On 12/17/2013 2:20 AM, Bruno Marchal wrote:
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 <stephe...@provensecure.com
<mailto:stephe...@provensecure.com>> 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.
But just writing a symbol "E" and calling it "exists" doesn't impress me as proving 17
exists in the same way that my refrigerator exists, I could write Ex(Refigerator_x &
Brent's_x) too.
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.
I chose my theoretical assumptions depending on the problem I need to solve. Sometimes
it's Newtonian mechanics, sometimes it's general relativity,...
Brent
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