Thomas Aquinas, Compendium of Theology

There were also some philosophers who argued that, even granting the diversification of the possible intellect in men, at any rate the agent intellect was but one for all. This view, while less objectionable than the theory discussed in the preceding chapter, can be refuted by similar considerations.

The action of the possible intellect consists in receiving the objects understood and in understanding them. And the action of the agent intellect consists in causing things to be actually understood by abstracting species. But both these functions pertain to one particular man. This man, for example, Socrates or Plato, receives the objects understood, abstracts the species, and understands what is abstracted. Hence the possible intellect as well as the agent intellect must be united to this man as a form. And so both must be numerically multiplied in accord with the number of men concerned.

Moreover, agent and patient must be proportionate to each other. Examples are matter and form, for matter is reduced to act by an agent. This is why an active potency of the same genus corresponds to every passive potency; for act and potency pertain to one genus. But the agent intellect is to the possible intellect what active potency is to passive potency, as is clear from this discussion. Hence they must both pertain to one genus. Therefore, since the possible intellect has no separate existence apart from us, but is united to us as a form and is multiplied according to the number of men, as we have shown, the agent intellect must likewise be something that is united to us as a form, and must be multiplied according to the number of men.