As the words τὰ μὲν δύο refer to the second contradictory pair (that is, C and D) in the first Quaternion, so the words τὰ δὲ δύο, οὔ designate the second contradictory pair (G and H) in the second Quaternion. Though G and H are included in the second Quaternion, they are here designated by the negative relation (τὰ δὲ δύο, οὔ) which they bear to A and B, the first contradictory pair of the first Quaternion. διχῶς λέγονται αἱ ἀντιθέσεις (line 20) is explained and illustrated by line 37 — αὗται μὲν οὖν δύο ἀντίκεινται, ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθέν. Lastly, Aristotle expressly states that the second Quaternion will stand independently and by itself (p. 20, a. 1), having noticed it in the beginning only in relation to the first.
Such is the result obtained when we take homo as the subject of the proposition; we get four propositions, of which the two last (C and D) stand to the two first (B and A) in the same relation as if they (C and D) were privative propositions. But if, instead of homo, we take non homo as Subject of the proposition (justus or non justus being predicates as before), we shall then obtain two other pairs of contradictory propositions; and the second pair of this new quaternion will not stand in that same relation to these same propositions B and A. We shall then find that, instead of B and A, we have a different negative and a different affirmative, as the appropriate correlates to the third and fourth propositions. The new quaternion of propositions, with non homo as subject, will stand thus —
(QUATERNION II.) (E) Est justus non homo … … … … (F) Non est justus non homo. (H) Non est non justus non homo … … … … (G) Est non justus non homo.[25]
| (QUATERNION II.) | ||
|---|---|---|
| (E) Est justus non homo | … … … … | (F) Non est justus non homo. |
| (H) Non est non justus non homo | … … … … | (G) Est non justus non homo.[25] |
Here we see that propositions G and H do not stand to B and A in the same relations as C and D stand to B and A; but that they stand in that same relation to two perfectly different propositions, F and E. That is, if in place of non justus, in propositions G and H, we substitute the privative term injustus (thus turning G into Est injustus non homo, and turning H into Non est injustus non homo), the relation of G, when thus altered, to F, and the relation of H, when thus altered, to E, will be the same as it was before. Or, in other words, if G be true, F will certainly be true, but not vice versâ; and if E be true, H will certainly be true, but not vice versâ.
[25] Aristot. De Interpr. p. 19, b. 36. αὗται μὲν οὖν δύο ἀντίκεινται (the two pairs — A B and C D — of the first quaternion), ἄλλαι δὲ δύο πρὸς τὸ οὐκ ἄνθρωπος ὡς ὑποκείμενόν τι προστεθέν·
(E) ἔστι δίκαιος οὐκ ἄνθρωπος … … … … (F) οὐκ ἔστι δίκαιος οὐκ ἄνθρωπος. (H) οὐκ ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος … … … … (G) ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος.
| (E) ἔστι δίκαιος οὐκ ἄνθρωπος | … … … … | (F) οὐκ ἔστι δίκαιος οὐκ ἄνθρωπος. |
| (H) οὐκ ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος | … … … … | (G) ἔστιν οὐ δίκαιος οὐκ ἄνθρωπος. |
πλείους δὲ τούτων οὐκ ἔσονται ἀντιθέσεις. αὗται δὲ χωρὶς ἐκείνων αὐταὶ καθ’ ἑαυτὰς ἔσονται, ὡς ὀνόματι τῷ οὐκ ἄνθρωπος χρώμεναι. The second αὗται alludes to this last quaternion, ἐκείνων to the first. I have, as in the former case, transposed propositions three and four of this second quaternion, in order that the relation of G to F and of H to E may be more easily discerned.
There are few chapters in Aristotle more obscure and puzzling than the tenth chapter of the De Interpretatione. It was found so by Alexander, Herminus, Porphyry, Ammonius, and all the Scholiasts. Ammonius (Schol. pp. 121, 122, Br.) reports these doubts, and complains of it as a riddle almost insolvable. The difficulties remain, even after the long note of Waitz, and the literal translation of M. Barthélemy St. Hilaire.