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It's quite common for mathematicians to consider the impact of axioms on a theorem. Mathematicians often consider whether a proof satisfies constructivist const
by Tloewald 13y ago
It's quite common for mathematicians to consider the impact of axioms on a theorem. Mathematicians often consider whether a proof satisfies constructivist constraints, requires the axiom of choice, and consider different geometric foundations (e.g. einstein's spacetime is non-euclidean). This doesn't cause religious disputes, and indeed mathematicians are happy to jump from one set of constraints to another.
I do agree that some axioms are grounded in observed reality (e.g. arithmetic, euclidean geometry) but discovering that axioms fail in unfamiliar situations is no generally a cause for soul searching or existential angst.
- Someone 13y ago"This doesn't cause religious disputes, and indeed mathematicians are happy to jump from one set of constraints to another." For me, that is the difference between an axiom and a belief. People with beliefs think their beliefs to be better than those of others. With axioms, that is not so. In fact, mathematicians like to doubt their axioms "do we really need the parallel postulate" was, for centuries, a subject of thought"
- Tloewald 13y agoActually for a while the parallel postulate was a matter of religious zeal. The studies of consistent geometries that had different behaviors for "parallel" lines was, for some reason, profoundly disturbing to some christians who tried to prove that the parallel postulate was not needed (i.e. That non-euclidean geometry was inconsistent). This was a matter of amusement for mathematicians, even though many mathematicians were a bit disturbed by non-euclidean geometry. Lewis Carrol, who was a mathematician and some kind of Anglican, couldn't stomach complex numbers. So religion can become confused with axioms, but it tends to start with religion, not axioms.