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>It's something we can't prove Edit: TL;DR: An axiom is not something that is provably unprovable, it something that remains to be proved. Yet you assume the
by posterboy 10y ago
>It's something we can't prove
Edit: TL;DR: An axiom is not something that is provably unprovable, it something that remains to be proved.
Yet you assume the axiom could have been proved wrong by aliens, which would give the opposite of the axiom as new universal law, which would be paradoxical. Thus, the axiom couldn't be wrong nor right, for it's not a statement, it's a paradox devoid of meaning. If that's what you implied, I might as well just be missing how that is useful. I understand that Hilbert's axioms of Geometry work the same way, so I am not dismissing the idea of axiomatics. I'm just saying that the axiom defines space and time under the presumption of an understanding of laws. Thus I think, obviously the conclusion, universal laws wouldn't exist or could be broken is rather unpractical, to put it mildly.
However, I am not (ever) sure what I am even saying. So take it with a pinch of salt. On the one hand, if axiomatics are part of our logic framework for laws, an axiom couldn't a priori define laws. On the other hand, I'm tossing the idea around for a while, that our understanding of logic arises by proving itself into existence, so we prove axiomatics a viable framework simply by using it to axiomatize.
In the likely case the the previous paragraph is written ineligibly: all I am saying is, that axioms should be self evident, so it isn't really worth the many words, except as an exercize in formalizing unfinished ideas in a dialog. Just to see if get any immediate push back, in case I am wrong, or ignorance, in case the topic is really self-evident or absurd or whatever.