Whether the hypostases remain if the relations are mentally abstracted from the persons?

❌ Objection 1 : It would seem that the hypostases remain if the properties or relations are mentally abstracted from the persons. For that to which something is added, may be understood when the addition is taken away; as man is something added to animal which can be understood if rational be taken away. But person is something added to hypostasis; for person is "a hypostasis distinguished by a property of dignity." Therefore, if a personal property be taken away from a person, the hypostasis remains.

❌ Objection 2 : Further, that the Father is Father, and that He is someone, are not due to the same reason. For as He is the Father by paternity, supposing He is some one by paternity, it would follow that the Son, in Whom there is not paternity, would not be "someone." So when paternity is mentally abstracted from the Father, He still remains "someone"---that is, a hypostasis. Therefore, if property be removed from person, the hypostasis remains.

❌ Objection 3 : Further, Augustine says (De Trin. v, 6): "Unbegotten is not the same as Father; for if the Father had not begotten the Son, nothing would prevent Him being called unbegotten." But if He had not begotten the Son, there would be no paternity in Him. Therefore, if paternity be removed, there still remains the hypostasis of the Father as unbegotten.