On 12/17/2013 8:07 AM, Jason Resch wrote:
On Tue, Dec 17, 2013 at 12:49 AM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:On 12/16/2013 10:13 PM, Jason Resch wrote:On Tue, Dec 17, 2013 at 12:06 AM, meekerdb <meeke...@verizon.net <mailto: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 <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. That's what I mean by mathematicians assuming that "satisfying a predicate" = "exists". All you need are truth values. If it is true that the recursive function containing an emulation of the wave function of the Hubble volume contains a self-aware process known as Brent which believes he has read an e-mail from Jason, then it is true that the aforementioned Brent believes he has read an e-mail from Jason. We don't need to add some additional "exists" property on top of it, it adds nothing.It does if you don't have an axiomatic definition of all those predicates such that satisfaction of the predicate is provable. Otherwise you're just assuming there's a mathematical description that implies existence. That might be true, but I think it's not knowable that it's true. It's like "the laws of physics". Truth is independent of axiomatic systems as shown by Godel.
I don't think that's quite right. Godel showed that *given an axiomatic system* there will be true sentences that are unprovable. But the form of such Godel a sentence, "This sentence is not provable." implicitly refers to the axiomatic system, i.e. the axioms and rules of inference. So it's not really independent. In general it can be proven within a different axiomatic system or even disproven.
This implies you don't need a universe containing a person who writes down a set of axioms to create the truth of some number's primality, or Brent meeker's thoughts in some large recursive function. With this understanding, you can get Wigner's effectiveness (a rational, law following, mathematically describable universe), the "first cause", and the answer to the existence and relation between mathematical truth and mathematicians' minds all for free.
You are aware aren't you that Wigner was mostly referring to mathematics over real and complex number fields and that Godels incompleteness does NOT apply there.
This is much simpler than proposing an independent physical reality, some nebulous undefinable connection between mathematics and mathematicians,
There's nothing nebulous in my idea of the relationship between mathematics and mathematicians. The latter evolved to know some simple mathematics and they (culturally) invented the rest (c.f. William S. Cooper "The Evolution of Reason".
and some shock at the absence of any magic (not mathematical describable, or not modelable) things in our own universe. Why should anyone who subscribes to Occam not favor "arithmetical realism" over "physical universe + unreasonable effectiveness + (either arithmatical realism or mystical source of truth in mathematicians' minds)"?
I'll favor it as soon as it provides some surprising but empirically true predictions - the same standard as for every other theory.
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