The same holds true for particular instances. A man’s knowledge that this mule does not conceive is just like his knowledge that that mule does not conceive, and that yet another does not conceive. He is not obliged to know that one given instance is identical, in the relevant respect, to another; he may be aware of one case while remaining unaware of the next. His grasp of particulars need not precede his grasp of the universal proposition, nor must he be more knowledgeable about the particulars. Likewise, his grasp of the general, all-inclusive statement—through which he derives a ruling for individual cases—need not be stronger than, or prior to, his grasp of those individual cases themselves. In other words, his knowledge that every mule does not conceive is not necessarily stronger, nor is the universal knowledge that he gains from particular cases necessarily earlier in his mind, than his knowledge that this animal is a mule. Indeed, he might be ignorant of the fact that it is a mule, just as he might be ignorant of the fact that a mule does not conceive.

Suppose, however, that he knows a mule does not conceive and bases this on the widely circulated reports of people. That knowledge embraces the particular animal exactly as it embraces whatever is more general—red mules, black mules, or those whose mother is a she-donkey. Should it occur to him that a creature born of a she-donkey and a stallion might conceive, one need only say to him: “Do you not know that this is a mule, and that a mule does not conceive?”

If his conviction that a mule does not conceive rests on personal experience, experience itself is never universal; he has merely experimented on certain mules. Whatever grounds allow him to judge that all other mules are like those he tested will equally allow him to judge that this particular mule is like them.

Consider analogous cases and it will become clear that one can dispense with the Aristotelian syllogism altogether; using it merely lengthens and multiplies thought, reflection, and speech without benefit. The need for premises varies with the state of the person reasoning: at times he may require one premise, at other times two, three, or even more. Occasionally he is unaware that the given animal is a mule; in that situation, once he learns that it is a mule he at once knows that it does not conceive—provided he already possesses a universal notion that encompasses all mules. Conversely, if he knows the particular, namely that the animal is a mule, but lacks the universal, he needs only the general premise, “A mule does not conceive.” Apply the same pattern to other matters and you will find it holds true.