Others, however, do not have so complete a conception and therefore recognize the attribute’s necessary connection to the subject only by means of a proof. Moreover, anything that entails another thing can serve as evidence for that thing, for a proof is defined as that whose occurrence entails the occurrence of what it proves. Hence the “middle term” is simply whatever entails the predicate, and the predicate thus becomes the consequence of a consequence.

They also concede that among accidental predicates are some that follow without any middle term. They illustrate this with evenness and oddness in numbers: it is self-evident that four is even and three is odd, whereas realizing that five hundred and forty-three is one-half of one thousand and eighty-six may require proof, or at least careful reflection and thought.

Furthermore, they contend—just as Ibn Sīnā, the foremost of their later representatives, and others have said—that the category of accident subdivided into quality, quantity, and the like is essential to the subjects it describes. Thus color, which breaks down into black and white, is essential to whatever is subject to coloration, and blackness and whiteness are two essential attributes, unlike evenness and oddness.

They explain this by saying: the fact that something is black or white and that these are accidents subsisting in something else needs no demonstration or investigation, whereas determining whether a particular number is even or odd may call for scrutiny and proof, namely by examining whether it can be divided into two equal parts or not.