You don't blindly believe axioms, it is just that certain sets of axioms happen to allow us to make useful predictions about the world. While you could have phi

You don't blindly believe axioms, it is just that certain sets of axioms happen to allow us to make useful predictions about the world. While you could have philosophical discussions about weather certain axioms are true (whatever that means), and what their exact relationship with the world is, you don't need to do this to see that axioms are useful to arrive at mathematical conclusions, which then can be used to make predictions about the world. Why do we believe that if we take 1111 apples and then add 2222 more we will get 3333 of them? Because we have seen from experience that a certain way of applying mathematics to the real world gives great results. The same for conclusions following known axioms, they seem to generally work well for describing our world.