Aristotle on Metaphysics(2004) - Bibotu.com

140 THE DEFENCE OF PNCin this way deny PNC generally assert not only that some things are both Fand not-F, but that all things are both F and not-F.It is crucial to emphasize here the distinction between the view that somethings are both F and not-F and the view that all things are both F andnot-F. In its original formulations, and as <strong>Aristotle</strong> sets out to defend it,PNC says that no things can be both F and not-F. Indeed it says that nothings, with regard to any property F, can be both F and not-F. So to denyPNC, one need only argue that some things, with regard to some propertyF, are both F and not-F. One may go further, and argue that all things,with regard to some property F, are both F and not-F, or even that allthings, with regard to every property F, are both F and not-F. But evidentlyone need not.It is, therefore, especially striking and puzzling that when <strong>Aristotle</strong>defends PNC against those who deny it, he concentrates largely on themost radical denial: all things, with regard to every property F, are both Fand not-F. This also immediately gives rise to a problem about hisdefence. For suppose that he succeeds in his response to the radical denialof PNC, i.e. in showing that some things, with regard to some property F,cannot be both F and not-F; or even that all things, with regard to someproperty F (their essence, it will emerge), cannot be both F and not-F.Still, this will not by itself show that all things, with regard to any propertyF, cannot be both F and not-F. So it will not show what <strong>Aristotle</strong>originally sets out to show (we will also return to this problem later in thischapter, §9).<strong>Aristotle</strong> is clearly aware of the distinction between the view that somethings are both F and not-F and the view that all things are both F andnot-F (see especially 1008 a 7–12). In particular, when he diagnoses whatleads Anaxagoras and Democritus to deny PNC (1009 a 22f.), he arguesthat they deny PNC only with regard to changing things, not with regardto all things. In other words, they argue that changing things are both Fand not-F, not that all things are both F and not-F. Indeed, they arguethat a thing is both F and not-F precisely if F is a property that the thinghas in so far as it is involved in change, i.e. in so far as it changes fromhaving to not having this property. That this is how <strong>Aristotle</strong> understandsthe way in which they deny PNC is especially clear from his response tothem (1009 a 30–38). For he responds that, on the one hand (1009 a 30–36),their argument for denying PNC with regard to changing things isfallacious, but also, on the other hand (1009 a 36–38), that there may bethings that are not subject to change, and to generation and destruction, inany way.