In my head there is a clear distinction between the axiomatic mode of thinking and the non-axiomatic one. It's fundamental to any mental activity. I cringe anyt

In my head there is a clear distinction between the axiomatic mode of thinking and the non-axiomatic one. It's fundamental to any mental activity. I cringe anytime I hear "but how can you even prove <non-axiomatic theory>?" or "but why is <an actual axiom> true?". It would be a shame not to have a very precise term for that, so I stick to "axiom" anyway.