In the Trinity is a plurality of persons but also a determinate number, which is three. There are therefore three persons unified under the divine nature. Three in one. One God, three persons. Terms which verify this unity are the ones best and proper to be used with the Trinity. Other holds the right meaning for the separate persons when used in distinguishing them as conversely opposed to different. So Jesus is other than the Father.
Categorematical is a fun word but I won’t use it here. To use the terms alone and only with God is to also use the terms associated with His essence as to show Him to be different from creatures in comparison. So we say “God alone is eternal” but would not say “God is only eternal”, just as we would not say “God is alone” by itself as if He is solitary. We must also not use alone and only with the persons if what we say does not properly belong to them. Therefore we will not say “the Son alone begets the Holy Spirit” or “God only processes the Son.”
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