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For any given cognitive faculty f and object o, fPo =df: o occurs/exists in f (where P = perceives). Nothing intelligible can inhere in a body or something bodily. If so, then take in what Tahtani, the author of al-Muhakamah (Qom: 1375, vol. 2), in commenting on Avicenna’s Isharat, says at II.3.13, 361 of that work:

With regard to its intelligible objects, the soul has three states: (1) perception, (2) absent-mindedness (ذهول), and (3) forgetfulness (نسيان). Perception (1) is the occurrence of the intelligible forms in the soul, and (3) forgetfulness is the disappearance of the intelligible forms from the soul, such that it’s not possible to attend (ملاحظة) to them except by a toilsome new acquisition. And in (2) the state of absent-mindedness, there’s no doubt that it’s possible to attend to the form without the pain of a new acquisition. So this form, then, either hasn’t obtained in the soul at all, in which case there’s no difference between (2) absent-mindedness and (3) forgetfulness; or it has obtained in the soul in a way that necessitates its occurrence either in the soul or in something else. The former is false; otherwise, (2) absent-mindedness will be the same as (1) perception, since [for the soul to] perceive the form means nothing other than its occurrence itself [in it]. Hence, it’s impossible to be unaware of it simultaneously with its occurrence [in the soul]. Therefore, it has become clear that there exists something other than the soul in which the intelligible form is impressed, which is not a body nor bodily, nor a soul; for the soul’s relation to the intelligibles is potential sometimes. […]. Therefore, there’s here an existent in which the intelligibles are impressed always in actuality, and it is the Active Intellect.

The Thomists will no doubt object: ‘the intelligible form that isn’t being actually thought resides in the soul insofar as the active intellect is a capacity of the soul’.

But don’t they grant that: for fPo is for o to exist in f?! I mean, what else is it for a perceptive cognitive capacity to perceive its proper object than for that object to exist in, or occur to, it? If the active intellect and its objects were internal to the soul, we’d be always thinking them – which is emprically false. As Tahtani points out, ‘the soul’s relation to the intelligibles is sometimes potential’. Or will the Thomist distinguish here, urging: ‘the soul’s material intellect’s relation to them is sometimes potential but not the relation of its active intellect’. Again though, it would follow, not only that you’re always thinking the form, but also that you’re always thinking them all (i.e., the one’s that you’ve previously come to acquire) – all of which is manifestly contrary to experience.