People make more working calculators than broken ones. Because they are useful because their answers model other parts of reality. And the axioms are in the human brains. Yes, you can’t derive axioms from physical equations without bridge laws. But you also need bridge laws for anything else high level like utility or physical description of gaining knowledge from experiments. And that is also fine for logic, because you couldn’t perfectly access logical truth by any other procedure anyway, because your implementation of it is failable.
People make more working calculators than broken ones. Because they are useful because their answers model other parts of reality. And the axioms are in the human brains. Yes, you can’t derive axioms from physical equations without bridge laws. But you also need bridge laws for anything else high level like utility or physical description of gaining knowledge from experiments. And that is also fine for logic, because you couldn’t perfectly access logical truth by any other procedure anyway, because your implementation of it is failable.