Date: Mar 21, 2013 7:32 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 21 Mrz., 11:36, William Hughes <wpihug...@gmail.com> wrote:

> On Mar 21, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote:

>

> <snip>

>

> > > There is such a thing as a sufficient set of

> > > lines (all sufficient sets are composed

> > > entirely of unnecessary lines, which means

> > > that you can remove any finite set of lines

>

> > Why only finite sets?

>

> You can only use induction to prove

> stuff about finite sets.

In fact? That's amazing. So we cannot prove that all lines of the

infinite set of lines are unnecessary?

Note: For every finite set of natural numbers, we can look at all

elements, at least in principle. We do not need induction for fixed

finite sets. Induction is not *necessary* then, so to speak.

I hope you see that your claim is nonsense, iff there is an infinite

set of natural numbers.

>

> > What property is changed if infinitely many are

> > there? If there are infinitely many unnecessary lines, they all can be

> > removed - by their property of being unnecessary.

>

> Nope, their property of being unnecessary means

> that *any one* line can be removed.

But you think that after all finite and unnecessary lines another one

is lurking like a dragon?

>

> Once we remove one line, we are left with

> a new set of unnecessary lines. We can

> remove one of these lines.

> From induction we get that

> any finite set of lines can

> be removed.

More. From induction we get that every set is finite. The error of

matheology is to assume that there is more than every finite set, but

this "more" obviously cannot be determined by induction (because it is

not part of mathematics). Therefore any desired property could be

attributed to this "more". However, it is not good taste to attribute

properties like "unnatural" or "green" or so to this "more".

Our result is:

If all natural numbers can be reached by induction, then nothing

remains that makes the set |N actually infinite, because |N is not

more than all natural numbers.

And if not all natural numbers can be reached by induction, then there

must be a first one of the "more" - at least, if the more consists of

natural numbers.

You see, your position is untenable - at least in mathematics.

Regards, WM