It is, in fact, the very substance of the proof itself, and that substance cannot be grasped from the formal patterns of syllogism they set out. Whoever recognizes the substance—such that he knows this proposition necessarily entails that one—has understood the indication, whether he casts it in the mold of a syllogism or not, and whether he phrases it in their terminology or in other words. Indeed, the expressions refined by the intellects and tongues of Muslims are far, far superior to theirs.

Every categorical (iqtirānī) syllogism ultimately comes down to the necessary implication of one matter for another and vice versa, exactly as has been noted; and this is precisely what the conditional (istithnāʾī) syllogism—made up of the conjunctive and the disjunctive—amounts to.

In the conjunctive conditional, one argues by way of implication: from the establishment of the implicant—the antecedent, which is the condition—to the establishment of the consequent, which is the result; or, conversely, from the negation of the consequent—the result—to the negation of the implicant, the condition.

As for the disjunctive conditional—called sabr wa-taqsīm by the juristic theorists and taqsīm wa-tardīd by some dialecticians—its purport is to reason from the affirmation of one of two contradictories to the negation of the other, and from its negation to the affirmation of its counterpart, or to reason from the affirmation of one of two contraries to the negation of the other. It has four divisions; hence, in the proposition that prevents both concurrence and absence (māniʿat al-jamʿ wa-l-khalū) there are four possible exceptions: if this is affirmed, its contradictory is negated, and likewise the converse; and if this is negated, its contradictory is affirmed, and likewise the converse.

The “preventer of concurrence” (māniʿat al-jamʿ) is the reasoning that, by affirming one of two contraries, negates the other, for the two are mutually incompatible.