Aristotle on Metaphysics(2004) - Bibotu.com

5THE DEFENCE OF THE PRINCIPLEOF NON-CONTRADICTION(Book IV.3–6, especially 3–4)1<strong>Aristotle</strong>’s characterization of the principle of noncontradiction(PNC)Here (in IV.3–6) <strong>Aristotle</strong> considers the principle of non-contradiction(PNC). This principle states that:PNC It is not possible for one and the same thing both to have andnot to have one and the same property.This can also be expressed in a more formal way: Fx);meaning ‘for any object x, and any property F, it is not possibly the case thatx is both F and not-F’. Or alternatively: (Fx & meaning‘for any object x, and any property F, it is necessarily not the case that x isboth F and not-F’.<strong>Aristotle</strong> formulates PNC in a number of ways:[1] It is impossible for the same thing both to belong and not tobelong to the same thing at the same time and in the samerespect.(1005 b 19–20)For example, it is impossible for motion both to belong and not to belongto one and the same spinning-top, at the same time and in the samerespect; i.e. one and the same spinning-top cannot at the same time and inthe same respect be both in motion and not in motion.