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A flaw in modern axiomatic geometry?
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Julio Di Egidio
Apr 30, 2013, 8:32:33 AM4/30/13
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Hello all,
This guy, Mr Reid Barnes, claims to have found a fundamental flaw in modern
axiomatic geometry that, essentially, invalidates non-Euclidean geometry.
The overview article is here:
<https://www.facebook.com/notes/reid-barnes/the-problem-with-math/288077664578148>
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.
Thank you,
Julio
This guy, Mr Reid Barnes, claims to have found a fundamental flaw in modern
axiomatic geometry that, essentially, invalidates non-Euclidean geometry.
The overview article is here:
<https://www.facebook.com/notes/reid-barnes/the-problem-with-math/288077664578148>
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.
Thank you,
Julio
David Hartley
Apr 30, 2013, 2:19:52 PM4/30/13
to
In message <klodnl$99m$1...@dont-email.me>, Julio Di Egidio
<ju...@diegidio.name> writes
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.
--
David Hartley
<ju...@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
><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.
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.
--
David Hartley
Julio Di Egidio
Apr 30, 2013, 8:14:31 PM4/30/13
to
"David Hartley" <m...@privacy.net> wrote in message
news:FOgypcHI...@212648.invalid...
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
news:FOgypcHI...@212648.invalid...
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
Butch Malahide
Apr 30, 2013, 9:56:38 PM4/30/13
to
On Apr 30, 7:14 pm, "Julio Di Egidio" <ju...@diegidio.name> wrote:
>
> 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.
Playfair's axiom? Isn't that the one that says that only one parallel
>
> 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.
to a given line can be drawn through a given point not on the line?
That axiom is common to Euclidean and non-Euclidean geometry?
Julio Di Egidio
May 1, 2013, 4:23:53 PM5/1/13
to
"Butch Malahide" <fred....@gmail.com> wrote in message
news:cea27a9c-4ebb-43ac...@r3g2000yqe.googlegroups.com...
I had misread. Thank you and David Hartley for the feedback, after more
reading I see he had nailed it since the beginning.
Julio
news:cea27a9c-4ebb-43ac...@r3g2000yqe.googlegroups.com...
reading I see he had nailed it since the beginning.
Julio
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