 Before embarking on this study of substance, however, Aristotle goes on in Book Γ to argue that first philosophy, the most general of the sciences, must also address the most fundamental principles—the common axioms—that are used in all reasoning. Thus, first philosophy must also concern itself with the principle of non-contradiction (PNC): the principle that “the same thing cannot at the same time belong and also not belong to the same thing and in the same respect” (1005b19). This, Aristotle says, is the most certain of all principles, and it is not just a hypothesis. It cannot, however, be proved, since it is employed, implicitly, in all proofs, no matter what the subject matter. It is a first principle, and hence is not derived from anything more basic.