Date: Apr 30, 2013 8:14 PM
Subject: Re: A flaw in modern axiomatic geometry?
"David Hartley" <email@example.com> wrote in message
> In message <firstname.lastname@example.org>, Julio Di Egidio
> <email@example.com> writes
>>The mathematical gist is here:
>>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.