Miscellanies 8.3.6
Summary: A syllogism draws a valid conclusion from agreed premises; a demonstration does so from true premises; and either everything needs proof or some things are credible in themselves.
Greek text · Stählin 2
Καὶ διαφέρει ἔνδειξις συλλογισμοῦ ᾗ τὸ μὲν ἐνδεικνύμενον ἑνός ἐστι δηλωτικὸν ἓν ὑπάρχον καὶ αὐτό, ὡς τοῦ μηκέτι εἶναι παρθένον ἔνδειξιν εἶναι τὸ κυεῖν φαμεν, τὸ δὲ συλλογισμῷ λαμβανόμενον ἓν ὑπάρχον ἕπεται πλείοσιν, ὡς τοῦ Πύθωνα προδιδόναι Βυζαντίους, εἰ οὕτως ἔτυχεν. οὐχ ἕν, ἀλλὰ πλείω λαμβάνεται τὰ δηλωτικά. καὶ τὸ μὲν περαίνειν ἐξ ὁμολογουμένων συλλογίζεσθαί ἐστιν, τὸ δέ γε ἐξ ἀληθῶν τι περαίνειν ἀποδεικνύειν ἐστίν, ὥστʼ εἶναι σύνθετόν τινα τῆς ἀποδείξεως τὴν ὄνησιν ἔκ τε τοῦ τὰ λαμβανόμενα πρὸς τὰ ζητούμενα ἀληθῆ λαμβάνειν κἀκ τοῦ τὸ συμπέρασμα αὐτοῖς ἀκόλουθον ἐπιφέρεσθαι. εἰ δʼ ἤτοι μὴ ὑπάρχοι τὸ πρότερον ἢ μὴ ἕποιτο αὐτῷ τὸ δεύτερον, οὐκ ἀπέδειξεν μέν, συνελογίσατο δέ. τὸ μὲν γὰρ οἰκεῖον ἐπενεγκεῖν συμπέρασμα τοῖς λήμμασιν συλλογίσασθαι μόνον ἐστίν, τὸ δὲ καὶ τῶν λημμάτων ἕκαστον ὑπάρχειν ἀληθὲς οὐ συλλογίσασθαι μόνον, ἀλλὰ καὶ ἀποδεδειχέναι. περαίνειν δʼ ἐστίν, ὡς καὶ ἐκ τοῦ ὀνόματος δῆλον, τὸ ἄγειν ἐπὶ τὸ πέρας. ἔστι δὲ δήπου πέρας ἐν ἑκάστῳ λόγῳ τὸ ζητούμενον, ὃ δὴ καὶ συμπέρασμα καλεῖται. οὐδεὶς δὲ ἁπλοῦς καὶ πρῶτος λόγος ὀνομάζεται συλλογισμός, κἂν ἀληθὴς ᾖ, ἀλλʼ ἔστι τοὐλάχιστον ἐκ τριῶν τοιούτων σύνθετον, δυεῖν μὲν ὡς λημμάτων, ἑνὸς δὲ ὡς συμπεράσματος. Ἤτοι δὲ πάντα ἀποδείξεως δεῖται ἢ καί τινα ἐξ αὑτῶν ἐστι πιστά.
English · Claude translation
Indication differs from syllogism in that what is indicated is a sign of one thing, being itself also one, as we say that pregnancy is an indication that a woman is no longer a virgin; but what is taken by syllogism, being one, follows from several things, as in the case of Python's betraying the Byzantines, if that is how it happened: not one sign but several are taken. And to conclude from agreed premises is to syllogize; but to conclude something from true premises is to demonstrate. So the benefit of demonstration is compound: it comes from taking premises that are true with respect to what is sought, and from drawing the conclusion that follows from them. If either the first is lacking or the second does not follow from it, one has not demonstrated, though one has syllogized. For to draw the proper conclusion from the premises is only to syllogize; but that each of the premises is also true is not only to have syllogized but also to have demonstrated. To conclude (περαίνειν) is, as is clear from the word itself, to bring to the end (πέρας); and the end in every argument is what is sought, which is also called the conclusion (συμπέρασμα). No single, primary statement is called a syllogism, even if it is true; it is compounded of at least three such statements, two as premises and one as conclusion. Either all things need demonstration, or some are credible of themselves.
About this passage
Notes
Translation notes
- Terms: ἔνδειξις “indication”, συλλογισμός “syllogism”, λῆμμα “premise”, συμπέρασμα “conclusion”, περαίνειν “conclude”. Python of Byzantium, who was suspected of betraying his city to Philip of Macedon, was a stock example in rhetoric and logic of a conclusion drawn from several signs.
Cite this passage
Clement of Alexandria, Strom. 8.3.6 (trans. Sophia Scriptura, https://sophiascriptura.com/fathers/clement-stromata/8/3/6/).
Plain text
Clement of Alexandria, Strom. 8.3.6 (trans. Sophia Scriptura, https://sophiascriptura.com/fathers/clement-stromata/8/3/6/).
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