If, however, one conceives of “a laughing animal,” what he envisages is likewise a composite of those two elements. The term, then, signifies the whole concept by direct correspondence, part of it by inclusion, and what lies outside the concept yet is inseparable from it by necessary implication. The whole is the total quiddity he has formed in his mind; the part is a part of that quiddity and is what the word indicates by inclusion; while what stands outside it yet is inseparable from it is what the word indicates by necessary implication. Thus the complete quiddity, its internal part, and its external concomitant all revert to what is denoted by correspondence, inclusion, and implication. This is all that can be distilled from the matter—as those who examined it have clarified—and it has been set out at length elsewhere.

As for the notion that some of the necessary attributes of a subject lie within its external essence while others lie outside that external essence, this is false. The threefold distinctions they advance between the “constitutive essential” and the “necessary accidental” have been conceded by themselves to be baseless, and their invalidity has been demonstrated by proof.

Likewise, what they speak of as a “middle” between certain concomitants—what their leading figures, such as Ibn Sīnā, meant by it is simply the proof, just as they speak of the “middle term.” They therefore treated part of the essence as knowable without proof and part as knowable only through proof. Yet this distinction pertains to the knower’s epistemic state, not to any reality inhering in the object itself. Some of their later followers imagined that by “middle” they meant that the necessary attributes are sometimes predicated of the subject directly, and at other times only through an intermediary in that predication.