In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 12 Jun., 06:38, Owen Jacobson <angrybald...@gmail.com> wrote: > > On 2009-06-11 16:49:49 -0400, WM <mueck...@rz.fh-augsburg.de> said: > > > > > On 11 Jun., 22:31, Virgil <virg...@nowhere.com> wrote: > > >> In article > > >> <1348b29b-3f39-40a7-be0e-5bd24a4e3...@s21g2000vbb.googlegroups.com>, > > > > >> WM <mueck...@rz.fh-augsburg.de> wrote: > > > > >>> I need no axioms. > > > > >> Then there is absolutely nothing that you take to be true? > > > > >> There are absolutely no truths from which you can deduce other things? > > > > > There are truths, like 1 + 1 = 2, or, for linear sets, ExAy <==> AyEx > > > > These "truths" are the axioms of the theory you're using, or are > > implied by them. > > I do not deny that. But I deny that axioms can be chosen. > > > > > Incorrect are such lies as the axiom of infinity or the axiom of > > > choice. > > > > The mathematics community mostly does not pursue a universally true set > > of axioms. > > But mathematics does.
Then how can mathematics deal with both Euclidean and non-Euclidean geometries? By WM's standards, only one of them can be true, so that mathematics, by WM's standards, should be forbidden from dealing with all but the true one.
Which one would that be, WM? You claim to know so much about what is really true, so tell us which geometry is the true one.
And then tell us how you know. > > > Instead, mathematics takes sets of axioms and attempts to > > demonstrate that they lead to interesting results. > > Here is an interesting quote by Weyl (1946):
Mathematics does not accept truth-by-authority.
> > The results derived > > from a given theory (a set of axioms) are only valid within that > > theory. > > Mathematics (if done correctly) is true without any theory.
Where do the first "truths" come from, that everything else derives from?
They cannot come from the world of physics because we have no direct perception of that world. > > > There are informal "families" of theories, within which the > > informal definitions of various terms are portable (for example, there > > is a family of "set theories," each of which has a loosely similar > > definition of what a "set" is), but informal similarity does not mean > > that proofs from theories in the same "family" can necessarily be used > > together. > > All transfinite set theories are nonsense, formal or informal.
Then all of WM's theories are informal nonsense, too.
And I prefer the coherent nonsense of mathematics to the inchoate idiotic nonsense of WM. > > > > ZF set theory is no more "true" or "false" > > It is false, no doubt.
To claim that without logical proof, as WM repeatedly does, is to proclaim oneself illogical.
> A man who believes in or even attempts to prove > something by means of "higher cardinals" is a fool.
The creative foolishness of mathematics can be, and historically has been, highly productive and useful, but WM's stupidity will never be. > > > > So it is with the idea that all sets are finite. The ZF axiom of > > infinity is only the contradiction of the axiom "there are no infinite > > sets," and the resulting theory is both consistent and useful. > > That is wrong.
The creative foolishness of mathematics can be, and historically has been, highly productive and useful, but WM's stupidity will never be.
> > > There > > are also consistent, useful theories that do not prove or require the > > existence infinite sets. > > This is a prerequisite of a consisten theory like the convergence of a > sequence to zero, shall the due series converge.
In a set theory without infinite sets, and therefore also without infinite sequences, there can be no convergence because every sequence must have a last term. > > > > If you would only name the theory you're using, or sketch out its > > fundamental truths (that is, its axioms), you'd probably find people a > > lot more receptive to your ideas. > > I am doing simply correct mathematics, at least I am striving for that > goal.
And failing. Partly because you have not, or cannot, sketch out what you consider to be the fundamental truths on which you base your theory.
Without being able to derive things from only fundamental truths and formal definitions, there is no way to check the validity of anything.
So if WM feels compelled to keep his list of fundamental truths secret, he cannot publicly validate any of his arguments.