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To consider also the things between these, which are sometimes contemplated in matter, and sometimes outside of matter, and are intermediate between the immaterial and the material, which is mathematics. For number is immaterial in itself, but it is also contemplated in matter, for instance in wheat or wine; for we say ten modii of wheat and ten sextarii of wine; and likewise for the other types of mathematics. The practical part adorns character and teaches how one ought to conduct oneself in a state; and if it educates one person, it is called ethical; if a whole household, it is called economic; if an entire city, it is called political. It must be known that there are four dialectical, or logical, methods: 1. divisive, which divides the genus into species through the means of differences; 2. definitive, which from the genus and the differences, which the divisive method divided, defines the subject; 3. analytic, which analyzes the more composite into the more simple, that is, the body into the humors, the humors into the fruits, the fruits into the four elements, the elements into matter and form; 4. demonstrative, which demonstrates the proposition through some medium; for instance, it is proposed for me to show that the soul is immortal; I take some medium, the ever-moving, and reason thus: The soul is ever-moving; the ever-moving is immortal; therefore, the soul is immortal. It must be known that the syllogisms belong to the demonstrative method. But one must know that the analytic is threefold: for there is the physical, as was said before; there is also logical analysis, when we analyze the proposed syllogism into its proper figure; and there is also mathematical, when we take what is sought as being agreed upon and arrive at something agreed upon, from which the proposition is captured. For instance, let the question be: If the soul is immortal. This question I take as being agreed upon and say: Since the soul is immortal, there are retributions for wicked and good deeds; and if there are retributions, there is that which is judged and that which judges; and if there is that which is judged and that which judges, there is a provider and providence. We have arrived, therefore, at providence, which is agreed upon by all. From there, then, by synthesis I say: Since there is providence and a judge, there are retributions; since there are retributions, there is that which is judged; and if there is that which is judged, therefore the soul is immortal. 50 Concerning the hypostatic union. It is necessary to know that the hypostatic union constitutes one composite hypostasis of the things united, preserving in itself the natures that have come together for union and their difference and their natural properties unconfused and unaltered. And this has no hypostatic difference with respect to itself; for the characteristic differences of each of the things that have come together for union, by which each is separated from those of the same kind, become its own, as is the case with soul and body. For one composite hypostasis, for instance that of Peter or of Paul, is constituted from both, and it preserves in itself the two perfect natures, that of the soul and that of the body, and their difference unmingled and their natural properties unconfused. And it has in itself the characteristic properties of each, those of the soul which separate it from the other souls and those of the body which separate it from the other bodies, in no way separating the soul from the body but uniting and joining them, and at the same time separating the one hypostasis composed from them from the other hypostases of the same kind. But once the natures have received hypostatic union with each other, they remain completely indivisible. For even if the soul is separated from the body in death, yet the hypostasis of both is one and the same; for hypostasis is the very constitution at the beginning of each one's existence. Therefore both the body and the soul remain, always having the one beginning of themselves

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Θεωρεῖν δὲ καὶ τὰ μέσα τούτων, ἃ ποτὲ μὲν ἐν ὕλῃ θεωροῦνται, ποτὲ δὲ ἐκτὸς ὕλης καὶ μέσα εἰσὶ τῶν ἀύλων καὶ ὑλικῶν, ὅπερ ἐστὶ τὸ μαθηματικόν. Ὁ γὰρ ἀριθμὸς ἄυλός ἐστι καθ' ἑαυτόν, θεωρεῖται δὲ καὶ ἐν ὕλῃ, σίτῳ τυχὸν ἢ οἴνῳ· λέγομεν γὰρ δέκα μοδίους σίτου καὶ δέκα ξέστας οἴνου· ὁμοίως καὶ ἐπὶ τῶν λοιπῶν εἰδῶν τοῦ μαθηματικοῦ. Τὸ δὲ πρακτικὸν ἦθος κοσμεῖ καὶ τὸ πῶς δεῖ πολιτεύεσθαι διδάσκει· καὶ εἰ μὲν ἕνα ἄνθρωπον παιδεύει, λέγεται ἠθικόν, εἰ δὲ οἶκον ὅλον, λέγεται οἰκονομικόν, εἰ δὲ πόλιν ὁλόκληρον, λέγεται πολιτικόν. Ἰστέον, ὡς τέσσαρές εἰσιν αἱ διαλεκτικαὶ μέθοδοι ἤγουν λογικαί· αʹ διαιρετική, ἥτις διαιρεῖ τὸ γένος εἰς εἴδη διὰ μέσων τῶν διαφορῶν· βʹ ὁριστική, ἥτις ἀπὸ τοῦ γένους καὶ τῶν διαφορῶν, ὧν διεῖλεν ἡ διαιρετική, ὁρίζει τὸ ὑποκείμενον· γʹ ἀναλυτικὴ ἡ τὸ συνθετικώτερον ἀναλύουσα εἰς τὰ ἁπλούστερα, τουτέστι τὸ σῶμα εἰς τοὺς χυμούς, τοὺς χυμοὺς εἰς τοὺς καρπούς, τοὺς καρποὺς εἰς τὰ τέσσαρα στοιχεῖα, τὰ στοιχεῖα εἰς ὕλην καὶ εἶδος· δʹ ἀποδεικτικὴ ἡ διὰ μέσου τινὸς δεικνύουσα τὸ προκείμενον· οἷον πρόκειταί μοι δεῖξαι, ὅτι ἡ ψυχὴ ἀθάνατός ἐστι· λαμβάνω τι μέσον, τὸ ἀεικίνητον, καὶ συλλογίζομαι οὕτως· Ἡ ψυχὴ ἀεικίνητός ἐστι· τὸ ἀεικίνητον ἀθάνατον· ἡ ψυχὴ ἄρα ἀθάνατος. Ἰστέον δέ, ὡς οἱ συλλογισμοὶ τῆς ἀποδεικτικῆς εἰσι. ∆εῖ δὲ γινώσκειν, ὅτι ἡ ἀναλυτικὴ τρισσή τίς ἐστιν· ἔστι γὰρ φυσικὴ ὡς ἡ προλεχθεῖσα· ἔστι δὲ καὶ λογικὴ ἀνάλυσις, ὅταν τὸν προτεθέντα συλλογισμὸν ἀναλύσωμεν εἰς τὸ οἰκεῖον σχῆμα· ἔστι δὲ καὶ μαθηματική, ὅταν λάβωμεν τὸ ζητούμενον ὡς ὁμολογούμενον καὶ καταντήσωμεν εἴς τι ὁμολογούμενον, ὅθεν ἀγρεύεται τὸ προκείμενον. Οἷον ἔστω τὸ ζητούμενον· Εἰ ἀθάνατος ἡ ψυχή. Τοῦτο τὸ ζητούμενον λαμβάνω ὡς ὁμολογούμενον καὶ λέγω· Ἐπειδὴ ἀθάνατος ἡ ψυχή, εἰσὶν ἀμοιβαὶ τῶν φαύλων καὶ ἀγαθῶν πράξεων· εἰ δέ εἰσιν ἀμοιβαί, ἔστι τὸ δικαζόμενον καὶ δικάζον· εἰ δέ ἐστι τὸ δικαζόμενον καὶ δικάζον, ἔστι προνοητὴς καὶ πρόνοια. Κατηντήσαμεν τοίνυν εἰς τὴν πρόνοιαν, ἥτις παρὰ πᾶσιν ὁμολογεῖται. Ἔνθεν λοιπὸν κατὰ σύνθεσιν λέγω· Ἐπειδὴ ἔστι πρόνοια καὶ δικαστής, εἰσὶν ἀμοιβαί· ἐπειδὴ εἰσὶν ἀμοιβαί, ἔστι τὸ κρινόμενον· εἰ δὲ ἔστι τὸ κρινόμενον, ἀθάνατος ἄρα ἡ ψυχή. 50 Περὶ τῆς καθ' ὑπόστασιν ἑνώσεως. Χρὴ γινώσκειν, ὅτι ἡ καθ' ὑπόστασιν ἕνωσις μίαν ὑπόστασιν τῶν ἑνουμένων ἀποτελεῖ σύνθετον σῴζουσα τὰς συνελθούσας πρὸς ἕνωσιν φύσεις καὶ τὴν τούτων διαφορὰν καὶ τὰ τούτων φυσικὰ ἰδιώματα ἀσύγχυτά τε καὶ ἄτρεπτα ἐν ἑαυτῇ. Αὕτη δὲ πρὸς ἑαυτὴν οὐδεμίαν ὑποστατικὴν ἔχει διαφοράν· αὐτῆς γὰρ γίνονται αἱ ἑκατέρου τῶν συνελθόντων πρὸς ἕνωσιν χαρακτηριστικαὶ διαφοραί, αἷς ἑκατέρων ἐκ τῶν ὁμοειδῶν χωρίζονται, ὡς ἐπὶ ψυχῆς ἔχει καὶ σώματος. Μία μὲν γὰρ ἐξ ἀμφοτέρων ἀποτελεῖται ἡ τοῦ Πέτρου τυχὸν ἢ τοῦ Παύλου ὑπόστασις σύνθετος, σῴζει δὲ ἐν ἑαυτῇ τὰς δύο τελείας φύσεις, τήν τε τῆς ψυχῆς καὶ τοῦ σώματος, καὶ τὴν τούτων διαφορὰν ἀσύμφυρτον καὶ τὰ τούτων φυσικὰ ἰδιώματα ἀσύγχυτα. Ἔχει δὲ ἐν ἑαυτῇ τὰ ἑκατέρας χαρακτηριστικὰ ἰδιώματα τά τε τῆς ψυχῆς τὰ χωρίζοντα αὐτὴν ἐκ τῶν λοιπῶν ψυχῶν καὶ τὰ τοῦ σώματος τὰ χωρίζοντα αὐτὸ ἐκ τῶν λοιπῶν σωμάτων, μηδαμῶς χωρίζοντα τὴν ψυχὴν ἐκ τοῦ σώματος ἀλλ' ἑνοῦντα καὶ συνάπτοντα, ἅμα δὲ τὴν ἐξ αὐτῶν συντεθειμένην μίαν ὑπόστασιν χωρίζοντα τῶν λοιπῶν ὁμοειδῶν ὑποστάσεων. Ἐπειδὰν δὲ ἅπαξ αἱ φύσεις τὴν πρὸς ἄλληλα καθ' ὑπόστασιν δέξωνται ἕνωσιν, ἀδιαίρετοι μένουσιν εἰς τὸ παντελές. Εἰ γὰρ καὶ χωρίζεται ἡ ψυχὴ τοῦ σώματος ἐν τῷ θανάτῳ, ἀλλ' ἡ ὑπόστασις ἀμφοτέρων μία καὶ ἡ αὐτή ἐστιν· ὑπόστασις γάρ ἐστιν ἡ ἐν τῇ ἀρχῇ τῆς ἑκάστου ὑπάρξεως κατ' αὐτὸ σύμπηξις. Μένει οὖν τό τε σῶμα καὶ ἡ ψυχή, ἀεὶ μίαν τὴν ἀρχὴν τῆς ἑαυτῶν ἔχοντα