οἷον δήποτε ἄν εἴη κυριώτερον

Ζητοῦμεν διὰ τί λέγει τὰς ἀντικειμένας προτάσεις, οἷον Σωκράρης βαδίζει, Σωκράτης οὐ βαδίζει ἀντίφασιν καὶ μὴ ἀντιπρότασιν. καὶ λέγουμεν ἐπειδὴ χρεία ἐστὶν ἐν ταῖς προτάσεσιν τὸ κυριὠτερον μέρος άνελεῖν οἷον δήποτε ἄν εἴη κυριώτερον, εἴτε ὁ κατηγορούμενος εἴτε ὁ τρίτος προσκατηγορούμενος εἴτε "προσδιορισμός. τὸ δὲ μέρος φάσις ἐλέγετο. ἐπειδὴ οὖν τὴν φάσιν ἀναιροῦμεν καὶ οὐχὶ ὅλην τὴν πρότασιν, διὰ τοῦτο ἀντίφασις τὸ τοιοῦτο λέγεται καὶ οὐκ ἀντιπρότασις.
We inquire why he calls opposite propositions, such as ‘Socrates walks’ and ‘Socrates does not walk’ contradiction and not counter propositions. So, we say that this is because it is necessary to negate the more significant part of the propositions, such as at some time may be more significant, either a predicate, or a third additional predicate, or a further definition. This part is called φάσις/utterance, diction. Since we negate the phasis and not the whole proposition, for this reason, it is called ‘contradiction and not ‘counter proposition’. The end, with God’s help, of the lecture.

I don’t understand why he is so repetitive here, does οἷον δήποτε ἄν εἴη κυριώτερον, add anything to what is already said?

Of course, προσδιορισμός should be translated as ‘quantifier’, as is clear from the context further. The lexicons, however, do not give this meaning.

It reads like the transcript of a lecture.

OK, last bit from me on Stephanus before I force myself to stop procrastinating and get back to work…

Yes, it adds something. There’s nothing really repetitive. “…whatever sort of part might be most salient, whether predicate, tertiary predicate, or limiter [πᾶς, τις, κτλ].” Why did Aristotle designate contradictory propositions ἀντιφάσεις and not ἀντιπροτάσεις? He did so rightly, because what’s negated is the most salient part of a proposition, which is called the φάσις.

got it