In my mind this is literally what math is. We start with axioms, and derive conclusions. There's probably more to it than that, but that's the understanding I'm at now.
But shouldn't it also be part of the axioms what are the rules that allow you to derive new theorems from them?
So then you could self-apply it and start ... deriving new rules of how you can derive new theorems and thus also new rules, from axioms?
I'm jusr confused a bit about "axioms" and "rules". What's the difference?
Choosing the axioms is difficult.
But shouldn't it also be part of the axioms what are the rules that allow you to derive new theorems from them?
So then you could self-apply it and start ... deriving new rules of how you can derive new theorems and thus also new rules, from axioms?
I'm jusr confused a bit about "axioms" and "rules". What's the difference?