Whether our intellect can know the infinite?

❌ Objection 1 : It would seem that our intellect can know the infinite. For God excels all infinite things. But our intellect can know God, as we have said above (Question [12], Article [1]). Much more, therefore, can our intellect know all other infinite things.

❌ Objection 2 : Further, our intellect can naturally know "genera" and "species." But there is an infinity of species in some genera, as in number, proportion, and figure. Therefore our intellect can know the infinite.

❌ Objection 3 : Further, if one body can coexist with another in the same place, there is nothing to prevent an infinite number of bodies being in one place. But one intelligible species can exist with another in the same intellect, for many things can be habitually known at the same time. Therefore our intellect can have an habitual knowledge of an infinite number of things.

❌ Objection 4 : Further, as the intellect is not a corporeal faculty, as we have said (Question [76], Article [1]), it appears to be an infinite power. But an infinite power has a capacity for an infinite object. Therefore our intellect can know the infinite.