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cf., Sent.I.D13.Q1.A4, Sent.I.D28.Q1.A1-2, Graecorum.Part1.C8
The answer to this is in the affirmative. St. Thomas proves this from a perfection conjunction of the possibilities of naming the Father. For, on the supposition of the first article that the Father is the first principle, he can either be known, 1. As he is the originator of others, or 2. As he is not himself originated. For, a first principle is known from two aspects, as originating others and not itself being originated.
Now, the Father is properly named as the Father in that he is the originator of the Son. Yet, should he not be properly named Spirator and Principle? No, for, as we saw above, a "proper name" cannot be common, now, to be spirator and to be principle are both names that are shared with others, thus, they cannot be proper names.
Thus, we are left with the proper names of "Father" and "Unbegotten." Yet, there are other "derived" and "related" proper names that we could also indicate, as is seen in the reply to the first objection.
What is meant by unbegotten?