…there be a concomitant entailed without a middle term, and it is now evident that such a concomitant cannot be dismissed even in imagination. One should therefore pay no heed to the assertion that whatever is not constitutive may be mentally set aside; they commonly illustrate this with the proposition that every number is either equal to, or different from, every other number.

I say: His purpose in this passage is to answer those logicians who claim that the distinction between an essential attribute and a necessary accident is that whatever is non-essential can be removed in thought, so that the subject may be conceived without conceiving that attribute, whereas an essential attribute cannot be so removed. He has shown that every chain of concomitants must terminate in a self-evident concomitant that needs no middle term, and that, once the subject is conceived, this concomitant cannot be eliminated even in the imagination. What he has said is correct, and it demolishes the very distinction on which they chiefly rely.

They advance a second criterion, saying that an essential attribute needs no cause, whereas a concomitant does, and that the cause is the middle term. This criterion is even more corrupt than the first, for it is false to claim that some necessary attributes require a cause while others do not. Whether one speaks of a cause or a middle term, and whether that middle term is deemed a proof or a cause of the attribute’s existence in external reality, there are concomitants that require no cause at all; thus the second distinction collapses as well.

Their third criterion concerns priority, either in the mind or in external reality. They maintain that the subject cannot be conceived except after conceiving its essential attribute, whereas the accidental concomitant is conceived only after the substratum is conceived, and they equate the essential attribute with the constitutive one. This distinction is likewise unsound: an attribute never precedes its subject in external reality. In the mind, one may conceive the attribute and the subject together, so the attribute’s conception does not in fact precede; and even if it should precede, that variance is due to a person’s more or less complete conception, not to any intrinsic difference among the concomitants themselves.

Yet they go on relying upon these three distinctions, or upon one of them, even those later scholars who placed logic at the very beginning of uṣūl al-fiqh; this is their mainstay, as al-Āmidī, Ibn al-Hājib, and others report. All of them, however, are invalid. External precedence, for instance, is plainly contradicted by evident reason…