 But it may be useful to point out that both in status and intended role there is a difference between Kennard’s inequality and Heisenberg’s previous formulation  (2).  The inequalities discussed here are not statements of empirical fact, but theorems of the quantum mechanical formalism. As such, they presuppose the validity of this formalism, and in particular the commutation relation  (1),  rather than elucidating its intuitive content or to create “room” or “freedom” for the validity of this formalism. At best, one should see the above inequalities as showing that the formalism is consistent with Heisenberg’s empirical principle.