Objection 1. It seems that those who see the divine essence, comprehend God. For the Apostle says (Philippians 3:12): "But I follow after, if I may by any means comprehend [Douay: 'apprehend']." But the Apostle did not follow in vain; for he said (1 Corinthians 9:26): "I... so run, not as at an uncertainty." Therefore he comprehended; and in the same way, others also, whom he invites to do the same, saying: "So run that you may comprehend."
Objection 2. Further, Augustine says (De Vid. Deum, Ep. cxlvii): "That is comprehended which is so seen as a whole, that nothing of it is hidden from the seer." But if God is seen in His essence, He is seen whole, and nothing of Him is hidden from the seer, since God is simple. Therefore whoever sees His essence, comprehends Him.
Objection 3. Further, if we say that He is seen as a "whole," but not "wholly," it may be contrarily urged that "wholly" refers either to the mode of the seer, or to the mode of the thing seen. But he who sees the essence of God, sees Him wholly, if the mode of the thing seen is considered; forasmuch as he sees Him as He is; also, likewise, he sees Him wholly if the mode of the seer is meant, forasmuch as the intellect will with its full power see the Divine essence. Therefore all who see the essence of God see Him wholly; therefore they comprehend Him.
On the contrary, It is written: "O most mighty, great, and powerful, the Lord of hosts is Thy Name. Great in counsel, and incomprehensible in thought" (Jeremiah 32:18-19). Therefore He cannot be comprehended.
I answer that, It is impossible for any created intellect to comprehend God; yet "for the mind to attain to God in some degree is great beatitude," as Augustine says (De Verb. Dim., Serm. xxxvii).
In proof of this we must consider that what is comprehended is perfectly known; and that is perfectly known which is known so far as it can be known. Thus, if anything which is capable of scientific demonstration is held only by an opinion resting on a probably proof, it is not comprehended; as, for instance, if anyone knows by scientific demonstration that a triangle has three angles equal to two right angles, he comprehends that truth; whereas if anyone accepts it as a probable opinion because wise men or most men teach it, he cannot be said to comprehend the thing itself, because he does not attain to that perfect mode of knowledge of which it is intrinsically capable. But no created intellect can attain to that perfect mode of the knowledge of the Divine intellect whereof it is intrinsically capable. Which thus appears--Everything is knowable according to its actuality. But God, whose being is infinite, as was shown above (Article 7) is infinitely knowable. Now no created intellect can know God infinitely. For the created intellect knows the Divine essence more or less perfectly in proportion as it receives a greater or lesser light of glory. Since therefore the created light of glory received into any created intellect cannot be infinite, it is clearly impossible for any created intellect to know God in an infinite degree. Hence it is impossible that it should comprehend God.
Reply to Objection 1. "Comprehension" is twofold: in one sense it is taken strictly and properly, according as something is included in the one comprehending; and thus in no way is God comprehended either by intellect, or in any other way; forasmuch as He is infinite and cannot be included in any finite being; so that no finite being can contain Him infinitely, in the degree of His own infinity. In this sense we now take comprehension. But in another sense "comprehension" is taken more largely as opposed to "non-attainment"; for he who attains to anyone is said to comprehend him when he attains to him. And in this sense God is comprehended by the blessed, according to the words, "I held him, and I will not let him go" (Canticles 3:4); in this sense also are to be understood the words quoted from the Apostle concerning comprehension. And in this way "comprehension" is one of the three prerogatives of the soul, responding to hope, as vision responds to faith, and fruition responds to charity. For even among ourselves not everything seen is held or possessed, forasmuch as things either appear sometimes afar off, or they are not in our power of attainment. Neither, again, do we always enjoy what we possess; either because we find no pleasure in them, or because such things are not the ultimate end of our desire, so as to satisfy and quell it. But the blessed possess these three things in God; because they see Him, and in seeing Him, possess Him as present, having the power to see Him always; and possessing Him, they enjoy Him as the ultimate fulfilment of desire.
Reply to Objection 2. God is called incomprehensible not because anything of Him is not seen; but because He is not seen as perfectly as He is capable of being seen; thus when any demonstrable proposition is known by probable reason only, it does not follow that any part of it is unknown, either the subject, or the predicate, or the composition; but that it is not as perfectly known as it is capable of being known. Hence Augustine, in his definition of comprehension, says the whole is comprehended when it is seen in such a way that nothing of it is hidden from the seer, or when its boundaries can be completely viewed or traced; for the boundaries of a thing are said to be completely surveyed when the end of the knowledge of it is attained.
Reply to Objection 3. The word "wholly" denotes a mode of the object; not that the whole object does not come under knowledge, but that the mode of the object is not the mode of the one who knows. Therefore he who sees God's essence, sees in Him that He exists infinitely, and is infinitely knowable; nevertheless, this infinite mode does not extend to enable the knower to know infinitely; thus, for instance, a person can have a probable opinion that a proposition is demonstrable, although he himself does not know it as demonstrated.
Source: Summa Theologica (New Advent)