Aristotle on Metaphysics(2004) - Bibotu.com

THE DEFENCE OF PNC 145PNC will not apply to anything, and in this sense PNC will not be true: itwill not be true of any thing.It is worth emphasizing this central idea, i.e. that PNC may not be trueof a thing precisely because the thing may be so radically indeterminatethat it is not possible to distinguish a particular respect in which it may beeither F or not-F but not both F and not-F. Graham Priest offers thefollowing argument against PNC and in favour of thinking that there aretrue contradictions:Another example: I walk out of the room; for an instant, I amsymmetrically poised, one foot in, one foot out, my center of gravitylying on the vertical plane containing the center of gravity of thedoor. Am I in or not in the room? By symmetry, I am neither inrather than not in, nor not in rather than in. The pure light ofreason therefore countenances only two answers to the question: Iam both in and not in, or neither in nor not in…. But wait aminute. If I am neither in nor not in, then I am not (in) and not(not in). By the law of double negation, I am both in and not in.(Even without it, I am both not in and not not in, which is still acontradiction.)(Priest 1998:415)But there is a very natural objection to this argument against PNC. Foreven if it shows that I can be both in the room and not in the room,indeed even if it shows that I can be just as much in the room as not in theroom (and it is natural to think that it shows this much), evidently it doesnot show that I can, in one and the same respect, be both in the room andnot in the room. On the contrary, as Priest describes the case, it is inrespect of the one side of my centre of gravity, i.e. of my centre of gravitythat for an instant lies on the vertical plane containing the centre of gravityof the door, that I am in the room, but in respect of the other side of mysame centre of gravity that I am not in the room. And this centre of gravityis, precisely, what distinguishes these two respects of mine. So, as Priestdescribes the case, it is, precisely, possible to distinguish a particular respectin which a thing may be either F or not-F but not both F and not-F.Because of this possibility, Priest’s argument against PNC fails. Certainly itfails against PNC as defended by <strong>Aristotle</strong>. For <strong>Aristotle</strong> emphasizes thatPNC is true of a thing only if we consider the thing in one and the samerespect. This also shows something crucial, namely that to deny that PNCis true of a thing, one must argue that it is not possible to consider the