Axioms are just another aspect of Mathematics and changing them has utility for mathematicians. Euclidean geometry for example uses one set and a wide range of non Euclidean geometry systems use different sets.
The universal truth that in Euclidean geometry the interior angles of a triangle add up to 180 degrees is not diminished because the interior angles of a triangle can add up to different numbers in spherical geometry. It’s just two different systems but they all fall under Mathematics.
This is a mistaken understanding. Axioms define the logic of Mathematics.
E: I guess I may have misinterpreted. I mixed up “supersede” with “precede” in my head. I mean to say axioms are a precursor to logic systems. The axiom has to be agreed upon before any truthful statements can be made.
If A, B, C … then Y is a self contained true statement. You can’t simply say Y alone is true because without A, B, C, … it’s not true.
People tend to assume A, B, C etc when they say things like 1 + 1 = 2 but that’s just a quark of language. Words like him or they work because people can work out the specifics from context.
This phrasing helps me to see your point; gives me something to think about. Thanks for your patience in explaining! I enjoyed the conversation.
> 1 = 1 isn’t inherently true on it’s own
This sounds a whole lot like "math isn't a universal truth". I guess we need to take a step back, since it seems this is where the disagreement lies: what does it mean for something to be a universal truth?
My position is that a truth is universal if it is self-evident; that is, it does not require an agreement between observers. These axioms are that agreement and therefore Mathematics, which stems from such axioms, is not universal truth.