It is commonly accepted that Aristoteles was a philosopher and George Boole was a mathematician. When I look at a boolean formula and compare it with an Aristotele's text, it is clear to my eyes which one is mathematics. However, both of them try to be rigorous as possible following certain rules, and the difference between mathematics and philosophy cannot be just a matter of notation. I can see that in the case of Boole rules are defined more strictly and precisely, but this intuitive observation isn't enough for my curiosity.
So, can anyone explain in a formal way when a rigorous reasoning is considered mathematics and when it is not?