On 17 Dec 2013, at 07:16, Stephen Paul King wrote:
Hi Jason,
On Tue, Dec 17, 2013 at 1:02 AM, Jason Resch <jasonre...@gmail.com>
wrote:
On Mon, Dec 16, 2013 at 11:56 PM, Stephen Paul King <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.
No, I am just trying to be consistent. If we make a claim, than
that claim is possibly true iff its consequences can be actually
observed, otherwise we are merely confused.
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.
Without the actual proof, what is there?
Truth.
Gödel's theorem, that you mentioned, makes clear that truth is far
bigger than what we can prove in consistent effective theories.
Even when limited to arithmetic.
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?
How could I possibly know? It is not my burden to show. I am only
claiming that if an actual computation of the primeness is not done
then the plain cannot be true in that universe, otherwise we are
appealing to a consciousness that is somehow beyond computation.
Consciousness and arithmetical truth are provably beyond computation
and theories, once we assume computationalism.
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.
Such is unprovable.
?
Merely claiming that some X has some property does not make it so.
If we declare that X is prime, it means in general that we have a
proof. But then we know that all consistent creature in all possible
universe will agree that X is prime.
"Proving" = showing that something is true in all interpretation, as
proof in effective theories does NOT depend on the interpretation (in
the logical sense) of the theories.
Bruno
Jason
On Tue, Dec 17, 2013 at 12:54 AM, Jason Resch <jasonre...@gmail.com>
wrote:
So you are arguing that doing the computations is what makes a
number prime or not?
When does the number first become prime, is it when the first person
anywhere in the universe checks it? What about people beyond the
cosmological horizon that compute it, or what about people in
hypothetical other universes? Does the first person ever to check
and verify that a number is prime, make it prime for all people, in
all universes, forever?
Jason
On Mon, Dec 16, 2013 at 11:50 PM, Stephen Paul King <stephe...@provensecure.com
> wrote:
I do not assume that computations can occur if there are no physical
means to implement them. My imagination that s 270 digit string is
prime is not equivalent to actually doing the computation that tests
for primeness.
On Tue, Dec 17, 2013 at 12:47 AM, Jason Resch <jasonre...@gmail.com>
wrote:
On Mon, Dec 16, 2013 at 11:33 PM, Stephen Paul King <stephe...@provensecure.com
> wrote:
No, your making the mistake of identifying a representation of a
thing with the thing. The symbol 10^80 does not have 10^80
components, so to act as it is does...
Tell me this, is the following (270 digit) number prime:
332694894848329434549105787414873502606112802712440024745636803095039036420080826797726325643727533347094562684200739500429461145303257192536463211027218435305302565244506232330240506160052373297550819467601665370364223791626506805746132690937677414
846877090853919880937
Either it is or it isn't. If it is, then this is no different from
the case of 17 being prime (even if the universe had only 16 objects).
Jason
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