We sped up last week, but this time slow down a bit. There are some fundamental metaphysical theorems we need before pressing on. These are not wholly difficult as presented by St Thomas, but they are somewhat incomplete. He expects some tacit knowledge. Thus I point you to an excellent resource.
 LEST, however, from the fact that God understands many things we be led to conclude that there is composition in the divine intellect, we must examine in what way the things He understands are many.
 Now they cannot be understood to be many, as though the many things God understands had a distinct being in Him. For these understood things would either be the same as the divine essence, and thus we should have multitude in the essence of God, which has been disproved above in many ways, or else they would be added to the divine essence, and thus there would be something accidental in God, and this again we have proved above to be impossible.
 Nor again can it be admitted that these intelligible forms exist per se: as Plato, in order to avoid the above impossibilities, seems to have maintained by holding the existence of ideas. Because the forms of natural things cannot exist apart from matter, since neither are they understood without matter.
Notes Metaphysics 101 again. Things exist as compositions of form and matter. You don’t have to be religious to believe this obvious truth. Plato held that forms actually existed in some, well, Platonic realm. Chair-forms, apple-forms, even iPhone-forms were somewhere, nobody knows where, in their perfection. Aristotle corrected this mistake. Best book on forms and such: Ed Feser’s Scholastic Metaphysics: A Contemporary Introduction.
 And even if the above supposition were admissible, it would not suffice to explain how God understands many things. For since the aforesaid forms are outside the essence of God, if God were unable without them to understand the multitude of things, as is requisite for the perfection of His intellect, it would follow that the perfection of His understanding depends on something else: and consequently the perfection also of His being, since His being is His act of intelligence: the contrary of which has been shown above.
Notes Perhaps the short way to say this is that God is not a computer with infinite storage space. He is also not the universe; the universe itself is not alive, not a computer. If God needed hard drives to remember everything, then He would have to rely on that which is not His essence. And we have already shown that God’s existence and essence are identical.
 Again. Since all that is beside His essence is caused by Him, as we shall prove further on, it must needs be that if the aforesaid forms are outside God, they are caused by Him. Now He is the cause of things by His intellect, as we shall show further on. Therefore in order that these intelligible forms may exist, it is required that previously in the order of nature God should understand them. And consequently God does not understand multitude through the fact that many intelligible things exist per se outside Him.
Notes And here is another step toward Omnipotence! We have already proved (last two posts) Omniscience. What we’re doing here, if it isn’t obvious, is seeing what the implications of omniscience are.
 Again. The intelligible in act is the intellect in act, even as the sensible in act is the sense in act. But so far as the intelligible is distinct from the intellect, both are in potentiality, as appears in the senses: for neither is the sight actually seeing, nor the visible actually seen, except when the sight is informed by the species of the visible object, so that one thing results from sight and visible. Accordingly if the intelligible objects of God are outside His intellect, it will follow that His intellect is in potentiality, and likewise His intelligible objects: and thus He will need something to reduce Him to actuality. But this is impossible, since this thing would be previous to Him.
Notes Recall to be in act differs from being in potential. The ability to see is different from that which is visible; they are not the same thing. If you haven’t yet seen the car, your sight is in potentiality, and so is the car being seen in potentiality. They only “collapse” to actuality when the car presents itself to your senses. And the same thing for the intellect and that which is intelligible. Finally, if God doesn’t yet know everything, then He is in potential to those things not yet known. And therefore there has to be something besides God to bring this potentiality to actuality. And that thing would have to be before or above God, which is impossible, as we have already proved nothing is or can be.
 Further. The object understood must be in the intellect. Therefore in order to explain how God understands the multitude of things it is not enough to suppose that the forms of things exist per se outside the divine intellect; but it is necessary that they be in the divine intellect itself.
 From these very same reasons it appears that it cannot be admitted that the multitude of the aforesaid intelligibles is in some other beside the divine intellect, either that of the soul, or that of an angel or intelligence. For in that case the divine intellect, in respect of one of its operations, would depend on some secondary intellect: which also is impossible.
 [MAY BE SKIPPED] Even as things that subsist in themselves are from God, so are those that exist in a subject. Wherefore the existence of the aforesaid intelligibles in some secondary intellect presupposes God’s act of intelligence whereby He is their cause. It would also follow that God’s intellect is in potentiality: since His intelligibles would not be united to Him. Even as each thing has its proper being so has it its proper operation. Wherefore it is impossible that because one intellect is disposed to operate, therefore another exercises intellectual operation, but only that same intellect where we find the disposition: even as a thing is by its own essence and not by another’s. Hence it does not become possible for the first intellect to understand multitude, through the fact that many intelligibles are in some second intellect.
Notes Aha! Number  is the real kicker. The forms must be in God’s intellect. And never forget our souls are our forms; that is, the rational soul is the form of man. The forms of angels souls are also in God’s intellect; they are not there as memory helpers.
You’ll notice that we did not come to the solution of this argument. Neither did St Thomas in this chapter. We have to wait until next week. Then we’ll speed up again until we get to God is Truth. Chs. xviii., xx., xlii.
 Ch. xxiii.
 Phoedo xlviii., xlix.: Timaeus (D., p. 204)
 Ch. xiii.
 Bk. II., xv.
 Bk. II., xxiii., xxiv.
 3 De Anima ii. 4; iv. 12; v. 2.
 Ch. lii.