In article <firstname.lastname@example.org>, "Julio Di Egidio" <email@example.com> wrote:
> "Zeit Geist" <firstname.lastname@example.org> wrote in message > news:email@example.com... > > On Saturday, July 13, 2013 7:40:24 AM UTC-7, Julio Di Egidio wrote: > >> "Zeit Geist" <firstname.lastname@example.org> wrote in message > >> news:email@example.com... > >> > On Friday, July 12, 2013 1:41:31 PM UTC-7, muec...@rz.fh-augsburg.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 non-sequitur, 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. > > You still have this idea of the standard vs. the cranks, but the one with no > arguments, the non-sequiturs and, in fact, no clue (e.g. as to the standard > and the non-standard), here is still you. > > >> > Why wouldn't I talk about the set of Naturals? > >> > >> That there is no such thing as a _set_ N (i.e. a finite-inductive set, an > >> "unfinished set") is a thesis of *strict finitism* already: > >> <http://en.wikipedia.org/wiki/Finitism#Classical_finitism_vs._strict_finiti > >> sm> > > > > Those ideas in Finitism are assumptions. > > You just don't know what you are talking about.
All mathematics is based on assumptions, since every theorem is ultimately an if-then statement, with much of the "if" clause very often assumed rather than stated.
Without SOME assumptions, even the simplest of finitisms cannot get started. > > > Although they may lead to consistent systems, > > they are far less powerful than a system that assumes > > an infinite set. > > Again, you don't know what you are talking about.
Sounds to me that he knows precisely what he is talking about, since it is well know among non-finitists at least, that not every theorem in standard analysis has a close analog within finitism. > > > 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. > > And, again, you just don't know what you are talking about...
Then lets see your finitist definition of a surface integral. > > So, no arguments, non-sequiturs, no clues: another dog of the empire? I > mean, either you get your head out of your ass, or you better go play > Captain America somewhere else...
It seems clear that you are the one with your head inconveniently placed.
And until you can give a simple but finitist definition of a surface integral, there it will remain. --