On Sat, Jan 24, 2015 at 12:43 PM, meekerdb <[email protected]> wrote:
> On 1/24/2015 1:23 AM, Jason Resch wrote: > > > > On Fri, Jan 23, 2015 at 10:15 PM, meekerdb <[email protected]> wrote: > >> On 1/23/2015 8:16 AM, Jason Resch wrote: >> >> >> >> On Friday, January 23, 2015, John Clark <[email protected]> wrote: >> > >> > On Thu, Jan 22, 2015 at 4:46 PM, Jason Resch <[email protected]> >> wrote >> > >> >>> >> Do we know that? Do we know that such a digit exists? >> >> >> >> > It follows from the axioms that there is a certain definite digit. >> > >> > They show you how to generate terms in a sequence and if you add up >> enough of them you'd get the the 10^(10^(10^100))th decimal digit of pi; >> but it assumes that there is no barrier that makes doing that impossible >> and states that assumption with 3 little dots (...). I don't know for >> certain but those 3 little dots *might* be saying something that is logical >> nonsense, I do know for certain that the first mathematicians who used >> those 3 little dots knew nothing about quantum mechanics or the >> computational limit of the universe, and that gives me pause. >> > >> >> What I explained is that if you think there is a largest number *that* is >> what definitely leads to logical nonsense. >> >> Say there is a largest number N, such that N+1 is not a bigger number, >> but is still N. That means N+0 = N+1. Now subtract N from both sides. >> >> >> Why should subtraction of the biggest number not obey special rules, >> e.g. Subtracting N from any normal number yields -N. Subtracting N from >> any Big number yields zero. >> > > I still don't know if that would escape the problems. Let's say M is the > number right before the biggest number (or any "Big numbers"). Then using > your rules you find that: > > M - (M+1) = 0 --- or is it -N? > but > (M - M) + 1 = 1 > > It might be possible to come up with axioms that allow you to have a > biggest number that operates in a consistent way, but I think it would be > very difficult, and probably not very useful. > > > It may be useful in computer science, c.f. > http://www.impan.pl/~kz/files/MKKZ_ArFM.pdf > > Nor do I see the point of hobbling a theory (supposedly about the > infinite natural numbers) by declaring some aspects of that theory to be > strictly off limits and beyond the possibility of discussion. > > > I'm not proposing that anything is off limits. I'm proposing that there > are different axiomatic systems which may equally correspond with our > finite observations, > How can it be said that any physical observation corresponds with entities that exist within an axiomatic system? Do you see the goal of physics being to provide mathematicians with a correct axiomatic system? > therefore it is not justified to pick one of them and claim that it is > empirically proven. Axiomatic systems may contradict one another and that > is why "X provable in A1" only implies "X true relative to A1" and not > "exists X". Plato was led to suppose that perfect forms existed because > in his day it seemed there was only one possible mathematics which was > something like arithmetic plus Euclid. > In our day we know that no axiomatic system can be perfect, and accordingly that axiomatic systems can at best approach/approximate rather than prescribe/define truth. In that way they're not much different from physical theories we develop about the objective physical universe: axiomatic systems are theories about objective mathematical objects. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
