On 4 Jun., 04:16, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > In article <103a00da-91c5-47fc-b40e-79f330393...@e24g2000vbe.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes: > > On 3 Jun., 04:37, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > ... > > > You apparently do not understand it at all. WM has posted this stuff for > > > years in the German newsgroup on mathematics, in German. Moreover, he > > > has two books about mathematics on his name, in German. > > > > And both say, in effect, about the existence of actual infinity, what > > Kant said about the proof of the existence of God: These assumptions > > (proof of God, axiom of infinity) are as ridiculous as a merchant who > > would try to improve his balance by adding some zeros behind his > > result. > > And you are deluded. An axiom is a statement of something that can not be > proven, neither disproven using the remainder of the theory.
The axiom can be contradicted. Simple example: The axiom could be: The binary tree has uncountably many paths. I show that the end of each path p of the set P can be mapped on a node, and that all paths p of P cover all nodes of the tree. Therefore, after having completed the covering of the whole tree, there remains no node that could be used to construct a path that does not belong to P. This disproves the mentioned axiom.
> So comparing > the "axiom of infinity" with a "proof of God" is pretty stupid. In > mathematics a theory depends on the axioms used. There is nothing sacred > about the axioms, but as long as you are discussing a theory you should > use the axioms of that theory.
That is same as with proofs of God. The Vatican published an axiom (they call it a dogma, but it is of the same meaning) according to which it is possible to prove the existence of God. As long as you are discussing catholicism, you should use it, i.e., believe in that axiom.
> So, if you are discussion Eucliedan > geometry you should use the parallel axiom. Of course you can reject it, > but in that case you are not discussing Euclidean geometry but something > else.
That means, you are willing to believe in what the Vatican says? Probably they think that the Dutch better should have stayed within the Spanish Empire.