Yes. It is absolutely impossible for one intellect to belong to all men because it is impossible for many distinct individuals to have one form, as it is impossible for them to have one existence, for the form is the principle of existence.
Intellectum esse unum omnium hominum, omnino est impossibile quia impossibile est enim plurium numero diversorum esse unam formam, sicut impossibile est quod eorum sit unum esse, nam forma est essendi principium.
It is likewise clear that this is impossible if, according to the opinion of Aristotle (De Anima ii, 2), it is supposed that the intellect is a part or a power of the soul which is the form of man.
Similiter etiam patet hoc esse impossibile, si, secundum sententiam Aristotelis, intellectus ponatur pars, seu potentia, animae quae est hominis forma.
Although the intellectual soul, like an angel, has no matter from which it is produced, yet it is the form of a certain matter; in which it is unlike an angel. Therefore, according to the division of matter, there are many souls of one species; while it is quite impossible for many angels to be of one species.
Licet anima intellectiva non habeat materiam ex qua sit, sicut nec Angelus, tamen est forma materiae alicuius; quod Angelo non convenit. Et ideo secundum divisionem materiae sunt multae animae unius speciei, multi autem Angeli unius speciei omnino esse non possunt.
And if to this we add that to understand, which is the act of the intellect, is not affected by any organ other than the intellect itself; it will further follow that there is but one agent and one action: that is to say that all men are but one "understander," and have but one act of understanding, in regard, that is, of one intelligible object.
Et si addamus quod ipsum intelligere, quod est actio intellectus, non fit per aliquod aliud organum, nisi per ipsum intellectum; sequetur ulterius quod sit et agens unum et actio una; idest quod omnes homines sint unus intelligens, et unum intelligere; dico autem respectu eiusdem intelligibilis.
But the phantasm itself is not a form of the possible intellect; it is the intelligible species abstracted from the phantasm that is a form. Now in one intellect, from different phantasms of the same species, only one intelligible species is abstracted; as appears in one man, in whom there may be different phantasms of a stone; yet from all of them only one intelligible species of a stone is abstracted; by which the intellect of that one man, by one operation, understands the nature of a stone, notwithstanding the diversity of phantasms. Therefore, if there were one intellect for all men, the diversity of phantasms which are in this one and that one would not cause a diversity of intellectual operation in this man and that man. It follows, therefore, that it is altogether impossible and unreasonable to maintain that there exists one intellect for all men.
Sed ipsum phantasma non est forma intellectus possibilis, sed species intelligibilis quae a phantasmatibus abstrahitur. In uno autem intellectu a phantasmatibus diversis eiusdem speciei non abstrahitur nisi una species intelligibilis. Sicut in uno homine apparet, in quo possunt esse diversa phantasmata lapidis, et tamen ab omnibus eis abstrahitur una species intelligibilis lapidis, per quam intellectus unius hominis operatione una intelligit naturam lapidis, non obstante diversitate phantasmatum. Si ergo unus intellectus esset omnium hominum, diversitas phantasmatum quae sunt in hoc et in illo, non posset causare diversitatem intellectualis operationis huius et illius hominis, ut Commentator fingit in III de anima. Relinquitur ergo quod omnino impossibile et inconveniens est ponere unum intellectum omnium hominum.
Whether the intellect be one or many, what is understood is one; for what is understood is in the intellect, not according to its own nature, but according to its likeness; for "the stone is not in the soul, but its likeness is," as is said, De Anima iii, 8. Yet it is the stone which is understood, not the likeness of the stone, except by a reflection of the intellect on itself; otherwise, the objects of sciences would not be things, but only intelligible species.
Sive intellectus sit unus sive plures, id quod intelligitur est unum. Id enim quod intelligitur non est in intellectu secundum se, sed secundum suam similitudinem, "lapis enim non est in anima, sed species lapidis," ut dicitur in III de anima. Et tamen lapis est id quod intelligitur, non autem species lapidis, nisi per reflexionem intellectus supra seipsum, alioquin scientiae non essent de rebus, sed de speciebus intelligibilibus.
Now it happens that different things, according to different forms, are likened to the same thing. And since knowledge is begotten according to the assimilation of the knower to the thing known, it follows that the same thing may happen to be known by several knowers, as is apparent in regard to the senses; for several see the same color, according to different likenesses. In the same way several intellects understand one object understood.
Contingit autem eidem rei diversa secundum diversas formas assimilari. Et quia cognitio fit secundum assimilationem cognoscentis ad rem cognitam, sequitur quod idem a diversis cognoscentibus cognosci contingit, ut patet in sensu, nam plures vident eundem colorem, secundum diversas similitudines. Et similiter plures intellectus intelligunt unam rem intellectam.
But there is this difference, according to the opinion of Aristotle, between the sense and the intelligence--that a thing is perceived by the sense according to the disposition which it has outside the soul --that is, in its individuality; whereas the nature of the thing understood is indeed outside the soul, but the mode according to which it exists outside the soul is not the mode according to which it is understood. For the common nature is understood as apart from the individuating principles; whereas such is not its mode of existence outside the soul.
Sed hoc tantum interest inter sensum et intellectum, secundum sententiam Aristotelis, quod res sentitur secundum illam dispositionem quam extra animam habet, in sua particularitate, natura autem rei quae intelligitur, est quidem extra animam, sed non habet illum modum essendi extra animam, secundum quem intelligitur. Intelligitur enim natura communis seclusis principiis individuantibus; non autem hunc modum essendi habet extra animam.
But, according to the opinion of Plato, the thing understood exists outside the soul in the same condition as those under which it is understood; for he supposed that the natures of things exist separate from matter.
Sed secundum sententiam Platonis, res intellecta eo modo est extra animam quo intelligitur, posuit enim naturas rerum a materia separatas.
Augustine (De Quant. Animae xxxii) says: "If I were to say that there are many human souls, I should laugh at myself." But there Augustine only denies a plurality of souls that would involve a plurality of species.
Augustinus dicit, in libro de quantitate animae, "si plures tantum animas humanas dixerim, ipse me ridebo." Augustinus intelligit animas non esse plures tantum, quin uniantur in una ratione speciei.