I always thought of axioms as "starting points" or "bases". The rules of logic require "starting points". You can't demonstrate anything from nothing. Those ar

I always thought of axioms as "starting points" or "bases". The rules of logic require "starting points". You can't demonstrate anything from nothing. Those are the axioms. It's worth noting that almost any statement can be used as an axiom. You can build a math on top of "2+2=5". It just won't be a very useful math. Which brings up the point of usefulness. Some sets of axioms are more useful than others. Usually because they seem to align with how the universe appears to work. But in other cases they are just convenient. So there are no "really, really true" axioms. But there are "really, really useful" ones.