On Tue, Dec 17, 2013 at 3:55 PM, meekerdb <meeke...@verizon.net> wrote:
> On 12/17/2013 8:07 AM, Jason Resch wrote: > > > > > On Tue, Dec 17, 2013 at 12:49 AM, meekerdb <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> 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". >>> >>> >> 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. > No axiomatic system can prove for any given Turing machine whether or not it halts. Any axiomatic system that is correct will agree that the Turing machine halts when it does, or does not halt when it does not. The truth that any given Turing machine halts or doesn't exists whether or not we have or know the axiomatic system that enables us to access that truth. > > > 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. > It applies to any axiomatic system that contains at least the integers. Axiomatic systems in use at Wigner's time which can describe real or complex fields certainly also contain the integers, and Godel's proof applies to them. > > > 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. > What if in some alternate history Bruno's UDA came before Everett's, and it provided a possible explanation of the appearance of random collapse through FPI as seen within an infinite reality? Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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