On 17 Dec 2013, at 15:37, Stephen Paul King wrote:
Hi Jason,
On Tue, Dec 17, 2013 at 1:27 AM, Jason Resch <jasonre...@gmail.com>
wrote:
On Tue, Dec 17, 2013 at 12:16 AM, Stephen Paul King <stephe...@provensecure.com
> wrote:
Truth. Truth =/= Proof.
Ummm, as I see things: Proof => Truth.
If that is true, it is not provable (with proof = "I prove"). "Bp ->
p" belongs to G* minus G.
Truth, taken as a priori, is indistinguishable from unverified
belief and slides into appeals to authority.
We can both believe that truth is bigger than proof, and yet keep
asserting only proved statement.
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.
It is something your world view ought to be able to account for
rationally or meaningfully, otherwise you might look to replace that
world view with one which can more adequately address these questions.
I agree!
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.
I don't understand your point. How are we appealing to a
consciousness beyond computation by assuming a number can be prime
or not prime irrespective of our capability or willingness to prove
it?
If we assume that becuase we can verify that some large but
accessible number is or is not prime can give us the ability top bet
(ala Bruno) that inaccessible large numbers are or are not prime,
but to claim that they actually "are" prime (or not) is a bridge too
far.
Let me ask two questions which might help clarify my understanding
of your view:
1. Is it possible for someone, in some universe, somewhere to
compute (without error) and find some number N to be prime, while
another person elsewhere finds it is not prime?
Sure! Only if that universe is capable of supporting the computation
required. My example of a universe of 16 objects is a case where it
is not computable.
Computability is an absolute notion, thanks to Church Turing thesis.
What you talk about is not "computability", but "computability by a
little automaton". You could say that addition is not a computable
function because my cup of coffee cannot compute it.
What you are doing is a change of meaning of a well established notion.
2. If your answer to question 1 is "no", then what is the mechanism
through which consistency is maintained between these causally
isolated observers (who may even be in different universes?)
Good question! How is consistency maintained globally? Does it
really need to be? Consider the SAT problem of Boolean logics... We
should not expect the mere possibility of solving hard problems to
support the belief that the solutions are accessible. As I see
things, it is accessibility to solutions that matters here.
That is tractability, not computability.
This is why I have a problem with Platonism: It postulates the
existence to Forms and proposes a mystical mechanism to explain the
accessibility of the Forms.
On the contrary. Computationalism assumes only that the brain works
like a machine, without added magic. Then some magic remains, but that
is a consequence of the richness of the elementary rule for a
universal system, like the closure for diagonalization.
Bruno
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 it did not already have the property X before it was observed,
then why is it that aliens a trillion light years beyond our
cosmological horizon get the same result when they compute whether
or not N is prime? Does the first entity to compute it "collapse
the mathematical wave function"?
You are reasoning with the assumption of a global time... :-( Given
GR and QM's empirical support, why do you use assumptions that are
proven to be false? There is no absolute "before and after". Sorry.
We need to be consistent.
Jason
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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