This, too, traces back to entailment: the existence of one contrary requires the absence of the other, and its absence requires the existence of the first; the two therefore cannot coexist, nor can both be absent.

However many figures one may enumerate, they all amount to one and the same point—namely, that the proof necessitates the thing proved. That necessity can be expressed in many guises, some of which they have cited, others not.

They declare that demonstration is limited to the conjunctive syllogism (iqtirānī) and the exceptive syllogism (istithnāʾī). The conjunctive, they say, is confined to four figures, and the exceptive to the connected conditional and the disjunctive conditional, yielding six figures in all. Most of them, however, omit the fourth conjunctive figure, deeming it counter-intuitive. They arrive at the number four by insisting that a proof must consist of two premises sharing a middle term. If that middle term is the predicate in the minor premise and the subject in the major, we have the first figure, which yields all four kinds of conclusion. If it is the subject in both premises, we have the second figure, which produces negative conclusions. If it is the predicate in both, we have the third figure, which produces affirmative conclusions. And if it is the predicate in the major and the subject in the minor—the reverse of the first—this is the fourth figure, farthest from natural usage; most logicians omit it. They thus count only five figures: the three just mentioned together with the exceptive connected conditional and the exceptive disjunctive conditional.

Should these figures prove helpful, they are but one way of casting arguments; the representation of proofs is no more restricted to them than it is to two premises. Such a restriction is mistaken both positively and negatively, for a proof may consist of a single premise or of several. These figures merely proliferate the ways in which a proof may be expressed; they do not stop at five or six. One can advance a proof without any of these figures at all and without two premises, when it rests on a single premise.

If they maintain that every argument must ultimately take one of these figures, we answer: rather, every argument reduces to the simple fact that the evidence entails the conclusion. At that point one must decide whether the criterion lies in the outward wording and shape of the figures they list, or in the meaning they intend; if the consideration is