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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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Posts: 4,165
From: London
Registered: 2/8/08
Re: A flaw in modern axiomatic geometry?
Posted: Apr 30, 2013 8:14 PM
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"David Hartley" <> wrote in message
> In message <klodnl$99m$>, Julio Di Egidio
> <> 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.


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