In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 9 Dez., 20:47, Zuhair <zaljo...@gmail.com> wrote: > > On Dec 9, 9:45 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > You believe in undefinable numbers. But what should that belief be > > > good for??? We can believe anything we like of undefinable numbers > > > like of unicorns. > > > > No you cannot of course. If you are working within the intended model > > of say Z, then you cannot believe for example that there are finitely > > many undefinable numbers, nor you can believe that there are countably > > many of them, also just because there is no parameter free finitary > > formula after which a number is defined this doesn't mean that you > > lose the known properties of the reals like trichotomy, total > > ordering, etc... > > If you don't know what x is, because x is completely undefined, then > you cannot know whether x is positive or negative. Hence there is no > trichotomy with respect to 0. Further you cannot know where x lies in > the order.
Until the question of position of x relative to 0 is asked, there is no need to know. So such lack of knowledge is no impediment.
And it is quite possible and occasionally necessary to speak of properties of some real x without knowing or caring about its position relative to 0.
Thus WM's argument is again, as so often, a mere red herring. --