On 17 December 2013 19:06, meekerdb <meeke...@verizon.net> 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> 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. That's what I mean by mathematicians assuming that
> "satisfying a predicate" = "exists".
I guess it depends on what you mean by existing (I also suspect you knew
I'd say that :). I generally consider things that exist are the ones that
kick back in some fashion, or as someone said, it's what doesn't go away
when you stop believing in it.
17 exists in the sense that it exhibits certain properties that will always
be discovered by anyone who performs the relevant calculations, in this
universe or any possible universe. And it will continue to do so whether I
think it does or not, or whether anyone is around to think it does or not,
or whether anyone has ever considered its existence, ever, or not. Whether
you think that's good enough to say it exists is, I guess, a matter of
Likewise, whether matter or energy exists comes down to what it actually
is, which so far nobody knows. My best description of (say) a photon is
that it is something that registers a result in certain experiments, e.g.
causes a photomultiplier to click or a grain of emulsion to darken. Are
those properties worthy of being called existence, any more than being
unable to divide 17 by any smaller integers except 1 is? I don't know.
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