§1.1.4#2Ἐὰν δὲ πρὸς τὸ ἔλαττον ἄκρον τὸ καθόλου τεθῇ ἢ κατηγορικὸν ἢ στερητικόν, οὐκ ἔσται συλλογισμός, οὔτε καταφατικοῦ οὔτε ἀποφατικοῦ τοῦ ἀδιορίστου ἢ κατὰ μέρος ὄντος, οἶον εἰ τὸ μὲν Α τινὶ τῷ Β ὑπάρχει ἢ μὴ ὑπάρχει, τὸ δὲ Β παντὶ τῷ Γ ὑπάρχει·
If, however, the universal is placed in relation to the minor extreme, whether as affirmative or privative, there will not be a syllogism, whether the indefinite or particular premise is affirmative or negative; for example, if A belongs or does not belong to some B, and B belongs to every Γ.
ὅροι τοῦ ὑπάρχειν ἀγαθόν—ἔξις—φρόντησις, τοῦ μὴ ὑπάρχειν ἀγαθόν—ἕξιςἄμαθία.
Terms of belonging: good—habitus—wisdom; of not belonging: good—habitus—ignorance.
πάλιν εἰ τὸ μὲν Β μηδενὶ τῷ Γ, τὸ δὲ Α τινὶ τῷ Β ἢ ὑπάρχει ἢ μὴ ὑπάρχει ἢ μὴ παντὶ ὑπάρχει, οὐδʼ οὕτως ἔσται συλλογισμός.
Again, if B belongs to no Γ, and A either belongs or does not belong or does not belong to every B, neither in this way will there be a syllogism.
ὅροι λευκόν—ἵππος—κύκνος, λευκόν—ἵππος—κόραξ.
Terms: white—horse—swan; white—horse—crow.
οἱ αὐτοὶ δὲ καὶ εἰ τὸ Β ἀδιόριστον.
The same terms also if B is indefinite.
᾿Οὐδʼ ὅταν τὸ μὲν πρὸς τῷ μείζονι ἄκρῳ καθόλου γέντηται ἢ κατηγορικὸν ἢ στερητικόν, τὸ δὲ πρὸς τῷ ἐλάττονι στερητικὸν κατὰ μέρος, οὐκ ἔσται συλλογισμός, οἶον εἰ τὸ μὲν A παντὶ τῷ B ὑπάρχει, τὸ δὲ B τινὶ τῷ Γ μή, ἢ εἰ μὴ παντὶ ὑπάρχει· ᾧ γὰρ ἄν τινι μὴ ὑπάρχῃ τὸ μέσον, τούτῳ καὶ παντὶ καὶ οὐδενὶ ἀκολουθήσει τὸ πρῶτον.
Nor when the premise related to the major extreme becomes universal, whether affirmative or privative, while that related to the minor is particular negative, will there be a syllogism; for example, if A belongs to every B, and B does not belong to some Γ, or does not belong to every Γ; for to whatever the middle does not belong, the first may follow both every and none of this.
ὑποκείσθωσαν γὰρ οἱ ὅροι ζῷον–ἄνθρωπος–λεθκόν· εἶτα καὶ ὧν μὴ κατηγορεῖται λευκῶν ὁ ἄνθρωπος, εἰλήφθω κύκνος καὶ χιών·
For let the terms be assumed as animal—man—white; then, of the white things of which man is not predicated, let swan and snow be taken.
οὐκοῦν τὸ ζῷον τοῦ μὲν παντὸς κατηγορεῖται, τοῦ δὲ οὐδενός, ὥστε οὐκ ἔσται συλλογισμός.
Now animal is predicated of every one of the former, and of none of the latter, so that there will not be a syllogism.
πάλιν τὸ μὲν Α μηδενὶ τῷ Β ὑπαρχέτω, τὸ δὲ Β τινὶ τῷ Γ μὴ ὑπαρχέτω· καὶ οἱ ὅροι ἔστωσαν ἄψυχον–ἄνθρωπος–λευκόν· εἶτα εἰλήφθωσαν, ὧν μὴ κατηγορεῖται λευκῶν· ὁ ἄνθρωπος, κύκνος καὶ χιών· τὸ γὰρ ἄψυχον τοῦ μὲν παντὸς κατηγορεῖται, τοῦ δὲ οὐδενός.
Again, let A belong to no B, and B not belong to some Γ; and let the terms be inanimate—man—white; then let those white things be taken of which man is not predicated: swan and snow; for inanimate is predicated of every one of the latter, and of none of the former.
ἔτι ἐπεὶ ἀδιόριστον τὸ τινὶ τῷ Γ τὸ Β μὴ ὑπάρχειν, ἀληθεύεται δέ, καὶ εἰ μηδενὶ ὑπάρχει καὶ εἰ μὴ παντί, ὅτι τινὶ οὐχ ὑπάρχει, ληφθέντων δὲ τοιούτων ὅρων ὥστε μηδενὶ ὑπάρχειν οὐ γίνεται συλλογισμός (τοῦτο γὰρ εἴρηται πρότερον), φανερὸν οὖν ὅτι τῷ οὕτως ἔχειν τοὺς ὅρους οὐκ ἔσται συλλογισμός· ἦν γὰρ ἂν καὶ ἐπὶ τούτων.
Furthermore, since it is indefinite for B not to belong to some Γ, and it is true both if it belongs to none and if it does not belong to all that it does not belong to some; and since when such terms are taken that it belongs to none, no syllogism comes about (for this has been said before), it is clear, then, that through the terms being so related there will not be a syllogism; for there would have been one in those cases too.
ὁμοίως δὲ δειχθήσεται καὶ εἰ τὸ καθόλου τεθείη στερητικόν.
And it will be shown similarly also if the universal is assumed as privative.
Οὐδὲ ἐὰν ἄμφω τὰ διαστήματα κατὰ μέρος ἢ κατηγορικῶς ἢ στερητικῶς, ἢ τὸ μὲν κατηγορικῶς τὸ δὲ στερητικῶς λέγηται, ἢ τό μὲν ἀδιόριστον τὸ δὲ διωρισμένον, ἢ ἄμφω ἀδιόριστα, οὐκ ἔσται συλλογισμός οὐδαμῶς.
Nor if both intervals are particular, whether affirmatively or privatively, or one is stated affirmatively and the other privatively, or one is indefinite and the other definite, or both indefinite, will there be a syllogism in any way.
ὅροι δὲ κοινοὶ πάντων ζῷον–λευκόν–ἵππος, ζῷον–λευκόν–λίθος.
Terms common to all: animal—white—horse; animal—white—stone.
Φανερὸν οὖν ἐκ τῶν εἰρημένων ὡς ἐὰν ᾖ συλλογισμός ἐν τούτῳ τῷ σχήματι κατὰ μέρος, ὅτι ἀνάγκη τοὺς ὄρους οὕτως ἔχειν ὡς εἴπομεν· ἄλλως γὰρ ἐχόντων οὐδαμῶς γίνεται.
It is clear, then, from what has been said, that if there is a particular syllogism in this figure, the terms must be related as we said; for if they are otherwise related, it does not come about in any way.
δῆλον δὲ καὶ ὅτι πάντες οἱ ἐν ᾳὐτῷ συλλογισμοὶ τέλειοί εἰσι· (πάντες γὰρ ἐπιτελοῦνται διὰ τῶν ἐξ ἀρχῆς ληφθέντων), καὶ ὅτι πάντα τὰ προβλήματα δείκνυται διὰ τούτου τοῦ σχήματος· καὶ γὰρ τό παντὶ καὶ τὸ μηδενὶ καὶ τὸ τινὶ καὶ τὸ μή τινι ὑπάρχειν.
And it is also clear that all the syllogisms in it are perfect; (for all of them are completed through the things assumed at the beginning), and that all problems are proved through this figure; for belonging to every, belonging to none, belonging to some, and not belonging to some are all proved.
καλῶ δὲ τὸ τοιοῦτον σχῆμα πρῶτον.
And I call such a figure the first.