On 17 Dec 2013, at 07:06, meekerdb wrote:
On 12/16/2013 10:02 PM, Jason Resch wrote:
On Mon, Dec 16, 2013 at 11:56 PM, Stephen Paul King <[email protected]
> wrote:
Yes, but why are you being anthropocentric?
I thought that was your position, or at least (observer-centric),
in that numbers only have properties when observed/checked/computed
by some entity somewhere.
If there can exist a physical process that is a bisimulation of the
computation of the test for primeness, then the primeness is true.
Otherwise, we are merely guessing, at best.
When we check the primaility of some number N, we may not know
whether or not it is prime. However, eventually we run the
computation and find out either it was, or it wasn't.
My question to you is when was it determined that N was or was not
prime? Any time we re-check the calculation we get the same
result. Presumably even causally isolated observers will also get
the same result. If humans get wiped out and cuttlefish take over
the world and build computers, and they check to see if N, is prime
is it possible for them to get a different result?
My contention is that it is not possible to get a different result,
that N was always prime, or it was always not prime, and it would
be prime (or not prime) even if we lacked the means or inclination
to check it.
That's fine. But it's a leap to go from the truth value of 17 is
prime, to 17 exists.
The truth of Ex(x = ssssssssssssssss(0)) is enough.
That's what I mean by mathematicians assuming that "satisfying a
predicate" = "exists".
That can be false. You need a non empty model, which is usually
assumed for simple sound and consistent theories. It is built in in
predicate logic.
"exist" is defined by the starting theoretical assumptions. I have
given mine. What is yours? If you assume anything physical, and assume
that you have to assume them, then you are no more working in the comp
theory.
Bruno
http://iridia.ulb.ac.be/~marchal/
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