Virgil
Posts:
4,482
Registered:
1/6/11
|
|
Re: Matheology � 210
Posted:
Feb 5, 2013 6:49 PM
|
|
In article
<5ba22415-f653-437c-9aef-cdd140fd92c9@fw24g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 5 Feb., 21:55, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 5, 6:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > <snip>
> >
> > >... one cannot even put all natural numbers in
> > > correspondence with all natural numbers.
> >
> > However, one can put every natural number in
> > correspondence with every natural number.
>
> One can have that by belief or decreed by the powers that be.
> n <--> n is the finite expression of this belief. But its validity is
> dubious because one cannot have possibly in a possible list that
> contains every finite initial sequence of the sequence of natural
> numbers the sequence s of every finite initial segment of the sequence
> of natural numbers.
If one cannot even justify an n to n correspondence for naturals n, then
one has thrown out a large baby with a very little bathwater, as one has
automatically thrown out induction as well.
Induction requires that one be able to conclude that something holds for
all n in |N.
But if one cannot anything for all n in |N, no induction!
--
|
|
