As for the method of elimination and division (sabr wa-taqsīm), its gist is nothing more than the claim that all the attributes of the original case can be confined to a definite list, after which everything save the retained attribute is dismissed. Yet this, too, is far from certain. The ruling may belong to the original simply by virtue of the original itself and not on account of anything external—otherwise one would be forced into an infinite regress. And even if it were granted that the ruling does arise from something external, it might still proceed from some other factor altogether, one that the investigation has failed to uncover.
The situation is unlike that of observed, habitual matters: with sound eyesight and no obstacles, we have no doubt that there is neither a sea of mercury nor a mountain of gold standing before us unseen. Even if the causal attribute were confined to a single factor, the ruling might be due to the whole complex of attributes, or to a part that is not realized in the branch. The fact that the ruling accompanies the shared attribute in one instance—while the other concomitant qualities found in the original are absent—does not prove that the shared attribute alone is causative; for that single instance may well be governed by some other cause, and there is nothing impossible in that. And should no cause be found except the shared attribute, it may still account for the ruling only in that particular instance, not in every instance. If, however, it can be demonstrated that the attribute, by the very universality of its essence, necessarily entails the ruling, then analogy becomes superfluous, however remote the demonstration may be.
They further contend that bodily physiognomy (firāsah) is itself a form of analogical inference, except that the link between the original and the branch is an indicator of the cause, not the cause itself. In juristic parlance this is called “evidential analogy” (qiyās al-dalālah). One reasons from an effect of a cause to the existence of the cause, and then from that cause to another of its effects. The premise is that temperament is the cause of both inner character and outward appearance: one therefore infers temperament from outward form, and then infers inner character from the temperament—such as inferring courage from the breadth of the upper chest on the assumption that both are products of the same temperament, as is observed in the lion.
To establish the cause in the original case one must again resort to positive and negative concomitance or to elimination and division, as noted earlier. And even if the two rulings in the original were assumed to share a single cause, nothing prevents one of them from being present in the branch without that cause; in that event the other ruling would not necessarily follow.
Such is their discourse as refined for them by Muslim dialecticians who raised these objections against analogical inference, for the statements of their own leading figures on the subject display none of this precision—