Date: Feb 18, 2013 4:21 PM
Author: Virgil
Subject: Re: WMytheology � 222 Rejects Induction

In article 
<386d5767-1eb5-4910-811f-8daf7aef60d3@g16g2000vbf.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 18 Feb., 14:11, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 18, 1:38 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > On 18 Feb., 11:53, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > Is there a potentially infinite sequence,
> > > > x, such that the nth FIS of x consists of
> > > > n 1's

> >
> > > Yes, of course
> >
> > Let y be a potentially infinite process

>
> There are no processes with respect to numbers and lists. They are
> existing or are not existing.


Then ther is no such thing a potentially infinite, as that would require
existence of a process that does not end.

> Potential infinity with respect to natural numbers means: You can
> consider every natural number you like. There is no upper threshold.
> So name any set of natural numbers - except using naive and
> couterfactual "all" of some kind like "all prime numbers" or all "even
> numbers".


So for any set of naturals you can name, there is a process for finding
a superset of that set, even in Wolkenmuekenheim.

If one cannot ever have something true for ALL natural numbers, how can
one ever use inductive proofs?

> Now realize what potential infinity means: There are no processes in
> above list.



It also means that induction can never conclude that anything is true
for all natural numbers.

In Wolkenmuekenheim one cannot say
"For all n, if n is a natural then n+1 is a natural."
because on cannot ever say "For all n"



> We simply write some lines and stop at some point.

Thus WM can never prove that anything by induction.
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