With respect to any given individual, this lapse may arise either because his knowledge of the universal has slipped from him, or because his knowledge of the particular has done so. The logicians—Avicenna among them—illustrate this with the man who thinks that a certain beast is pregnant. He is asked, “Do you not know that this animal is a mule?” He replies, “Yes.” He is then asked, “Do you not know that mules do not conceive?” Only then does he realize that it cannot be pregnant. Although he has been reminded of something he had forgotten, he has not thereby acquired knowledge that was previously unknown to him; and unless this point crosses his mind, the mere fact that he knows the beast is a mule does not oblige him to know that it cannot conceive.

Yet the case may call for no more than a single premise—the one that must be recalled. If he knows that the animal is a mule but has forgotten that mules do not conceive, he needs only the universal premise. Conversely, if he knows that mules do not conceive but has forgotten that this animal is a mule, then recalling the particular premise alone suffices.

On this question two camps have disagreed: Avicenna and those who follow him, and Fakhr al-Rāzī and his circle. Their dispute springs from the unsound principle they accepted in deference to Aristotle. Avicenna maintained:

“Besides the two premises, one must also be aware that the particular is subsumed under the universal.”

He explained:

“A person may know that this specific animal is a mule and know that the mule does not conceive, yet be oblivious to the fact that this particular falls under that universal. When he becomes aware of it, the conclusion emerges; otherwise it does not.”

Al-Rāzī retorted:

“This would require three premises: that this is a mule, that the mule does not conceive, and that this falls under that. My own view is that only two premises are needed—namely, that this is a mule and that the mule does not conceive. If one is heedless of the universal proposition, he is not actually cognizant of it; once it is present to his mind, it becomes impossible for him not to know that this mule does not conceive.”

The decisive word is that the desired conclusion may need one premise, or two, or three, or even four. The root of the confusion is their claim that theoretical conclusions both require and are sufficiently produced by two premises. They insisted that every theoretical conclusion must involve exactly two premises and that two premises suffice for every theoretical conclusion. Both assertions are false.