Here are some laws of logic:http://en.wikipedia.org/wiki/Three_clas ... #Aristotlehttp://en.wikipedia.org/wiki/Law_of_identityhttp://en.wikipedia.org/wiki/Law_of_noncontradictionhttp://en.wikipedia.org/wiki/Law_of_excluded_middle
Here are Euclid's five axioms which generates Euclidean geometry:http://en.wikipedia.org/wiki/Euclidean_axioms#Axioms
As you know, Einstein made use of non-Euclidean geometry in his general relativity. The non- part comes in when the fifth axiom is no longer assumed.
What makes Euclid's five axioms flexible but Aristotle's three axioms of reason not flexible?
If I, for example, no longer assume the first axiom (of identity), then I can say S can be a square and a circle simultaneously.
Even QM is saying that one particle can exist in two places, which makes me suspicious of the axiom of identity.
The axioms of Aristotle have an application of course but I do not think they are inviolate, any more than Euclid's axioms can be bent or broken.
If everything requires proof, where is the proof of the three laws of thought? And if there is no proof, then they are axioms. Axioms are not inviolate.