In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 4 Jun., 04:21, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > In article > > <5b9b7d5b-11d3-4125-8052-ad45e6e7a...@x5g2000yqk.googlegroups.com> WM > > <mueck...@rz.fh-augsburg.de> writes: > > > On 3 Jun., 04:25, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > > > There is no difference between finite unions and infinite > > > > unions. > > > > > > There should not be, but there is --- at least if ZF is taken to be > > > true. > > > > You are again wrongly interpreting things. There is no question about ZF > > being true or not. ZF is only one of the many possible theories. > > It is an impossible theory because finished infinity is impossible.
What WM decalred to be impossible in WM' world of mathUnrealism is not binding anywhere else. > > > > Mathematics is not a science that tries to find truth, > > There is a mathematics, namely basic arithmetic of integers, that is > right.
If so, the WM has no access to it.
>And there are some logical rules that are right.
If so, the WM has no access to them.
> And from these > foundations some theorems can be obtained that are right.
Without a comprehensive description of what one is required to accept as true, and reject as false, there is no way to tell which statements are theorems and which are not in that system.
> There is no > need and no space for any axiom at all.
If there are any statements which must be accepted in WM's "system" then those statements are 'axioms' of that system whether WM likes it or not.
> There is no need , in > particular, for "a set N" with some "binary relations". It is > impossible, to change that stuff. And Hilberts famous model including > 1 + 1 = 0 does nothing but express the display of the last wheel of a > binary calculator (or Leibniz's calculator that all time long had > problems with the digit transfer).
Without some explicit method for determining any naturals that are not explicitly listed, there will be a last natural beyond which not even WM's potential infinity can proceed, and that last one will be too small to allow much practical mathematics.
> > it is a science where > > it is determined what a given set of axioms (i.e. presupposed valid > > statements) > > leads to. > > A given set of axioms is sometimes impossible.
Then one ow does one decide which statements are theorems and which are not?
> This is so with the > axiom of infinity that Zermelo created, misunderstanding Dedekind's > idea of potential infinity.
Only in WM's world. > > > > The union of FISONs (of natural numbers or of other finite linear > > > sets) is the last FISON. > > > > ZF does agree, when there is a last FISON. Your problem is that the axiom > > of infinity states that here is no last FISON of all FISONs. > > That is not my problem.
It is if you want to do actual mathematics instead of your own personal psuedomath.
> For potentially infinite sets it is not a > problem at all.
There is no self-consistent logical system which Wm has ever shown to allow such abominations.
> For a completely existing set ZF is wrong. But that is > usually veiled by applying potential infinity whenever the problem > occurs.
The thing is that ZF's alleged wrongness produces nothing that conflict with its axioms whereas WM's system's alleged rightness produces too many things that conflict with his own assumptions.