That proof, then, is the middle term.
This, however, varies from one person to another: one thinker may need a separate proof in order to recognise the implication, whereas another may not.
Whoever fails to grasp what they mean here supposes that by “middle” they intend something that lies within the very subject, so that the necessary predicate is affirmed of the subject by means of that internal medium rather than by the subject itself. A number of scholars—Fakhr al-Rāzī among them—have understood the doctrine in this way. Yet, as we have shown elsewhere from their own words, that reading misrepresents them, and the notion itself is unsound.
There is no doubt, in their view, that some concomitants require a middle term while others do not. This was one of the three criteria they proposed for distinguishing an essential attribute from an accidental concomitant of a quiddity, though they later retracted the distinction. Some of them, Ibn al-Ḥājib for example, express the point in the language of “causation.”
Now, once it is acknowledged that among the concomitants there are those that hold in reality without any middle or cause, the distinction between the essential and such concomitants falls apart. Nevertheless, the person who conceives the essence together with these concomitants attains a fuller conception than one who omits them.
If, on the other hand, “middle” is taken to mean the proof that justifies mental assent rather than external existence, this too depends on the individual. There is no doubt that the evidence employed—whether one calls it a syllogism, a demonstration, or something else—may itself be the cause of the judgment’s real existence; this is what is termed the “analogy of cause,” the “demonstration of cause,” or the “why” demonstration. It may also function merely as general evidence; in that case it is called the “analogy of indication,” the “demonstration of indication,” or the “that” demonstration. This is what Ibn Sīnā and others mean by the middle term, and here people’s capacities naturally differ.