  Aristotle says that PNC is one of the common axioms, axioms common to all the special sciences. It has no specific subject matter, but applies to everything that is. It is a first principle and also the firmest principle of all. Like modus ponens, as Lewis Carroll memorably showed, PNC does not function as a premise in any argument. Unlike modus ponens, PNC is not a rule of inference. Aristotle says that it is a principle which “is necessary for anyone to have who knows any of the things that are” (Metaph IV 3 1005b15). It is no mere hypothesis.