Failed mathematical and scientific 'self-evident truths'?

Euclid's parallel lines never meeting (doesn't hold good in actual space/time); the law of excluded middle (doesn't hold good for fuzzy sets). Can you think of similar examples of 'truths' taken to be absolutely self-evident which are now rejected or questioned ?

amansscientiae : I never spoke of truths but of 'truths'. The scare-quotes were deliberate. I had in mind drastic revisions to what had once been taken to be self-evident. The law of excluded middle was once taken to hold good universally, without qualification. All I said was that it doesn't hold good for fuzzy sets. This doesn't mean I am confusing axiomatic systems. The parallel lines axiom was taken to hold good for actual space and not only within a geometrical system. That space is Euclidean once appeared self-evident. The prevailing view is that it no longer does so. And please, just make your points - don't add personal abuse.

Another example is the law of conservation of mass and the law of conservation of energy. They were considered "axioms" of physics until the theory of relativity showed that energy and mass are equivalent. Now we have the law of conservation of mass-energy, which is still unchallenged. Science and mathematics are based on assumed principles called "laws" or "axioms", and the resulting theories are only valid as long as those principles hold. However, there is nothing in the scientific method that prevents a law or axiom from being changed or discarded. One such set of laws are the laws of thermodynamics which predict the "heat death" of the universe. As my college physics instructor told us long ago "maybe we will find that these laws do not hold everywhere". Experimental evidence can overthrow any law or principle.

Actually, Euclid's parallel lines postulate was never considered self-evident by everyone. A number of mathematicians since Euclid spent considerable time trying to prove it from Euclid's other postulates. Which means that they wanted to believe it, but were not comfortable simply assuming it. Report It

A 'truth' which many would take to be self-evident is the existence of simultaneity. Einstein disproved this in 1905.

Euclid's parallel lines are an axiom. It is absolutely valid. One just can't find a realization in the real world for it. But one does not have to. Math does not have a requirement that the objects it talks about need to exist physically. There is, in my experience, not a single basic mathematical object of importance that has a real world implementation. And yet, all real world objects have a multitude of mathematical models. Bummer.

The law of excluded middle is an axiom. It is absolutely valid in naive Boolean logic. If you don't understand the difference between (and independence of) one axiom system and another (like that of fuzzy sets), you don't understand the first thing about mathematics.

Science does not have truths. Only religion and philosophy talk about truths. Science talks about facts. And it comes up with approximative descriptions of facts. It never requires that these descriptions be perfect. In science we are perfectly happy with "good enough". If you don't understand that concept, you will never understand science.

Sorry... but you need to go back and learn pretty much everything you think you know about these things anew. Because as it is, you do not understand the most trivial things about either math or science.

Good luck! You have a long way to go before you will see the light.

If you're talking science, then you KNOW only one thing for sure: that nothing is 'self-evident' and that nothing will hold forever.
No straight lines in this universe, not even for light itself; no perfect this or absolutely that...
Einstein was certain that the speed of light was THE absolute limit, and it seems that nowadays, some scientists may very well prove him wrong.
If you talk about science, you have to go with ninety-some percent of the time, never 100.