ARISTOTLE'S PRIOR AND POSTERIOR ANALYTICS

THE PURE OR ASSERTORIC SYLLOGISM 37accordance with the proper order of things that it should be thefirst to be worked out.Aristotle not infrequently speaks as if there were other fonns ofinference than syllogism-induction, example, enthymeme. Butthere is an important chapterl in which he argues that if inferenceis to be valid it must take the syllogistic fonn; and that this washis predominant view is confinned when we look at what he saysabout these other types. He means by induction, in differentplaces, quite different things. There is the famous chapter of thePrior Analytics in which induction is reduced to syllogistic fonn!But the induction which is so reduced is the least important kindof induction-the perfect induction in which, having noted thatmembership of any of the species of a genus involves possessionof a certain attribute, we infer that membership of the genusinvolves it. More often 'induction' is used by Aristotle to denotesomething that cannot be reduced to syllogistic fonn, viz. theprocess by which, from seeing for instance that in the triangle wehave drawn (or rather in the perfect triangle to which this is anapproximation) equality of two sides involves equality of twoangles, we pass to seeing that any isosceles triangle must have twoangles equal. This cannot be regarded as an inference; if youregard the first proposition as a premiss you find that the seconddoes not follow from it; the 'induction' is a fresh act of insight.Thus the only sort of induction which Aristotle, in all probability,regarded as strict inference is that which he reduces to syllogism.The kind of inference which he calls example is just an inductionfollowed by a syllogism; and enthymeme is just a syllogism inwhich the propositions are not known to be true but believed tobe probable.There are, however, two kinds of inference which Aristotleregards as completely valid and yet not syllogistic. One is thenon-syllogistic part of reductio ad impossibile. In connexion withreductio he makes the remark that the propositions by which aproposition is refuted are not necessarily premisses, and thenegative result the conclusion, sc. of a syllogism. 3 The samepoint is made in another passage, in which he points out theexistence of arguments which, while conclusive, are not syllogistic;e.g. 'Substance is not annihilated by the annihilation ofwhat is not substance; but if the elements out of which a thing ismade are annihilated, that which is made out of them is dez..I An. Pr. i. 23.11. 23. 3 An. Post. 87a2