Virgil
Posts:
7,005
Registered:
1/6/11


Re: Matheology � 300
Posted:
Jul 15, 2013 2:58 AM


> Am Montag, 15. Juli 2013 07:51:47 UTC+2 schrieb Albrecht: > > Am Samstag, 13. Juli 2013 21:35:22 UTC+2 schrieb Virgil: > > > In article <2fa13865ebcf431ea1fff322889609be@googlegroups.com>, > > > Zeit Geist <tucsondrew@me.com> wrote: > > > > On Saturday, July 13, 2013 7:40:24 AM UTC7, Julio Di Egidio wrote: > > > > > "Zeit Geist" <tucsondrew@me.com> wrote in message > > > > > > news:41be4197cc38420fa4edb90e196ddc2b@googlegroups.com... > > > > > > > On Friday, July 12, 2013 1:41:31 PM UTC7, > > > > > > > muec...@rz.fhaugsburg.de > > > > > > > wrote: > > > > > > >> On Friday, 12 July 2013 19:13:19 UTC+2, Zeit Geist wrote: > > > > > > >> > > > > > > >> > It is rather silly to expect the process that creates each of > > > > > > >> > the > > > > > > >> > Naturals would produce the set of all Naturals, as that set > > > > > > >> > is, > > > > > > >> > itself, not a Natural. > > > > > > >> > > > > > > >> Each natural belongs to a finite initial segment. None of them > > > > > > >> requires a number that is larger than every natural number. In > > > > > > >> fact the contrary. If you do not talk about the set, then there > > > > > > >> is > > > > > > >> no reason to talk about alephs. > > > > > > > > > > > > > > Yes, but for every Natural there is a larger natural, hence the > > > > > > > number > > > > > > > of Naturals is larger than any Natural. > > > > > > > > Since the number of natural numbers is not itself a natural > > > > > > > > number, that is > > > > > > a nonsequitur, despite standardly the conclusive statement is > > > > > > correct: > > > > > > indeed, a fallacy of relevance. Plus, the standard here is in > > > > > > question, so > > > > > > one should rather qualify statements as well as objections (not > > > > > > that WM > > > > > ever > > > > > > does it, of course). > > > > > The are numbers that are not Natural Numbers. > > > > The number of Naturals Numbers is a number, > > > > and it greater than any finite number, that is to say, > > > > It is greater than any Natural Number. > > > > Here, number means Cardinality, of course. > > > > In most Mathematical circles the standard is ZF(C). > > > > Yes, standard Set Theory is being questioned here. > > > > And most who question it here have not come up with > > > > a good reason to reject. Nor have they come up with > > > > a suitable replacement. > > > > > > > Why wouldn't I talk about the set of Naturals? > > > > > > > > That there is no such thing as a _set_ N (i.e. a > > > > > > > > finiteinductive set, an > > > > > > "unfinished set") is a thesis of *strict finitism* already: > > > > > > <http://en.wikipedia.org/wiki/Finitism#Classical_finitism_vs._strict > > > > > > _finitis > > > > > m> > > > > > Those ideas in Finitism are assumptions. > > > > Although they may lead to consistent systems, > > > > they are far less powerful than a system that assumes > > > > an infinite set. > > > > I can count head of cattle or stones with a Strictly Finite system. > > > > However, it is very difficult to define a Surface Integral and > > > > most likely impossible to prove FLT in any form of Finitism. > > > > > > Julio > > > > ZG > > > It is well known that finitist analogues of theorems in standard > > > analysis, when they exist, are much more difficult to prove that the > > > theorems themselves, so nothing is gained except greater difficulty in > > > prooving things. > > >  > > Modern math ist the only "science"
Math is not a science at all.
Nothing is proved or disproved in mathematics by looking at physical evidence.
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. It seems to me that complete clearness as to this state of things first became common property through that new departure in mathematics which is known by the name of mathematical logic or Axiomatics.¹ The progress achieved by axiomatics consists in its having neatly separated the logicalformal from its objective or intuitive content; according to axiomatics the logicalformal alone forms the subjectmatter of mathematics, which is not concerned with the intuitive or other content associated with the logicalformal. . . . [On this view it is clear that] mathematics as such cannot predicate anything about perceptual objects or real objects. In axiomatic geometry the words point,¹ straight line,¹ etc., stand only for empty conceptual schemata."
Albert Einstein 

