Aristotle on Metaphysics(2004) - Bibotu.com

THE DEFENCE OF PNC 129<strong>Aristotle</strong> characterizes PNC as a ‘principle of reasoning’ (sullogistikēarchē, 1005 b 7) and as an ‘axiom’ in just the sense of a ‘principle ofreasoning’ (see 1005 a 20). He argues that PNC is true of all things, andthat everyone and all sciences make use of it. So he thinks that PNC is aprinciple of all reasoning. But an axiom, as he uses the term ‘axiom’, issomething that one must presuppose if one is to learn anything (seePosterior Analytics I. 2, 72 a 16–17). Hence PNC is a principle of allreasoning in the sense that if one is to reason at all about anything, and solearn anything in a way that involves reasoning, one must presuppose PNC.Unfortunately, he does not spell out how we presuppose PNC in allreasoning. In the Prior Analytics he uses the term ‘reasoning’ (sullogismos)in particular to mean ‘deductive argument’ (I. 1, 24 b 18–20). So apparentlyhis view is that we presuppose PNC in all deductive argument. But hedoes not say how we do this.Here is an attempt to show how we presuppose PNC in all deductiveargument. A deductively valid argument is an argument in which, if thepremises are true, then necessarily the conclusion is also true:A deduction [sullogismos] is an argument in which, if certain things aresupposed [i.e. the truth of the premises], then something other thanthe things supposed [i.e. the conclusion and its truth] follows ofnecessity from their being true [i.e. from the premises being true].(Prior Analytics, I. 1, 24 b 18–20)In short, a deductively valid argument is an argument in which thepremises entail the conclusion. But this means that, in a deductively validargument, to assert the premises and deny the conclusion is to assert acontradiction. This shows that the principle that it is impossible to assert acontradiction, i.e. the principle of non-contradiction in one of itsformulations, is part of the definition of a deductively valid argument. Forthe impossibility, in a deductively valid argument, of asserting the premisesbut denying the conclusion, is precisely the impossibility of asserting acontradiction. So, if we think that some arguments are deductively valid,we must think that it is impossible to assert a contradiction. In short, PNCis part of the concept of deductive validity, and it is in this way that wepresuppose PNC in all deductive argument.However, to conclude that we presuppose PNC in all reasoning, andnot just in all deductive reasoning and deductive argument, wemust suppose that <strong>Aristotle</strong> thinks that deductive argument is central to allreasoning and rational thought, and that there would be no reasoning orrational thought if there were no deductive argument. Or at least we must