it and just do it, start the Sigma 1 PARA Hardware Corporation and
change the world!
Straw man.
> Physical material can do that [computation] in the physical
world
Yes and only physical material can do that
Sure, but circular with computationalism as we have to explain mind
and matter appearance from number relations. It works up to now.
, and I have a explanation of why that is so. You do not.
You don't read it, that's all. You said it so.
> but here we talk about the computation done in arithmetic.
No, here we talk about the computation done TO
arithmetical objects (by physics).
No, we talk about computation done by universal number, through the
Turing universal part of arithmetic.
Arithmetic is unchanging, nothing can be done in it;
The block universe is unchanging too. Time is an indexical in both
arithmetic and some model of GR.
if you want to actually DO something and not just define
something physics is needed.
You assume a physical universe, and I have explained this does not
work if we are digitalizable machine.
> obviously, we cannot use them in any direct way, like we can do
with a physical machine.
If mathematics is more fundamental than physics as you say
then it's about as far from obvious as you can get to
understand WHY we can't do calculations directly
but must instead get our hands dirty and mess around
with elements such as silicon.
The notion of computation does not assume silicon, nor QM or anything
like that.
> you accept comp,
I do not accept "comp".
You do. You only don't accept that "computationalism" to be
abbreviated by "comp".
> All your post illustrates that you are a sort of comp believer.
None of my posts illustrates that
I am a "comp" believer.
> Comp is put for computationalism.
No it is not. Over the years I have heard you say hundreds
maybe thousands of times "according to comp this and according to
comp that",
Because that hs been proved, published, peer-reviewed, and accepted by
any scientists doing the work needed. It is mock by philosophers and
religious believers in the Aristotelian dogma, like yourself.
but I am still unable to form a coherent picture of what
you're talking about; but I have a very clear
understanding of computationalism so I know that whatever
"comp" is it certainly isn't computationalism.
Because you stop at step 3, without having been able to ever explain
why (just rhetorical hand-waving).
> That computations exist in arithmetic (even in the small
sigma_1 complete part) is accepted by all experts
And yet for some strange reason like you none of these experts have
become filthy rich by starting a computer hardware company that
doesn't need to manufacture hardware.
Same straw man as above.
I find that very odd.
> Of course. But once Turing defined calculation/computation
[...]
If definitions could make calculations INTEL
would make definitions instead of silicon microchips because
making definitions is one hell of a lot easier than making
physical objects.
> it has been proved that it exists in any model of arithmetic,
a fortiori in the standard model.
Proofs are no more adept than definitions at making
calculations.
Sigma_1 proof are Turing universal. So a particular case of proving is
provably equivalent to computing.
> You need a physical reality only to implement a physical
computation. But that is trivial,
Try telling the stockholders
and scientists at INTEL it's trivial!
Straw man again.
>> if you want to know a particular solution to a particular problem
in arithmetic because neither proofs nor theorems can make a
calculation; for that you need physics.
> Yes, but it happens that we are not interested in having a
solution, but only in their existence,
Then you're not interested in computations
. There is no disputing matters of taste but I am
interested in computations and so is INTEL.
No, you are interested in a particular (physical) implementation of
the computations, but I have proved that if we are digital machine, or
better digitalizable machines, locally, then we have to explain the
appearance of the physical by the interference of the arithmetical
computation. Of course we know that you have not read the proof, so I
can only suggest you do. But the arithmeticalness of computations is
not mine, it is already implicit in Gödel 1931 paper, and fully
explicit in the work of Kleene and others.
Bruno
John K Clark
> How could a universal Turing machine makes the difference between
an implementation in arithmetic and an implementation in a physical
reality?
"I compute therefore I am physical", or even more fundamentally "I
am not static therefore I am physica l".
John K Clark
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