Thomas Aquinas

“ 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. ”

“ I answer that, According to the opinion that the properties do not distinguish and constitute the hypostases in God, but only manifest them as already distinct and constituted, we must absolutely say that the relations in our mode of understanding follow upon the notional acts, so that we can say, without qualifying the phrase, that "because He begets, He is the Father." ”

“ The difference between these two abstractions consists in the fact that in the abstraction of the universal from the particular, that from which the abstraction is made does not remain; for when the difference of rationality is removed from man, the man no longer remains in the intellect, but animal alone remains. ”

“ Firstly, because, in order that two things be understood as distinct, their distinction must be understood as resulting from something intrinsic to both; thus in things created it results from their matter or their form. Now origin of a thing does not designate anything intrinsic, but means the way from something, or to something; as generation signifies the way to a thing generated, and as proceeding from the generator. Hence it is not possible that what is generated and the generator should be distinguished by generation alone ”

“ Hence, if the distinguishing property be removed from the person, the hypostasis no longer remains; whereas it would remain were the rationality of the nature removed; for both person and hypostasis are individual substances. Consequently, in God the distinguishing relation belongs essentially to both.
Reply to Objection 2: By paternity the Father is not only Father, but is a person, and is "someone," or a hypostasis. It does not follow, however, that the Son is not "someone" or a hypostasis; just as it does not follow that He is not a person. ”

“ 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. ”