Date: Mar 25, 2013 7:47 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 24 Mrz., 23:16, Virgil <vir...@ligriv.com> wrote:

> In article

> <af556b1e-2874-41ec-9821-a4bf61acf...@7g2000yqy.googlegroups.com>,

>

>

>

>

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 24 Mrz., 16:47, William Hughes <wpihug...@gmail.com> wrote:

> > > On Mar 24, 4:26 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > > > On 24 Mrz., 16:13, William Hughes <wpihug...@gmail.com> wrote:

>

> > > > > On Mar 24, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > > > > Induction proves that every

>

> > > > > True

>

> > > > > and all

>

> > > > > False

>

> > > > So you do no longer adhere to ZFC+FOPL?

> > > > There a proof "for every" is a proof "for all".

>

> > > However, in WM speak a proof "for every"

> > > is not always a proof "for all".

>

> > That is correct and reasonable, but irrelevant here. This proof is in

> > ZFC. There for every is same as for all.

>

> But the grammatical rules in ZFC require that the "for every" and "for

> all" statements be logically equivalent, so that each such argument can

> be equally validly expressed either way.

For every and for all in my example are equivalent. Every and all

elements of the inductive set of FISONs can be removed without

changing the union, iff actual infinity exists.

Regards, WM