vi. 1, 30, 594, A: πῶς δὲ ἓν τὸ πὼς ἔχον, πολλῆς διαφορᾶς ἐν αὐτοῖς

οὔσης; πῶς γὰρ τὸ τρίπηχυ καὶ τὸ λευκὸν εἰς ἓν [γένος θετέον], τοῦ μὲν ποσοῦ τοῦ δὲ ποιοῦ ὄντος; πῶς δὲ τὸ ποτὲ καὶ τὸ ποῦ; πῶς δὲ ὅλως πὼς ἔχοντα τὸ χθὲς καὶ τὸ πέρυσι καὶ τὸ ἐν Λυκείῳ καὶ ἐν Ἀκαδημίᾳ; καὶ ὅλως πῶς δὲ ὁ χρόνος πὼς ἔχον; ... τὸ δὲ ποιεῖν πῶς πὼς ἔχον ... καὶ ὁ πάσχον οὐ πὼς ἔχον ... ἴσως δ’ ἂν μόνον ἁρμόσει ἐπὶ τοῦ κεῖσθαι τὸ πὼς ἔχον καὶ ἐπὶ τοῦ ἔχειν· ἐπὶ δὲ τοῦ ἔχειν οὐ πὼς ἔχον ἀλλὰ ἔχον. Simpl. Categ. 94, ε: The Stoics included ἔχειν under πὼς ἔχον. In saying as Simpl. 16, δ, does that the Stoics omitted ποσὸν, time, and place, it must be meant that they did not treat these conceptions as separate categories. What they did with them Simpl. explains l.c. εἰ γὰρ τὸ πὼς ἔχον νομίζουσιν αὐτοῖς τὰ τοιαῦτα περιλαμβάνειν. Trendelenburg, 229, with justice, observes that, wherever the species-forming difference lies in ποσὸν as in mathematical conceptions, there ποσὸν comes under ποιόν.

[204] Simpl. 42, ε: οἱ δὲ Στωϊκοὶ ἀνθ’ ἑνὸς γένους δύο κατὰ τὸν τόπον τοῦτον ἀριθμοῦνται, τὰ μὲν ἐν τοῖς πρός τι τιθέντες, τὰ δ’ ἐν τοῖς πρός τί πως ἔχουσι, καὶ τὰ μὲν πρός τι ἀντιδιαιροῦντες τοῖς καθ’ αὑτὰ, τὰ δὲ πρός τί πως ἔχοντα τοῖς κατὰ διαφοράν. (Ibid. 44, β: οἱ Στωϊκοὶ νομίζουσι πάσης τῆς κατὰ διαφορὰν ἰδιότητος ἀπηλλάχθαι τὰ πρός τί πως ἔχοντα.) Sweet and bitter belong to τὰ πρός τι· to the other class belong δεξιὸς, πατὴρ, &c., κατὰ διαφορὰν δέ φασι τὰ κατά τι εἶδος χαρακτηριζόμενα. Every καθ’ αὑτὸ is also κατὰ διαφορὰν (determined as to quality), and every πρός τί πως ἔχον is also a πρός τι, but not conversely. Conf. 43, β. εἰ δὲ δεῖ σαφέστερον μεταλαβεῖν τὰ λεγόμενα, πρός τι μὲν λέγουσιν ὅσα κατ’ οἰκεῖον χαρακτῆρα διακείμενά πως ἀπονεύει πρὸς ἕτερον (or, according to the definition in Sext. Math. viii. 454: πρός τι ἐστὶ τὸ πρὸς ἑτέρῳ νοούμενον), πρός τι δέ πως ἔχοντα ὅσα πέφυκε συμβαίνειν τινὶ καὶ μὴ συμβαίνειν ἄνευ τῆς περὶ αὐτὰ μεταβολῆς καὶ ἀλλοιώσεως μετὰ τοῦ πρὸς τὸ ἐκτὸς ἀποβλέπειν, ὥστε ὅταν μὲν κατὰ διαφοράν τι διακείμενον πρὸς ἕτερον νεύσῃ, πρός τι μόνον τοῦτο ἔσται, ὡς ἡ ἕξις καὶ ἡ ἐπιστήμη καὶ ἡ αἴσθησις· ὅταν δὲ μὴ κατὰ τὴν ἐνοῦσαν διαφορὰν κατὰ ψιλὴν δὲ τὴν πρὸς ἕτερον σχέσιν θεωρῆται, πρὸς τί πως ἔχοντα ἔσται· ὁ γὰρ υἱὸς καὶ ὁ δεξιὸς ἔξωθεν τινῶν προσδέονται, πρὸς τὴν ὑπόστασιν· διὸ καὶ μηδεμιᾶς γινομένης περὶ αὐτὰ μεταβολῆς γένοιτ’ ἂν οὐκέτι πατὴρ, τοῦ υἱοῦ ἀποθανόντος, ὁ δὲ δεξιὸς τοῦ παρακειμένου μεταστάντος· τὸ δὲ γλυκὺ καὶ πικρὸν οὐκ ἂν ἀλλοῖα γένοιτο εἰ μὴ συμμεταβάλλοι καὶ ἡ περὶ αὐτὰ δύναμις. In this sense, therefore, πρός τι belongs to ποιὸν, being composed (as Simpl. 43, α, says) of ποιὸν and πρός τι. On the other hand, πρός τί πως ἔχον only expresses, to quote Herbart, an accidental relation. Prantl’s quotation (I. 437, 108) from Simpl. 44, β, we have no special reason to refer to the Stoics.

[205] Trendelenburg, 220, considers that these genera are in so far subordinate to one another, that the previous one continues in the next, but with the addition of a fresh determination; a better name for the second category would be ὑποκείμενα ποιά· for the third, ὑποκείμενα ποιά πως ἔχοντα· for the fourth, ὑποκείμενα ποιὰ πρός τί πως ἔχοντα. In support of this, he refers to Simpl. 43, α: ἕπεται δὲ αὐτοῖς κἀκεῖνο ἄτοπον τὸ σύνθετα ποιεῖν τὰ γένη ἐκ προτέρων τινῶν καὶ δευτέρων ὡς τὸ πρός τι ἐκ ποιοῦ καὶ τοῦ πρός τι. Plut. C. Not. 44, 6: τέτταρά γε ποιοῦσιν ὑποκείμενα περὶ ἕκαστον, μᾶλλον δὲ τέτταρα ἕκαστον ἡμῶν. Plot. Enn. vi. 1, 29, 593, A: ἄτοπος ἡ διαίρεσις ... ἐν θατέρῳ τῶν εἰδῶν τὸ ἕτερον τιθεῖσα, ὥσπερ ἂν [εἴ] τις διαιρῶν τὴν ἐπιστήμην τὴν μὲν γραμματικὴν λέγοι, τὴν δὲ γραμματικὴν καὶ ἄλλο τι· if ποιὰ are to be ὕλη ποιὰ, they are composed of ὕλη and εἶδος or λόγος. See p. 48, 2.

[206] See p. 103, 1.

[207] See p. 107, 2; Plotin. vi. 1, 30: Why are πὼς ἔχοντα enumerated as a third category, since πάντα περὶ τὴν ὕλην πὼς ἔχοντα; the Stoics would probably say that ποιὰ are περὶ τὴν ὕλην πὼς ἔχοντα, whereas the πὼς ἔχοντα, in the strict sense of the term, are περὶ τὰ ποιά. Yet since the ποιὰ themselves are nothing more than ὕλη πως ἔχουσα, all categories must be ultimately reduced to ὕλη.

[208] Prantl, Gesch. d. Logik, i. 440–467.

[209] In Diog. 66; Sext. Math. viii. 70; Ammon. De Interp. 4, a (Schol. in Arist. 93, a; 22, b, 20); Simpl. Cat. 103, α; Boëth. De Interp. 315; Cramer, Anecd. Oxon. iii. 267, conf. I. 104, a distinction is drawn between ἀξίωμα (a judgment), ἐρώτημα (a direct question, requiring Yes or No), πύσμα (an enquiry), προστακτικὸν, ὁρκικὸν, ἀρατικὸν (wishes), εὐκτικὸν (a prayer), ὑποθετικὸν (a supposition), ἐκθετικὸν (as ἐκκείσθω εὐθεῖα γραμμὴ), προσαγορευτικὸν (an address), θαυμαστικὸν, ψεκτικὸν, ἐπαπορητικὸν, ἀφηγηματικὸν (explanatory statements), ὅμοιον ἀξιώματι (a judgment with something appended, as: ὡς Πριαμίδῃσιν ἐμφερὴς ὁ βουκόλος! by Sextus called Πλεῖον ἢ ἀξίωμα). Ammon. in Waitz, Arist. Orig. i. 43, speaks of ten forms of sentences held by the Stoics, mentioning, however, only two, προστακτικὸς and ἐβκτικός (so reads the MS. Waitz suggests ἐφεκτικὸς, more probably it is εὐκτικός). Diog. 191, mentions treatises of Chrysippus on interrogatory and hortatory sentences. On the relation of an oath to ἀξίωμα light is thrown by Simpl. l.c., also by Chrysippus’ distinction between ἀληθορκεῖν and εὐορκεῖν ψευδορκεῖν and ἐπιορκεῖν in Stob. Floril. 28, 15.

[210] Diog. 65: ἀξίωμα δέ ἐστιν ὅ ἐστιν ἀληθὲς ἢ ψεῦδος. Questions and other similar sentences are neither true nor false (Ibid. 66 and 68). This definition of a judgment is constantly referred to, see p. 83, 2, by Simpl. Cat. 103, α; Cic. Tusc. i. 7, 14; De Fato, 10, 20; Gell. N. A. xvi. 8, 8; Schol. in Arist. 93, b, 35. The purport of the expression λόγος ἀποφαντικὸς, λεκτὸν ἀποφαντὸν (in Diog. 65; Gell. xvi. 8, 4; Ammon. De Interp. 4, a; Schol. in Arist. 93, b, 20) is the same.

[211] Sext. Math. viii. 93: τῶν γὰρ ἀξιωμάτων πρώτην σχεδὸν καὶ κυριωτάτην ἐκφέρουσι διαφορὰν οἱ διαλεκτικοὶ καθ’ ἣν τὰ μέν ἐστιν αὐτῶν ἁπλᾶ τὰ δ’ οὐχ ἁπλᾶ. Ibid. 95 and 108. Diog. 68 gives the definitions of both.

[212] Sext. l.c., by whom Diog. must be corrected, see p. 113, 3.

[213] Diog. 69: ἐν δὲ τοῖς οὐχ ἁπλοῖς τὸ συνημμένον καὶ τὸ παρασυνημμένον καὶ τὸ συμπεπλεγμένον καὶ τὸ αἰτιῶδες καὶ τὸ διεζευγμένον καὶ τὸ διασαφοῦν τὸ μᾶλλον καὶ τὸ διασαφοῦν τὸ ἧττον. Further details presently respecting the συνημμένον and διεζευγμένον. For the παρασυνημμένον—a conditional sentence, the first part of which is introduced by ἐπειδὴ—see Diog. 71 and 74; for the συμπεπλεγμένον, the characteristic of which is the καὶ and καὶ, see Diog. 72; Sext. Math. viii. 124; Gell. N. A. xvi. 8 and 9; Ps. Galen, Εἰσαγ. διαλ. 13; Dexipp. in Cat. 27, 3, Speng.; (Schol. in Arist. 44. a, 9—Prantl, 446, says this passage is not quite correct; it only implies that the term συμπλοκὴ was confined to a copulative judgment); for the αἰτιῶδες, which is characterised by a διότι, and therefore is not identical with the παρασυνημμένον, Diog. 72 and 74; for the διασαφοῦν τὸ μᾶλλον and the διασαφοῦν τὸ ἧττον, Diog. 72; conf. Cramer, Anecd. Oxon. i. 188; Apollon. Synt. (Bekker’s Anecd. ii.), 481. These are only some of the principal forms of composite judgments, their number being really indefinite. Chrysippus estimated that a million combinations might be formed with ten sentences. The celebrated mathematician, Hipparchus however, proved that only 103,049 affirmative and 310,952 negative judgments could be formed with that material (Plut. Sto. Rep. 29, 5, p. 1047; Qu. Symp. viii. 9, 3, 11, p. 732).

[214] There is no notice of a division of judgments into general and particular. Instead of that, Sext. (Math. viii. 96) distinguishes ὡρισμένα as οὗτος κάθηται, ἀόριστα as τὶς κάθηται, and μέσα as ἄνθρωπος κάθηται, Σωκράτης περιπατεῖ. When the subject stood in the nominative, ὡρισμένα were called καταγορευτικὰ (Diog. 70); the others κατηγορικά· a καταγορευτικὸν is οὗτος περιπατεῖ· a κατηγορικὸν, Δίων περιπατεῖ.

[215] An affirmative judgment was called καταφατικὸν, a negative ἀποφατικὸν, by Chrysippus in the fragment about to be quoted, and Simpl. Cat. 102, δ, ζ. Apul. Dogm. Plat. iii. 266, Oud. renders these terms by dedicativa and abdicativa. For the manner in which they expressed negative sentences, see Boëth. De Interp. 373; Schol. in Arist. 120.

[216] Diog. 69 gives an example of ἀρνητικὸν, οὐδεὶς περιπατεῖ· one of particular negation, στερητικὸν—ἀφιλάνθρωπός ἐστιν οὗτος· one of double negation, ὑπεραποφατικὸν—as, οὐχὶ ἡμέρα οὐκ ἐστί.

[217] Sext. Math. viii. 89; Diog. 73: ἀντικείμενα are ὧν τὸ ἕτερον τοῦ ἑτέρου ἐστὶν ἀποφατικὸν or (according to the outward treatment of these determinations) ἀποφάσει πλεονάζει—as, It is day, and It is not day. Aristotle called such a contradictory ἀντίφασις, a contrary ἐναντιότης, putting both under the class conception of ἀντικείμενα. The Stoics reserved ἀντικείμενα for contradictories (Simpl. Cat. 102, δ and 102, ζ, a Stoic discussion intended to show that the conception of ἐνάντιον is not applicable to negative sentences and conceptions), which is after all only a difference in terminology. Ἐναντίον they also call μαχόμενον (Apollon. Synt. 484, Bekk.). Otherwise, following Aristotle, they distinguished between ἐναντίον and ἐναντίως ἔχον· ἐναντία are conceptions which are in plain and immediate contrast, such as φρόνησις and ἀφρόνησις· ἐναντίως ἔχοντα are those which are only contrasted by means of the ἐναντία, such as φρόνιμος and ἄφρων (Simpl. Categ. 98, γ). The former, therefore, apply to abstract, the latter to concrete notions. That every negative judgment has an affirmative judgment opposed to it is elaborately proved by a series of quotations from poets, each one of which is four times repeated in the fragment περὶ ἀποφατικῶν first edited by Letronne (Fragments inédits, Paris, 1838), and subsequently emended, explained, and with a great degree of probability referred to Chrysippus by Bergk (De Chrysippi libro περὶ ἀποφατικῶν, Cassel, 1841, Gymn. progr.). In explaining the fragment Prantl, Gesch. d. Log. I. 451 appears to have hit the truth in one point, where Bergk is not satisfied.

[218] Simpl. Categ. 103, β; Cic. De Fato, 16, 37; N. D. i. 25, 70. Further particulars above p. 83, 2; 110, 3.

[219] Viz. that the members of a disjunction, as well as their contradictory opposites, must also be contraries (adversa or pugnantia), and that from the truth of the one the falsehood of the other follows. A disjunction which does not satisfy one or the other of these conditions is false (παραδιεζευγμένον). Gell. N. A. xvi. 8, 12; Sext. Pyrrh. ii. 191; Alex. Anal. Pr. 7, b.

[220] Diog. 71; Sext. Math. 109; Galen, De Simpl. Medicamen. ii. 16, vol. xi. 499; Ps. Galen, Εἰσαγ. διαλ. p. 15. The Stoics distinguish most unnecessarily, but quite in harmony with their ordinary formal punctiliousness, the case in which the leading clause is identical with the inferential clause (εἰ ἡμέρα ἐστὶν, ἡμέρα ἔστιν) and the case in which it is different (εἰ ἡμέρα ἐστὶν, φῶς ἔστιν). Conditional sentences of the first kind are called διφορούμενα συνημμένα. Sext. viii. 281; 294; and 466; Pyrrh. ii. 112; conf. viii. 95; Diog. 68. That in all these passages διφορούμενον must be read, and not διαφορούμενον, appears according to Prantl’s (p. 445, 122) very true observation from the remarks of Alex. Top. 7, a; Anal. Pr. 7, b, on διφορούμενοι συλλογισμοί.

[221] Sext. Math. viii. 112; κοινῶς μὲν γάρ φασιν ἅπαντες οἱ Διαλεκτικοὶ ὑγιὲς εἶναι συνημμένον, ὅταν ἀκολουθῇ τῷ ἐν αὐτῷ ἡγουμένῳ τὸ ἐν αὐτῷ λῆγον. περὶ δὲ τοῦ πότε ἀκολουθεῖ καὶ πῶς, στασιάζουσι πρὸς ἀλλήλους καὶ μαχόμενα τῆς ἀκολουθίας ἐκτίθενται κριτήρια. Cic. Acad.