that this animal is a mule and that a mule does not conceive, it necessarily follows that the idea of its not conceiving will also occur to him.

The conclusion is inseparably tied to the proof. Whenever a person forms a mental image of the proof together with the fact that the conclusion follows from it, he at once forms a mental image of the conclusion. Thus, when he conceives that the creature is a mule and understands the corollary—that pregnancy is negated for every mule—he inevitably conceives the negation of pregnancy for this particular animal. A mere awareness of the proof, without awareness of the conclusion’s entailment, does not yield knowledge.

Corollaries whose connection to the proof is manifest are grasped as soon as one knows the proof and its entailment. Hidden corollaries, whose entailment requires a middle term—namely, a second proof demonstrating that entailment—must be established by that additional step. Minds differ in this: one mind may need the middle term to perceive the entailment, while another does not.

Dialecticians have disagreed about the knowledge that arises from the proof: does it follow from the proof by ordinary causal linkage (as satiety follows eating), or by a rational indispensability called “implication,” such that separation is impossible, just as knowledge and will cannot exist without life? The first view was held by the early dialecticians, among them al-Ashʿarī; for that reason the Muʿtazilites classed it under the heading of “generation.” It is like sight that accompanies deliberate staring, or hearing that accompanies attentive listening.

Otherwise, the occurrence of knowledge of the proof without knowledge of what it proves is not intrinsically impossible; rather, the first is a cause and inducement of the second according to Allah’s established way with His servants. Life, by contrast, is a prerequisite for knowledge, which is why knowledge exists together with life without life being temporally prior to it, whereas knowledge of the proof does precede knowledge of that which is proved.

Despite their debate on this point, Muslim dialecticians agree that the proof is a single premise, as we have said. What has been illustrated with the mule applies to every theoretical inquiry: a person may know the particular without knowing the universal, and he may know the universal without knowing the particular. He may know that this animal is a mule yet be unaware that mules do not conceive, or he may know that a mule does not conceive yet be unaware that this animal is a mule. His knowledge of the particular need neither precede nor follow his knowledge of the universal; for some people the particular comes first, while for others the universal precedes.