In article <59abfe03-8386-4d06-8f54-acfbf19a50d0@x15g2000vbj.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 11 Feb., 16:40, William Hughes <wpihug...@gmail.com> wrote: > > On Feb 11, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 11 Feb., 11:55, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Feb 11, 8:50 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > There exists a natural number m such that d is line number m is false. > > > > > Yes so, alas not quite correct if d is assumed to "exist". > > > > > If d is assumed to exist, we have > > > > > 1) We cannot *find* a natural number m such that d is the m-th line of > > > the list. > > > > According to you > > > > if L is a potentially infinite list, and d is > > the potentially infinite diagonal > > > > if for every natural number n, d is not the nth > > line of L then > > > > *There does not exist* a natural number m such that > > d is the mth line of L > > > > Do you wish to withdraw this claim? > > No. This claim is obviously correct. > > Only *if the complete existence of the not completely existing > diagonal d is assumed*, it would be necessary to have it in the list > and (since every line of the list contains everything that is > contained by its predecessors) to have it in a line of the list. But > obviously a potentially infinite diagonal does not exist completely > (as the potentially infinite list does not exist completely). > > So why should anything be withdrawn?
The notion of potential infiniteness should be withdrawn as it is incompatible with the notion of "set". One cannot have a set whose membership is only potentially determined.
In all standard set theories there is a set which contains {} as a member and which for each of its members, m, also contains (m union {m}).
Since this is apparently not the case in WMytheology , then no set theory in WMytheology is compatible with standard mathematics , and thus WMytheology irreleveant to standard mathematics. --
