Whether God can know infinite things?

❌ Objection 1 : It seems that God cannot know infinite things. For the infinite, as such, is unknown; since the infinite is that which, "to those who measure it, leaves always something more to be measured," as the Philosopher says (Phys. iii). Moreover, Augustine says (De Civ. Dei xii) that "whatever is comprehended by knowledge, is bounded by the comprehension of the knower." Now infinite things have no boundary. Therefore they cannot be comprehended by the knowledge of God.

❌ Objection 2 : Further, if we say that things infinite in themselves are finite in God's knowledge, against this it may be urged that the essence of the infinite is that it is untraversable, and the finite that it is traversable, as said in Phys. iii. But the infinite is not traversable either by the finite or by the infinite, as is proved in Phys. vi. Therefore the infinite cannot be bounded by the finite, nor even by the infinite; and so the infinite cannot be finite in God's knowledge, which is infinite.

❌ Objection 3 : Further, the knowledge of God is the measure of what is known. But it is contrary to the essence of the infinite that it be measured. Therefore infinite things cannot be known by God.