On 15-05-2018 02:06, John Clark wrote:
On Mon, May 14, 2018 at 7:01 PM, Russell Standish
<[email protected]> wrote:
> How do you establish that the proof has no error? Why are we
supposing
that the ZFC axiom correctly describes the mathematical system? How
do
you establish that the computers haven't made an error?
It seems to me you're trying very hard to understand my question. In
arithmetic if ZFC or any set of axioms says that a number with
certain mathematical traits can not exist but a computer finds a
number with exactly those mathematical traits then both of them can't
be correct, and in that situation I simply don't believe you'd take
the part of the axioms because you are not insane.
> It really underscores Chaitin's point that at some level of
complexity, mathematics becomes an empirical subject, perhaps not
all
that different from physics.
Yes mathematics can be empirical, and that means regardless of how
beautiful your axioms are if the experimental evidence conflicts with
them then those axioms then they have to be junked because
experimental evidence outranks everything. The mathematical
counterpart to a test tube is a computer and the fundamental operating
system of any computer is the laws of physics. So physics can exercise
veto power even in pure mathematics.
John K Clark
But then, without a solid mathematical model that describes experimental
outcomes, how can one draw any nontrivial conclusions from experiments
at all? Take e.g. experimental bounds on the photon mass:
https://arxiv.org/abs/hep-ph/0306245
which is shown to depend on the underlying model. In case of the photon
charge, it turns out that the experimental results are totally junk:
https://arxiv.org/abs/hep-ph/0505250
Saibal
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
