It is shown that the mathematical formalization of the concept of determinism and separability in the derivation of Bell's inequality is too restrictive to express the standard meaning of these concepts as used in classical physics. In fact, classical physical systems which are non-problematic and nonparadoxical are exhibited which violate Bell's inequality. For this reason it is concluded that Bell's inequality, as it has been used so far in the physical experiments related to the socalled Einstein-Podolsky-Rosen paradox cannot exclude a realistic interpretation of quantum mechanics. New kinds of experiments are proposed to test the validity of these concepts in the physical world.