Date: Apr 30, 2013 8:14 PM
Author: LudovicoVan
Subject: Re: A flaw in modern axiomatic geometry?

"David Hartley" <me9@privacy.net> wrote in message 
news:FOgypcHItAgRFwfN@212648.invalid...
> In message <klodnl$99m$1@dont-email.me>, Julio Di Egidio
> <julio@diegidio.name> writes

>>The mathematical gist is here:
>><https://www.facebook.com/notes/reid-barnes/the-lite-triangle-axiom/230992473620001>
>>
>>Can anyone tell whether he is correct or not? If not, please tell where
>>the mistake is.

>
> At a quick glance, his mistake is in assuming that, because Pasch's Axiom
> can be proved in a system having Playfair's axiom and his lite-triangle
> axiom, then to assume Pasch's Axiom is to implicitly include Playfair's.
> I.E. the fallacy that (A -> B and B) implies A.


As I gather it, what he says is that from Playfair's axiom and his
lite-triangle axiom one can prove Pasch's axiom. But the two former axioms
are common to Euclidean and non-Euclidean geometry, while Pasch's axiom is
Euclidean only: hence the contradiction.

Julio