§1.2.3#2Φανερὸν δὲ καὶ ἐπὶ τῶν ἐν μέρει συλλογισμῶν· οὐδὲν γὰρ κωλύει τὸ τῷ μὲν Β παντὶ τῷ δὲ Γ τινὶ ὑπάρχειν, καὶ τὸ Β τῷ Γ τινὶ μὴ ὑπάρχειν, οἷον ζῷον παντὶ ἀνθρώπῳ λευκῷ δὲ τινί, ἄνθρωπος δὲ τινὶ λευκῷ οὐχ ὑπάρξει.
This is also evident in the case of particular syllogisms; for nothing prevents [A] from belonging to every B and to some C, while B does not belong to some C, for instance, animal belongs to every man and to some white thing, but man will not belong to some white thing.
ἐὰν οὖν τεθῇ τὸ Α τῷ μὲν Β μηδενὶ ὑπάρχειν τῷ δὲ Γ τινὶ ὑπάρχειν, ἡ μὲν καθόλου πρότασις ὅλη ψευδής, ἡ δʼ ἐν μέρει ἀληθής, καὶ τὸ συμπέρασμα ἀληθές.
If, therefore, it should be assumed that A belongs to no B and to some C, the universal premise indeed is wholly false, and the particular true, and the conclusion is true.
ὡσαύτως δὲ καὶ καταφατικῆς λαμβανομένης τῆς Β· ἐγχωρεῖ γὰρ τὸ τῷ μὲν Β μηδενὶ τῷ δὲ Γ τινὶ μὴ ὑπάρχειν, καὶ τὸ Β τῷ Γ τινὶ μὴ ὑπάρχειν, οἷον τὸ ζῷον οὐδενὶ ἀψύχῳ, λευκῷ δὲ τινί, καὶ τὸ ἄψυχον οὐχ ὑπάρξει τινὶ λευκῷ.
And similarly also when the premise B is assumed as affirmative; for it is possible for [A] to belong to no B and to fail to belong to some C, while B does not belong to some C, for instance, animal belongs to no inanimate thing, but to some white thing, and the inanimate thing will not belong to some white thing.
ἐὰν οὖν τεθῇ τὸ α τῷ μὲν Β παντὶ τῷ δὲ Γ τινὶ μὴ ὑπάρχειν, ἡ μὲν Α Β πρότασις, ἡ καθόλου, ὅλη ψευδής, ἡ δὲ Α Γ ἀληθής, καὶ τὸ συμπέρασμα ἀληθές.
If, therefore, it should be assumed that A belongs to every B and does not belong to some C, the premise AB, which is universal, is wholly false, but AC is true, and the conclusion is true.
καὶ τῆς μὲν καθόλου ἀληθοῦς τεθείσης, τῆς δʼ ἐν μέρει ψευδοῦς.
And also when the universal is placed as true, and the particular as false.
οὐδὲν γὰρ κωλύει τὸ Α μήτε τῷ Β μήτε τῷ Γ μηδενὶ ἕπεσθαι, τὸ μέντοι Β τινὶ τῷ Γ μὴ ὑπάρχειν, οἷον ζῷον οὐδενὶ ἀριθμῷ οὐδ᾿ ἀψύχῳ, καὶ ὁ ἀριθμὸς τινὶ ἀψύχῳ οὐχ ἕπεται.
For nothing prevents A from following neither B nor C, while B does not belong to some C, for instance, animal follows no number nor any inanimate thing, and number does not follow some inanimate thing.
ἐὰν οὖν τεθῇ τὸ τῷ μὲν 8 μηδενὶ τῷ δὲ Γ τινί, τὸ μὲν συμπέρασμα ἔσται ἀληθὲς καὶ ἡ καθόλου πρότασις, ἡ δʼ ἐν μέρει ψευδής.
If, therefore, it should be assumed that [A] belongs to no B and to some C, the conclusion indeed will be true, as well as the universal premise, but the particular false.
καὶ καταφατικῆς δὲ τῆς καθόλου τιθεμένης ὡσαύτως.
And similarly also when the universal is placed as affirmative.
ἐγχωρεῖ γὰρ τὸ Α καὶ τῷ Β καὶ τῷ Γ ὅλῳ ὑπάρχειν, τὸ μέντοι Β τινὶ τῷ Γ μὴ ἕπεσθαι, οἷον τὸ γένος τῷ εἴδει καὶ τῇ διαφορᾷ· τὸ γὰρ ζῷον παντὶ ἀνθρώπῳ καὶ ὅλῳ πεζῷ ἕπεται, ἄνθρωπος δʼ οὐ παντὶ πεζῷ.
For it is possible for A to belong to the whole of both B and C, while B does not follow some C, for instance, a genus in relation to species and difference; for animal follows every man and the whole of pedestrian, but man does not follow every pedestrian.
ὥστ᾿ ἂν ληφθῇ τὸ Α τῷ μὲν Β ὅλῳ ὑπάρχειν, τῷ δὲ Γ τινὶ μὴ ὑπάρχειν, ἡ μὲν καθόλου πρότασις ἀληθής, ἡ δʼ ἐν μέρει ψευδής, τὸ δὲ συμπέρασμα ἀληθές.
So that if it should be assumed that A belongs to the whole of B and does not belong to some C, the universal premise is true, but the particular is false, and the conclusion is true.
Φανερὸν δὲ καὶ ὅτι ἐξ ἀμφοτέρων ψευδῶν ἔσται τὸ συμπέρασμα ἀληθές, εἴπερ ἐνδέχεται τὸ Α καὶ τῷ Β καὶ τῷ Γ ὅλῳ ὑπάρχειν, τὸ μέντοι Β τινὶ τῷ Γ μὴ ἕπεσθαι.
It is also evident that the conclusion will be true from both premises being false, if indeed it is possible for A to belong to the whole of both B and C, while B does not follow some C.
ληφθέντος γὰρ τοῦ Α τῷ μὲν Β μηδενὶ τῷ δὲ Γ τινὶ ὑπάρχειν, αἰ μὲν προτάσεις ἀμφότεραι ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές.
For when it is assumed that A belongs to no B and to some C, both premises indeed are false, but the conclusion is true.
ὁμοίως δὲ καὶ κατηγορικῆς οὔσης τῆς καθόλου προτάσεως, τῆς δʼ ἐν μέρει στερητικῆς.
And similarly also when the universal premise is predicative (affirmative), and the particular is negative.
ἐγχωρεῖ γὰρ τὸ τῷ μὲν Β μηδενὶ τῷ δὲ Γ παντὶ ἕπεσθαι, καὶ τὸ Β τινὶ τῷ Γ μὴ ὑπάρχειν, οἷον ζῷον ἐπιστήμῃ μὲν οὐδεμιᾶ ἀνθρώπῳ δὲ παντὶ ἕπεται, ἡ δʼ ἐπιστήμη οὐ παντὶ ἀνθρώπῳ.
For it is possible for [A] to follow no B and to follow every C, while B does not belong to some C, for instance, animal follows no science but follows every man, and science does not belong to every man.
ἐὰν οὖν ληφθῇ τὸ τῷ μὲν Β ὅλῳ ὑπάρχειν, τῷ δὲ Γ τινὶ μὴ ἕπεσθαι, αἱ μὲν προτάσεις ψευδεῖς, τὸ δὲ συμπέρασμα ἀληθές.
If, therefore, it should be assumed that [A] belongs to the whole of B and does not follow some C, the premises indeed are false, but the conclusion is true.