On 04 Jan 2017, at 18:59, John Clark wrote:
On Wed, Jan 4, 2017 at 11:31 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
>> I say matter is always needed to make a calculation
you keep pointing out this textbook or that textbook in an effort to
prove me wrong.
> because those textbook explain what is a computation, without
assuming anything physical,
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 based on the unique
decomposition of number into prime factors. Then taking a number from
that list is realized by their divisibility properties. I can give
more detailed, but you can consult a textbook. The fact is that a
universal digital machine cannot distinguish from its first person
perspective if she is run by a computation from a block-physical-
universe or from a bloc-computational-structure like elementary
arithmetic.
In fact who is that textbook talking to if it's not a collection of
atoms that obeys the laws of physics.
That is a confusion of level. When I say that the computation are
realized in elementary arithmetic, I point to a fact which does not
depend on the existence of matter or any physicalness. Now, relatively
to us, we will express such fact through books, but as far as we know
such books can be first person appearance, and those can be proved to
exist, in the internal (to arithmetic) relative way in elementary
arithmetic, and that is all what count for my point.
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. The whole chapter of
mathematical logic known as recursion theory studies and classifies
the degree of unsolvability of such set. The partially computable one
are the so-called Sigma_1 set, and the non computable are the Pi_1,
Sigma_2, Pi_2, ... Sigma_i, Pi_i, ... Again this is explained in all
good books. All you need to be able to define non-computable sets of
numbers is the excluded middle principles, and we do this all the time
in many branches of math. We can tlak about the set of total
computable functions, despite their set of descriptions is also not
computable.
> "The hell with the antic greeks" was also the motto of the
catholic teachers I met. The tabula rasa on theology is where
gnostic atheists and institutionalized religious fundamentalist
match perfectly.
Oh dear, we're back to that again. Now where did I put my rubber
stamp, I know it's around here somewhere.... oh there it is:
Wow, calling a guy known for disliking religion religious, never
heard that one before, at least I never heard it before I was 12.
It is just a fact.
By mocking the possibility of doing theology in the scientific way,
the gnostic-atheists (believers in a Primary Physical Reality and
believer in the zero personal gods theory) maintain the field in the
hands of the clericals and institutionalized religions, making it
impossible to transform the Period of Enlightenment. This shows that
among the atheists, the non agnostics one (the gnostics) side with the
institutionalized charlatan again the coming back of the field in
Science, where it was born. They are de facto allies of the Churches.
You might read the book by Daniel E. Cohen "Equation from Gods Pure
Mathematics and Victorian Faith(*)" to see that even the "modern"
mathematical Logic is born from theological questions and the will of
making theology coming back to science, by Unitarian mathematicians
who were tired of the imposed Trinitarian view. The main people here
where Benjamin Peirce (the father of Charles S. Peirce), Augustus de
Morgan, George Boole, and even Lewis Carroll (Charles L. Dodgson).
Then, later, the mathematicians put some pressure to hide this
theological motivation in the process of making mathematics itself
into a profession in the 19th century. Note also the irony, given that
the canonical theology of the Universal Machine, due to incompleteness
is more Trinitarian-like (3 main hypostases) than Unitarian, but the
early logicians could not foreseen the incompleteness of the universal
machine and the Löbian machine. It is incompleteness which introduces
the modal nuances of provability which separates the hypostases (cf p,
[]p, []p & p, []p & <>t, etc.).
Bruno
(*) The Johns Hopkins University Press, 2007.
John K Clark
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