"David Hartley" <email@example.com> wrote in message news:FOgypcHItAgRFwfN@212648.invalid... > In message <firstname.lastname@example.org>, Julio Di Egidio > <email@example.com> 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.