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Summa Theologica II-II q. 102 (on the virtue of observance) a. 1 co. is a very good, concise/precise definition of fatherhood, typical for St. Thomas:
just as a carnal father partakes of the character of principle in a particular way, which character is found in God in a universal way, so too a person who, in some way, exercises providence in one respect, partakes of the character of father in a particular way, since a father is the principle of generation, of education, of learning and of whatever pertains to the perfection of human life
Sicut autem carnalis pater particulariter participat rationem principii, quae universaliter invenitur in Deo; ita etiam persona quae quantum ad aliquid providentiam circa nos gerit, particulariter participat proprietatem patris, quia pater est principium et generationis et educationis et disciplinae, et omnium quae ad perfectionem humanae vitae pertinent.
I've always liked the relationship between principio or ἀρχή (principle/beginning) and princeps (prince). I wonder if these words are etymologically related to pater. It seems characteristic of manly thinking to be principled, favoring deduction over induction.