Ps 146:5

“"Great is our Lord" [Psalm 147:5]. The Psalmist is filled with joy, he has poured out his words wonderfully: yet somewhat he was unable to speak, and how availed he to think on it? "And great is His power, and of His understanding is no numbering." He who "numbers the stars," Himself cannot be numbered. Who can expound this? Who can worthily even imagine what is meant by, "and of His understanding is no number"?...Whatsoever then that is infinite this world contains, though it be infinite to man, yet is not to God: too little is it to say, to God: even by the angels it is numbered. His understanding surpasses all calculators; it cannot be counted by us. Numbers themselves who numbers? What than is there with God? Wherewith made He all things, and where made He all things, to whom it is said, "You have arrayed all things in measure, number, and weight"? [Wisdom 11:20] Or who can number, or measure, or weigh, measure and number and weight themselves, wherein God has ordered all things? Therefore, "of His understanding is no number." Let human voices be hushed, human thoughts still: let them not stretch themselves out to incomprehensible things, as though they could comprehend them, but as though they were to partake of them, for partakers we shall be....Partakers then we shall be: let none doubt it: Scripture says it. And of what shall we be partakers, as though these were parts in God, as though God were divided into parts? Who then can explain how many become partakers of one single substance? Require not then that which I think ye see cannot fitly be said: but return to the healing of the Saviour, bruise your heart. He will guide it, He will bind it up where it is broken, He will make it perfectly sound; and then those things will not be impossible with us, which now are impossible. For it is good that he confess weakness, who desires to attain to the divine nature.”

“You have indeed concerning him who is the image, that "being in the form of God, he did not consider it robbery to be equal with God." Where certainly both his rectitude in the form of God, and his majesty in the equality, are indicated to you: so that when rectitude is compared to rectitude, and greatness to greatness, that which is to the image and the image may appear to correspond to each other harmoniously on both sides; just as the image also no less corresponds in both respects to him whose image it is. For he is the one of whom you have heard holy David singing in the psalms, now indeed: "Great is our Lord, and great is his power"; and now: "The Lord our God is upright, and there is no iniquity in him." From this upright and great God, his image has it that it too is upright and great: the soul has it, which is to the image.”

“God by the knowledge of simple intelligence knows and comprehends infinite things. I respond: For the understanding of the foregoing, it must be noted that according to the ancient doctors we are compelled to hold that God knows infinite things, as the Prophet David says in the Psalm: "Great is our Lord and great is his power, and of his wisdom there is no number"; and as Augustine not only asserts this but also proves it in the twelfth book of the City of God, the eighteenth chapter, where he speaks thus: "Therefore, as for that which certain ones, namely the philosophers, say—that not even by God's knowledge can infinite things be comprehended—it remains for them to dare to say, and to plunge themselves into this abyss of impiety, that God does not know all numbers. For it is most certain that they are infinite, since in whatever number you may think the end should be placed, that same number—I do not say can be increased by adding one—but however great it may be and however vast a multitude it may contain, it can by the very theory and science of numbers not only be doubled but even multiplied. Indeed, each number is so bounded by its own properties that none of them can be equal to any other: therefore they are both unequal among themselves and diverse, and each one individually is finite, and all together are infinite. Does God then not know all numbers on account of their infinity, and does the knowledge of God reach up to a certain sum of numbers and remain ignorant of the rest? Who, even the most demented, would say this?" And a little further on: "The infinity of number, therefore, although there is no number of infinite numbers, is nevertheless not incomprehensible to him whose understanding has no number. Wherefore, if whatever is comprehended by knowledge is made finite by the comprehension of the knower, then assuredly all infinity is in some ineffable manner made finite to God, because it is not incomprehensible to his knowledge. Therefore, if the infinity of numbers cannot be infinite to the knowledge of God by which it is comprehended, who are we, mere little men, to presume to fix a limit to his knowledge?" By these testimonies, therefore, as by the most certain witnesses, we are compelled to say or to hold that God knows infinite things. The manner of this position, however, is assigned by the more modern doctors, who have said that there is a threefold mode of divine cognition, not on account of a diversity of divine knowledge in itself, but in its connotation. For in God there is a knowledge of approbation, of vision, and of intelligence. The knowledge of approbation is of good things only, and of finite things. The knowledge of vision is of evil things and good things, but of finite things, inasmuch as it concerns time: for it is only of those things which were, are, and will be. But the knowledge of intelligence is of infinite things, inasmuch as God understands not only future things but also possible things: and the things possible to God are not finite but infinite. The reason for this position, namely why we hold that God knows infinite things and does not make or will or dispose them, is that the divine knowing according to the third mode of understanding is an intrinsic act of God. By intrinsic I mean not only because it proceeds from what is intrinsic, but also because it is toward what is intrinsic and through what is intrinsic and according to an intrinsic mode. Toward what is intrinsic, I say, because the divine gaze in knowing does not leap outside itself, but by beholding itself as truth knows every truth. Through what is intrinsic, because through the eternal reasons, which are identical with himself, he knows whatever he knows. According to an intrinsic mode, because the divine knowing not only abstracts from the notion of actual cause, but also from that of cause absolutely. For he knows evils, of which he is not the cause; he also knows future things, which he does not yet bring about; he also knows possible things, which he will never bring about. And therefore, because knowing itself neither involves nor connotes anything actual outside, it signifies there an act in the mode of a habit, an act, I say, commensurate with the power itself — for whatever God can know, he knows — it also signifies an act in no way restricted, neither with respect to itself nor with respect to what is connoted, therefore universal with respect to places, with respect to times, and with respect to objects. For whatever he knew somewhere he knows everywhere, and whatever he knows once he knows always, and just as he knows one thing, so he knows all knowable things. Whence, because knowable things are not only beings in act, but also in potency: since it is not unfitting to hold that there are infinite things in potency, it is not unfitting to hold that infinite things are actually known by God.”