Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Mathematics in brief
Posted:
Dec 9, 2012 5:58 PM
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In article
<1fb292ce-e98c-4e19-a401-9dacc9d4b00b@b8g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> 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.
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