On 6/4/2020 4:27 AM, Bruno Marchal wrote:
On 3 Jun 2020, at 21:47, 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 6/3/2020 3:26 AM, Lawrence Crowell wrote:
On Tuesday, June 2, 2020 at 12:34:37 PM UTC-5, Brent wrote:
On 6/2/2020 2:49 AM, Bruno Marchal wrote:
>> On 1 Jun 2020, at 22:43, 'Brent Meeker' via Everything List
<[email protected] <javascript:>> wrote:
>>
>>
>>
>> On 6/1/2020 2:08 AM, Bruno Marchal wrote:
>>> Brent suggest that we might recover completeness by
restricting N to a finite domain. That is correct, because all
finite function are computable, but then, we have incompleteness
directly with respect to the computable functions, even limited
on finite but arbitrary domain. In fact, that moves makes the
computer simply vanishing, and it makes Mechanism not even
definable or expressible.
>> That's going to come as a big shock to IBM stockholders.
>
> Why? On the contrary. IBM bets on universal machine
No, they bet only on finite machines, and they will be very
surprised to
hear that they have vanished.
Brent
For the most part computers are meant to run various algorithms that
solve some restricted set of problems, say business applications. We
use them largely as tools.
Mathematics is largely a tool. My pure mathematics friends over on
math-fun seem to have most of their fun on Mathematica.
Of course, this is close to Aristotelian theology. It assumes that
there is something which is not mathematical in some reality. A
platonism or a pythegaorean think that he physical universe is but a
tool, invented by the numbers to figure out what happens, and what is
real.
But once you grasp that all computations exists in arithmetic (or more
exactly, that they are enabled by the arithmetical true relations),
even without Mechanism, the charge are reversed. It is those who claim
(in metaphysics, not in physics) that there is a primitive universe
who have the task to provide evidence.
You have implicitly asserted that computation=reality. With not proof,
or even evidence.
Brent
I have given the way to test this, and, thanks to QM, we can say that
there are not yet any evidence found for a primitive physical
universe. On the contrary, nature seems to obey exactly to what is
needed for mechanism to be true.
Then, if we assume furthermore Mechanism, there is no more choice in
this matter. Physics cannot be the fundamental science, it reduces to
arithmetic (or any model of any Turing equivalent machinery)
“seen-from inside”.
Bruno
Brent
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