4 ms·

It’s a matter of scope. Axioms are assumptions that undergird the formal edifice (those or mathematics or arithmetic) whereas assumptions are local to the theor

by qubex 4y ago

It’s a matter of scope. Axioms are assumptions that undergird the formal edifice (those or mathematics or arithmetic) whereas assumptions are local to the theory. ‘Assumptions’ is a synonym of ‘postulates’. Axioms are foundational, such as m×n=m×n (which is true for scalars, but not true in general for matrices).

defined 4y ago
Did you mean m×n=n×m?
- HWR_14 4y ago
  Both are axioms. a = a (and by extension mxn = mxn) is another axiom.
  - goldenkey 4y ago
    Don't forget ©=©
- qubex 4y ago
  Yes. Oops.
naasking 4y ago
It's a distinction without a real difference. Calling an "assumption local to a theory" an axiom is fine. We have axiomatizations of both general relativity and quantum mechanics, for instance.