1. All axioms are assumptions. 2. You mean Logic? The foundation which axioms and theorems themselves rely on? Logic is like a recursive axiom. We assume logic

1. All axioms are assumptions. 2. You mean Logic? The foundation which axioms and theorems themselves rely on? Logic is like a recursive axiom. We assume logic is true (aka an axiom) then, logic allows us to create axioms themselves and build theorems off the axiom. The thing with logic is that it's almost a thought driven endeavor. We don't need to observe the world to go deeper. But we can't. The buck ends here. To answer the question "why?" we have to go deeper, but there's nothing left.