On 15 Feb 2016, at 00:14, John Clark wrote:
On Sun, Feb 14, 2016 at 8:35 AM, Bruno Marchal <[email protected]>
wrote:
> Obviously, 2 divides 4 without any help of physics,
Obviously 2 never changes so by itself 2 has never dived 4 nor
done anything else; 2 just is. If 2 is going to actually do
something like perform a mathematical operation it's going to need
the help of matter that obeys the laws of physics,
By defining doing by "primarily physically doing", yes. But that is
not used in the proof of the execution of computation by arithmetic,
and so is not relevant here if we use the standard definitions.
>> Giuseppe Peano may have proven some things but then
Giuseppe Peano had a brain made of matter that obeyed the laws of
physics.
> You don't know that. And we know today that this is just
false if we assume digital mechanism.
Giuseppe Peano did not have a brain made of matter that obeyed
the laws of physics?! Was he headless or just brainless?
Perhaps Giuseppe's mother had the Zika virus when she was pregnant.
I mean that there are zero evidence that his brain is made of primary
matter. Easy: there are no evidence at for primary matter. I gave a
precise criterium for showing that primary matter exists, and up to
now, it fails the test. Newton physics would have shown that primery
matter exist, but the available evidence today contradicts Newton's
theory, unlike quantum physics (without collapse).
> the arithmetical truth is independent of both arithmetical
proofs and physical proofs.
I agree. But to determine the difference between arithmetical
truth and arithmetical falsehood matter that obeys the
laws of physics is required.
PA proves ~(2+3= 7), without any need of primary matter.
A human might need locally some physical implementation to get the
point, but you have already agreed that the theorem of PA are
independent of you and me, and human in general, and so that point
would not be relevant.
That distinction is important, if Michelangelo had just displayed a
huge block of natural marble and said David was inside few would say
he was a great artist.
The analogy is misleading. A marble is a not a digital machine, nor an
effective theory, for which the presence theorem-hood in an
arithmetical property.
>> You confuse what works from what doesn't; and machines
made of nothing but pure mathematics DON'T WORK.
> They don't work in the physical reality,
I know, and I can explain why it doesn't work and you can't.
But the point is that they actually work well in arithmetic. Without
this, the incompleteness proof would not go through.
> It is up to you to tell us what a physical machine can do
that a universal machine cannot do,
A machine made of matter that obeys the laws of physics can
correctly inform John Clark that 2^57,885,161 − 1 is prime,
I doubt this, but even if true, that would only shows that JC needs a
physical implementation to get a physical result, but that would not
change the fact that no primary matter is needed for that, given that
the physical *must* be redefined by a purely mathematical statistics
on computations.
a machine made of nothing but pure mathematics can not.
A digital machine is not made of anything, and can do a lot of things,
including make JC believes correctly in matter, and even believing
incorrectly in primary matter. No problem with that.
You are using again and again a metaphysical notion to oppose to the
standard definitions and mathematical reasoning. What you say already
would either make Church-Thesis wrong or would give to matter a
magical role in the computations, but then we are outside the scope of
the study of the consequences of computationalism (alias digital
mechanism, or more simply Mechanism).
Bruno
http://iridia.ulb.ac.be/~marchal/
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