  (1) equates the PC with the Principle of Identity. (3) through (5) bring together the Law of Non-Contradiction (hereafter LNC) and the Law of the Excluded Middle (hereafter LEM) within the PC. These versions of the PC rely upon opposition based in contradictories. That is, P and ~P are mutually inconsistent and cannot be both true (LNC), and they are mutually exhaustive (LEM). (6) relies upon the LNC only, and not the LEM. This formulation of the PC, that is, relies upon opposition based in contraries. For example, “P is happy”, and “P is sad” are contraries and thus mutually inconsistent and cannot both be true (LNC). But they are not mutually exhaustive, because they both can be false (and thus, the LEM does not hold in these cases). The PC can be intended as a logical, ontological or psychological principle. As a logical principle, the PC is about opposite assertions. As an ontological principle, the PC is about properties in a subject. As a psychological principle, the PC is about what is possible and, especially, impossible to believe. Finally, the PC can operate in different realms. For example, it can operate in the realm of modality, perhaps serving to pick out necessary truths. Alternatively, it can operate in the realm of standard areas of human inquiry, perhaps serving as the foundation of mathematics (but perhaps not in metaphysics, natural theology, physics, and many other disciplines).