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Topic: A flaw in modern axiomatic geometry?
Replies: 4   Last Post: May 1, 2013 4:23 PM

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LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
Re: A flaw in modern axiomatic geometry?
Posted: Apr 30, 2013 8:14 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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





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