Objection 1. It seems that God does not understand Himself. For it is said by the Philosopher (De Causis), "Every knower who knows his own essence, returns completely to his own essence." But God does not go out from His own essence, nor is He moved at all; thus He cannot return to His own essence. Therefore He does not know His own essence.
Objection 2. Further, to understand is a kind of passion and movement, as the Philosopher says (De Anima iii); and knowledge also is a kind of assimilation to the object known; and the thing known is the perfection of the knower. But nothing is moved, or suffers, or is made perfect by itself, "nor," as Hilary says (De Trin. ii.), "is a thing its own likeness." Therefore God does not understand Himself.
Objection 3. Further, we are like to God chiefly in our intellect, because we are the image of God in our mind, as Augustine says (Gen. ad lit. vi). But our intellect understands itself, only as it understands other things, as is said in De Anima iii. Therefore God understands Himself only so far perchance as He understands other things.
On the contrary, It is written: "The things that are of God no man knoweth, but the Spirit of God" (1 Corinthians 2:11).
I answer that, God understands Himself through Himself. In proof whereof it must be known that although in operations which pass to an external effect, the object of the operation, which is taken as the term, exists outside the operator; nevertheless in operations that remain in the operator, the object signified as the term of operation, resides in the operator; and accordingly as it is in the operator, the operation is actual. Hence the Philosopher says (De Anima iii) that "the sensible in act is sense in act, and the intelligible in act is intellect in act." For the reason why we actually feel or know a thing is because our intellect or sense is actually informed by the sensible or intelligible species. And because of this only, it follows that sense or intellect is distinct from the sensible or intelligible object, since both are in potentiality.
Since therefore God has nothing in Him of potentiality, but is pure act, His intellect and its object are altogether the same; so that He neither is without the intelligible species, as is the case with our intellect when it understands potentially; nor does the intelligible species differ from the substance of the divine intellect, as it differs in our intellect when it understands actually; but the intelligible species itself is the divine intellect itself, and thus God understands Himself through Himself.
Reply to Objection 1. Return to its own essence means only that a thing subsists in itself. Inasmuch as the form perfects the matter by giving it existence, it is in a certain way diffused in it; and it returns to itself inasmuch as it has existence in itself. Therefore those cognitive faculties which are not subsisting, but are the acts of organs, do not know themselves, as in the case of each of the senses; whereas those cognitive faculties which are subsisting, know themselves; hence it is said in De Causis that, "whoever knows his essence returns to it." Now it supremely belongs to God to be self-subsisting. Hence according to this mode of speaking, He supremely returns to His own essence, and knows Himself.
Reply to Objection 2. Movement and passion are taken equivocally, according as to understand is described as a kind of movement or passion, as stated in De Anima iii. For to understand is not a movement that is an act of something imperfect passing from one to another, but it is an act, existing in the agent itself, of something perfect. Likewise that the intellect is perfected by the intelligible object, i.e. is assimilated to it, this belongs to an intellect which is sometimes in potentiality; because the fact of its being in a state of potentiality makes it differ from the intelligible object and assimilates it thereto through the intelligible species, which is the likeness of the thing understood, and makes it to be perfected thereby, as potentiality is perfected by act. On the other hand, the divine intellect, which is no way in potentiality, is not perfected by the intelligible object, nor is it assimilated thereto, but is its own perfection, and its own intelligible object.
Reply to Objection 3. Existence in nature does not belong to primary matter, which is a potentiality, unless it is reduced to act by a form. Now our passive intellect has the same relation to intelligible objects as primary matter has to natural things; for it is in potentiality as regards intelligible objects, just as primary matter is to natural things. Hence our passive intellect can be exercised concerning intelligible objects only so far as it is perfected by the intelligible species of something; and in that way it understands itself by an intelligible species, as it understands other things: for it is manifest that by knowing the intelligible object it understands also its own act of understanding, and by this act knows the intellectual faculty. But God is a pure act in the order of existence, as also in the order of intelligible objects; therefore He understands Himself through Himself.
Source: Summa Theologica (New Advent)