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LudovicoVan
Posts:
3,780
From:
London
Registered:
2/8/08


Re: A flaw in modern axiomatic geometry?
Posted:
Apr 30, 2013 8:14 PM


"David Hartley" <me9@privacy.net> wrote in message news:FOgypcHItAgRFwfN@212648.invalid... > In message <klodnl$99m$1@dontemail.me>, Julio Di Egidio > <julio@diegidio.name> writes >>The mathematical gist is here: >><https://www.facebook.com/notes/reidbarnes/thelitetriangleaxiom/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 litetriangle > 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 litetriangle axiom one can prove Pasch's axiom. But the two former axioms are common to Euclidean and nonEuclidean geometry, while Pasch's axiom is Euclidean only: hence the contradiction.
Julio



