Categorical μὴ κατὰ χρόνον propositions in Alexander of Aphrodisias' modal syllogistic (Q904227)

To solve the problem of the validity of what Aristotle thinks is a valid imperfect syllogism, namely \textit{Barbara XQ-M}, Alexander of Aphrodisias introduced μὴ κατὰ χρόνον propositions. These are understood by the author to be propositions true both at time ``\(t_1\) (i.e. at the present instant in time) and at \(t_2\) (namely, when the conjunction between subject and predicate expressed by the minor contingency premise is realized)''. They enable a solution to the problem of the validation of \textit{Barbara} and of \textit{Celarent XQ-M}, which ``does not imply a revision of the general semantic scheme for modal propositions: μὴ κατὰ χρόνον propositions fall under the kind of categorical propositions, since they are true at the present instant in time and they are not (necessarily) always true. In other words, since these propositions are not necessity propositions, there could be instants in time in which they are false; but they are not true only at the present instant in time, but, at least, at two instants in time. From this viewpoint, it is possible to make sense of Aristotle's claim in \textit{Pr. Anal.} A, 15, 34 a34-b2.'' (p.\ 475) The author also concludes that ``only \textit{propria} can be suitable candidates for predicates of a μὴ κατὰ χρόνον proposition'' and that ``this aspect of Alexander's modal theory of predication presents, indeed, many similarities with modern reconstructions which try to justify Aristotle's modal claims on the basis of his theory concerning predicative relations.'' (p.\ 480)