On 24 Jan 2014, at 22:26, meekerdb wrote:
On 1/23/2014 11:59 PM, Bruno Marchal wrote:
Only the idealized computations of Turing. Computations in my
computer always stop.
Because you assume that it exists in some ontological sense. That
might be possible. My point is that if this was really the case,
you can't say "yes" to the doctor "qua computatio". You can say
"yes" to the doctor by invoking some magic.
You've written that several times, but I don't understand the
point. What difference does it make if all computations stop?
Wasn't that part of Turing's definition of a computation - a Turing
computer process that stopped.
No. That is a successful computation. But in the mathematical space of
all computations, many will not stop.
If we want all successful computation in a well defined computational
space, we have to tolerate all those which do not stop. It is the
price of universality. I can prove that again.
If all computations stop, then arithmetic is inconsistent.
Well, if you believe that there is a biggest natural number, then
arithmetic is already inconsistent. There will be some k such that k =
k+1, and thus 0 = 1.
You are doing the move to a small non robust but "real and primitive"
physical universe. But step 8 is supposed to show how much ad hoc is
that move.
Just because I note that my computer will always stop and presumably
my neurons will stop, doesn't entail that all processes must stop.
OK.
And even if they did, why would that cause me to say "no" to the
doctor.
By the UDA. If you say "yes" to the doctor, physics emerges from all
computations, and even plausibly from those who do not stop, which
have a higher measure than those which stops.
Bruno
http://iridia.ulb.ac.be/~marchal/
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