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From Cornelius a Lapide commentary:
My Father only: because from eternity He had determined in His own mind, and appointed this day, which He keeps secret. Now by the word only, the Son is not excluded, neither the Holy Ghost, for They know the day and the hour of the Judgment equally with the Father, since They have all the same essence, majesty, will, mind, power, understanding, and knowledge. For it is a theological principle, that if the word “only” be added to any of the essential attributes of the Godhead, such as wisdom, and be ascribed to one of the Divine Persons, it does not exclude the other two Persons, but only creatures, which are of a different nature and essence. But in Personal Attributes, the expression “only” does exclude two of the, Divine Persons, as when it is said, “The Father only begets;” “The Son only is begotten.”
You will say, Mark adds (xiii. 32), neither the Son, for so it is in the Greek, Latin, Syriac, Arabic, Persian, Egyptian, Ethiopic. Various answers are given. The best is that which is common among the Fathers. It is that the Son, both as God and as man, by infused knowledge, knows the Day of Judgment and of the end of the world, for it pertains for Him to know this, inasmuch as He has been appointed the Judge of the world. But Christ denies that He knoweth this as man, and as He is Gods messenger to us, because He did not know it so that He could reveal it to us, or because He had not been commissioned by the Father to reveal it to us. As an ambassador who was questioned concerning the secrets of his prince would reply that he did not know them, although he did know them, because he did not know them as an ambassador. For an ambassador declares only those things which he has a commission to declare.
Christs meaning then is, “God only knows what year and day and hour the end of the world and the Judgment shall be. And although God has caused Me, Christ, as I am man, to know the same, as I am that one man who is united to the WORD; yet as I am the Fathers ambassador to men, He hath not willed Me to make known that day, but to keep it secret, and to stir them up continually to prepare themselves for it.” There is a like mode of expression in S. John xv. 15.
There are some who explain thus: that Christ, qua man, knoweth not the Day of Judgment; but that He knoweth it as He is the God-man. That is to say, Christ as man knoweth it not by virtue of His humanity, but of His divinity. So S. Athanasius (Serm. 4, contra Arian.), Nazianzen (Orat. 4, de .Theolog.), Cyril (lib. 9, Thesaur. c. 4), Ambrose (lib. 5, de Fide, c. 8).
Maldonatus gives another explanation. He says that Christ, even as He is God, knoweth not the Day of Judgment in, as it were, an ex officio sense, because it is the office of the Father, alone to predestinate, decree, and determine the Day of Judgment; and, by consequence, that He knows it, and reveals it when He wills. For providence, in which predestination is included, is a special attribute of the Father. But this explanation is somewhat too subtle and abstruse.