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

In article 
WM <> wrote:

> On 18 Feb., 14:11, William Hughes <> wrote:
> > On Feb 18, 1:38 pm, WM <> wrote:
> >

> > > On 18 Feb., 11:53, William Hughes <> 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.