Date: Dec 28, 2012 10:07 PM
Author: ross.finlayson@gmail.com
Subject: Re: The Diagonal Argument
On Dec 28, 5:13 pm, Virgil <vir...@ligriv.com> wrote:

> In article

> <01f18004-18e2-429a-b93b-bbbde1129...@t6g2000pba.googlegroups.com>,

> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

>

> > Hancher, the "puke parrot" bit is largely for comedic effect, yes it

> > seems clear that you do actually read the attempts of others to

> > develop frameworks and structures of what would be developments in

> > mathematics, but it is as well clear that you definitely have a

> > penchant for tearing down said arguments without building them up.

>

> It is the duty of every mathematician to tear down such bad mathematics

> as is thrust upon him or her.

>

> And both you and WM thrust a lot of it here.

> --

Cantor's nested intervals theorem <-> Finlayson's EF as counterexample

Cantor's antidiagonal argument <-> Finlayson's EF as counterexample

continued fractions <-> Finlayson's EF as counterexample

Cantor's indicator function theorem <-> Finlayson's symmetrical

mapping as counterexample

Zuhair's binary tree theorem <-> Finlayson's BT = EF as counterexample

Cantor's powerset theorem <-> Finlayson's powerset as order type as

successor construction, and a dialetheic ur-element

Russell's negated correlates <-> Finlayson's note on statement of

structurally true languages

irrationals uncountable <-> Finlayson's "A function surjects the

rationals onto the irrationals"

I've been busy. And, that's not bad mathematics.

Now, I am very interested in:

a) results standardly establishing uncountability

b) applications solely due transfinite cardinals

Basically, that's with the notion that this symmetry between limit

ordinals has particular results for the diagonal arguments and may

well be a general consideration about them, and particularly a

generally unique result about them, and then, that applications solely

due transfinite cardinals would be of incredible interest for the

possibility they might advance science in, say, physics.

Regards,

Ross Finlayson