Compound Propositions, Modality, and Structure of Arguments — Lives and Opinions of Eminent Philosophers §7.1.72-7.1.76 (Diogenes Laertius) | Greek text & English translation

συμπεπλεγμένον δέ ἐστιν ἀξίωμα ὃ ὑπό τινων συμπλεκτικῶν συνδέσμων συμπέπλεκται, οἷον καὶ ἡμέρα ἐστὶ καὶ φῶς ἐστι. διεζευγμένον δέ ἐστιν ὃ ὑπὸ τοῦ ἤτοι διαζευκτικοῦ συνδέσμου διέζευκται, οἷον ἤτοι ἡμέρα ἐστὶν ἢ νύξ ἐστιν. ἐπαγγέλλεται δʼ ὁ σύνδεσμος οὗτος τὸ ἕτερον τῶν ἀξιωμάτων ψεῦδος εἶναι. αἰτιῶδες δέ ἐστιν ἀξίωμα τὸ συντασσόμενον διὰ τοῦ διότι, οἷον διότι ἡμέρα ἐστί, φῶς ἐστιν· οἱονεὶ γὰρ αἴτιόν ἐστι τὸ πρῶτον τοῦ δευτέρου. διασαφοῦν δὲ τὸ μᾶλλον ἀξίωμά ἐστι τὸ συνταττόμενον ὑπὸ τοῦ διασαφοῦντος τὸ μᾶλλον συνδέσμου καὶ τοῦ 〈ἢ〉 μέσου τῶν ἀξιωμάτων τασσομένου, οἷον μᾶλλον ἡμέρα ἐστὶν ἢ νύξ ἐστι.

A conjunctive proposition is one which is conjoined by certain conjunctive conjunctions, for example: "Both it is day and there is light." A disjunctive proposition is one which is disjoined by the disjunctive conjunction "either... or," for example: "Either it is day or it is night." And this conjunction promises that one of the propositions is false. A causal proposition is one constructed by means of "because," for example: "Because it is day, there is light;" for the first is, as it were, the cause of the second. A proposition declaring the more is one constructed by means of the conjunction declaring the more and "than," which is placed between the propositions, for example: "It is more day than it is night."

διασαφοῦν δὲ τὸ ἧττον ἀξίωμά ἐστι τὸ ἐναντίον τῷ προκειμένῳ, οἷον ἧττον νύξ ἐστιν ἢ ἡμέρα ἐστίν. ἔτι τῶν ἀξιωμάτων κατά τʼ ἀλήθειαν καὶ ψεῦδος ἀντικείμενα ἀλλήλοις ἐστίν, ὧν τὸ ἕτερον τοῦ ἑτέρου ἐστὶν ἀποφατικόν, οἷον τὸ ἡμέρα ἐστί καὶ τὸ οὐχ ἡμέρα ἐστί. συνημμένον οὖν ἀληθές ἐστιν οὗ τὸ ἀντικείμενον τοῦ λήγοντος μάχεται τῷ ἡγουμένῳ¹, οἷον εἰ ἡμέρα ἐστί, φῶς ἐστι. τοῦτʼ ἀληθές ἐστι· τὸ γὰρ οὐχὶ φῶς, ἀντικείμενον τῷ λήγοντι, μάχεται τῷ ἡμέρα ἐστί. συνημμένον δὲ ψεῦδός ἐστιν οὗ τὸ ἀντικείμενον τοῦ λήγοντος οὐ μάχεται τῷ ἡγουμένῳ, οἷον εἰ ἡμέρα ἐστί, Δίων περιπατεῖ· τὸ γὰρ οὐχὶ Δίων περιπατεῖ οὐ μάχεται τῷ ἡμέρα ἐστί.

A proposition declaring the less is the opposite of the preceding, for example: "It is less night than it is day." Further, among propositions, those are mutually opposed in respect of truth and falsehood of which the one is the negative of the other, for example: "It is day" and "It is not day." A conditional proposition is therefore true when the contradictory of the consequent conflicts with the antecedent, for example: "If it is day, there is light." This is true; for "Not: there is light," being the contradictory of the consequent, conflicts with "It is day." And a conditional is false when the contradictory of the consequent does not conflict with the antecedent, for example: "If it is day, Dion walks;" for "Not: Dion walks" does not conflict with "It is day."

Παρασυνημμένον δʼ ἀληθὲς μέν ἐστιν ὃ ἀρχόμενον ἀπʼ ἀληθοῦς εἰς ἀκόλουθον λήγει, οἷον ἐπεὶ ἡμέρα ἐστίν, ἥλιός ἐστιν ὑπὲρ γῆς. ψεῦδος δʼ 〈ὃ〉 ἢ ἀπὸ ψεύδους ἄρχεται ἢ μὴ εἰς ἀκόλουθον λήγει, οἷον ἐπεὶ νύξ ἐστι, Δίων περιπατεῖ, ἂν ἡμέρας οὔσης λέγηται. αἰτιῶδες δʼ ἀληθὲς μέν ἐστιν ὃ ἀρχόμενον ἀπʼ ἀληθοῦς εἰς ἀκόλουθον λήγει, οὐ μὴν ἔχει τῷ λήγοντι τὸ ἀρχόμενον ἀκόλουθον², οἷον διότι ἡμέρα ἐστί, φῶς ἐστι· τῷ μὲν γὰρ ἡμέρα ἐστίν ἀκολουθεῖ τὸ φῶς ἐστι, τῷ δὲ φῶς ἐστιν οὐχ ἕπεται τὸ ἡμέρα ἐστίν. αἰτιῶδες δὲ ψεῦδός ἐστιν ὃ ἤτοι ἀπὸ ψεύδους ἄρχεται ἢ μὴ εἰς ἀκόλουθον λήγει ἢ ἔχει τῷ λήγοντι τὸ ἀρχόμενον ἀνακόλουθον, οἷον διότι νύξ ἐστι, Δίων περιπατεῖ.

A pseudo-conditional is true when, beginning from a true proposition, it ends in a consequent, for example: "Since it is day, the sun is above the earth." And it is false when it either begins from a false proposition or does not end in a consequent, for example: "Since it is night, Dion walks," if it is spoken while it is day. A causal proposition is true when, beginning from a true proposition, it ends in a consequent, yet does not have the initial proposition as a consequence of the concluding proposition, for example: "Because it is day, there is light;" for while to "It is day" there follows "There is light," yet to "There is light" there does not follow "It is day." And a causal proposition is false when it either begins from a false proposition, or does not end in a consequent, or has the initial proposition as non-consequent to the concluding proposition, for example: "Because it is night, Dion walks."

πιθανὸν δέ ἐστιν ἀξίωμα τὸ ἄγον εἰς συγκατάθεσιν, οἷον εἴ τίς τι ἔτεκεν, ἐκείνη ἐκείνου μήτηρ ἐστί. ψεῦδος δὲ τοῦτο· οὐ γὰρ ἡ ὄρνις ᾠοῦ ἐστι μήτηρ. Ἔτι τε τὰ μέν ἐστι δυνατά, τὰ δʼ ἀδύνατα· καὶ τὰ μὲν ἀναγκαῖα, τὰ δʼ οὐκ ἀναγκαῖα. δυνατὸν μὲν τὸ ἐπιδεκτικὸν τοῦ ἀληθὲς εἶναι, τῶν ἐκτὸς μὴ ἐναντιουμένων πρὸς τὸ ἀληθὲς εἶναι³, οἷον ζῇ Διοκλῆσ· ἀδύνατον δὲ ὃ μή ἐστιν ἐπιδεκτικὸν τοῦ ἀληθὲς εἶναι, οἷον ἡ γῆ ἵπταται. ἀναγκαῖον δέ ἐστιν ὅπερ ἀληθὲς ὂν οὐκ ἔστιν ἐπιδεκτικὸν τοῦ ψεῦδος εἶναι, ἢ ἐπιδεκτικὸν μέν ἐστι, τὰ δʼ ἐκτὸς αὐτῷ ἐναντιοῦται πρὸς τὸ ψεῦδος εἶναι, οἷον ἡ ἀρετὴ ὠφελεῖ. οὐκ ἀναγκαῖον δέ ἐστιν ὃ καὶ ἀληθές ἐστιν καὶ ψεῦδος οἷόν τε εἶναι, τῶν ἐκτὸς μηδὲν ἐναντιουμένων, οἷον τὸ περιπατεῖ Δίων.

A plausible proposition is one that leads to assent, for example: "If someone brought forth someone, she is his mother." Yet this is false; for a bird is not the mother of an egg. Furthermore, some propositions are possible, others impossible; and some are necessary, others not necessary. Possible is that which is receptive of being true, external circumstances not opposing its being true, for example: "Diocles lives;" and impossible is that which is not receptive of being true, for example: "The earth flies." Necessary is that which, being true, is not receptive of being false, or, while being receptive of it, external circumstances oppose its being false, for example: "Virtue is beneficial." Not necessary is that which is capable of being both true and false, external circumstances in no way opposing, for example: "Dion walks."

εὔλογον δέ ἐστιν ἀξίωμα τὸ πλείονας ἀφορμὰς ἔχον εἰς τὸ ἀληθὲς εἶναι, οἷον βιώσομαι αὔριον. Καὶ ἄλλαι δέ εἰσι διαφοραὶ ἀξιωμάτων καὶ μεταπτώσεις αὐτῶν ἐξ ἀληθῶν εἰς ψεύδη καὶ ἀντιστροφαί, περὶ ὧν ἐν τῷ πλάτει⁴ λέγομεν. Λόγος δέ ἐστιν, ὡς οἱ περὶ τὸν Κρῖνίν φασι, τὸ συνεστηκὸς ἐκ λήμματος καὶ προσλήψεως καὶ ἐπιφορᾶς, οἷον ὁ τοιοῦτος, εἰ ἡμέρα ἐστί, φῶς ἐστι· ἡμέρα δέ ἐστι· φῶς ἄρα ἐστί. λῆμμα μὲν γάρ ἐστι τὸ εἰ ἡμέρα ἐστι, φῶς ἐστι· πρόσληψις τὸ ἡμέρα δέ ἐστιν· ἐπιφορὰ δὲ τὸ φῶς ἄρα ἐστί. τρόπος δέ ἐστιν οἱονεὶ σχῆμα λόγου, οἷον ὁ τοιοῦτος, εἰ τὸ πρῶτον, τὸ δεύτερον· ἀλλὰ μὴν τὸ πρῶτον· τὸ ἄρα δεύτερον.

A reasonable (well-grounded) proposition is one having more inducements towards being true, for example: "I shall be alive tomorrow." There are also other differences among propositions, and transitions of them from true to false, and conversions, concerning which we speak at large. An argument is, as Crinis and his followers say, that which consists of a major premise, an additional premise (minor premise), and a conclusion, such as the following: "If it is day, there is light; and it is day; therefore there is light." For the major premise is "If it is day, there is light;" the minor premise is "And it is day;" and the conclusion is "Therefore there is light." A mood is, as it were, the schema of an argument, such as the following: "If the first, the second; but indeed the first; therefore the second."

Syntax notes4 items

7.1.73οὗ τὸ ἀντικείμενον τοῦ λήγοντος μάχεται τῷ ἡγουμένῳ
The genitive relative pronoun οὗ depends on the antecedent συνημμένον, denoting possession with respect to the subject within the clause, τὸ ἀντικείμενον τοῦ λήγοντος ("a conditional proposition of which the contradictory of the consequent ..."). This expresses the Chrysippean criterion of connection/consequence.
7.1.74οὐ μὴν ἔχει τῷ λήγοντι τὸ ἀρχόμενον ἀκόλουθον
Syntactically, τὸ ἀρχόμενον ("the beginning proposition", antecedent) is the direct object of ἔχει, with ἀκόλουθον serving as a predicate accusative ("as a consequence"), complemented by the dative τῷ λήγοντι ("to the concluding proposition"). It signifies that while the consequent follows from the antecedent, the antecedent does not conversely follow from the consequent, establishing the asymmetry of causal propositions.
7.1.75τῶν ἐκτὸς μὴ ἐναντιουμένων πρὸς τὸ ἀληθὲς εἶναι
A genitive absolute expressing circumstance/condition: "external circumstances not opposing its being true." In Stoic modal logic, this construction introduces the absence of external hindrance as a crucial criterion alongside internal receptivity.
7.1.76ἐν τῷ πλάτει
An idiomatic prepositional phrase meaning "at length," "in detail," or "at broad scope" (in contrast to ἐν ἐπιτομῇ, "in summary"). It indicates that these advanced dialectical topics are treated in an extended or comprehensive discussion elsewhere.

Model: gemini-3.8-flashurn:cts:greekLit:tlg0004.tlg001.humanitext-grc2:7.1.72-7.1.76