Page - 175 - in The Complete Aristotle

attributable-G, let us say, which is attributable to all B-and there may still be another term H prior to G, which is attributable to all G. The same questions arise, I say, because in these cases too either the series of prior terms to which a is not attributable is infinite or it terminates. One cannot ask the same questions in the case of reciprocating terms, since when subject and predicate are convertible there is neither primary nor ultimate subject, seeing that all the reciprocals qua subjects stand in the same relation to one another, whether we say that the subject has an infinity of attributes or that both subjects and attributes-and we raised the question in both cases-are infinite in number. These questions then cannot be asked- unless, indeed, the terms can reciprocate by two different modes, by accidental predication in one relation and natural predication in the other. 20 Now, it is clear that if the predications terminate in both the upward and the downward direction (by ‘upward’ I mean the ascent to the more universal, by ‘downward’ the descent to the more particular), the middle terms cannot be infinite in number. For suppose that A is predicated of F, and that the intermediates-call them BB’B”… -are infinite, then clearly you might descend from and find one term predicated of another ad infinitum, since you have an infinity of terms between you and F; and equally, if you ascend from F, there are infinite terms between you and A. It follows that if these processes are impossible there cannot be an infinity of intermediates between A and F. Nor is it of any effect to urge that some terms of the series AB… F are contiguous so as to exclude intermediates, while others cannot be taken into the argument at all: whichever terms of the series B… I take, the number of intermediates in the direction either of A or of F must be finite or infinite: where the infinite series starts, whether from the first term or from a later one, is of no moment, for the succeeding terms in any case are infinite in number. 21 Further, if in affirmative demonstration the series terminates in both directions, clearly it will terminate too in negative demonstration. Let us assume that we cannot proceed to infinity either by ascending from the ultimate term (by ‘ultimate term’ I mean a term such as was, not itself attributable to a subject but itself the subject of attributes), or by descending towards an ultimate from the primary term (by ‘primary term’ I mean a term predicable of a subject but not itself a subject). If this assumption is justified, the series will also terminate in the case of negation. For a negative 175