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Two straight lines parallel at one point will remain parallel at every other point, and never cross. That is a basic postulate. 1 + 1 = 2, another postulate. Postulates are where you start from, they are the base around which a system of logic or proof is built and yet they are truths "outside" the proof-system.

No, actually, they're not. Congratulations, your understanding of mathematics hasn't progressed beyond what was known in the mid-1850's...

With the advent of consistent non-Euclidean geometries in the 19th century, it was realized that postulates are *not* "truths outside the proof-system", and there are in fact opposing postulates which can still be used as the foundation of consistent, meaningful formal systems.

The Holy Text and Revelation at Sinai are not hypotheis nor theory, they are Primal Truth.

That's one hypothesis, certainly.

A little bit of "learning" just puts them deeper in the hole. I got him in #137.

With the advent of consistent non-Euclidean geometries in the 19th century, it was realized that postulates are *not* "truths outside the proof-system", and there are in fact opposing postulates which can still be used as the foundation of consistent, meaningful formal systems.

Quite a lot for one little word *not*.

It's been quite awhile since I've used any non-Euclidean geometry, so please be patient with me here.

By *not*, did you mean:
a) postulates NEED NOT be "truths outside the proof-system"
b) postulates are NEVER "truths outside the proof-system"
(they are either meaningless, or non sequiturs)
c) the whole idea of universal truths is valid, but much less common than previously assumed d) the whole idea of universal truths is a misunderstanding based on a limited philosophical system?

Perspiring minds want to know! :-) Full Disclosure: Just stirring the pot, here.

Experimental results are one way of resolving discrepancies between otherwise consistent, but conflicting, models...