§1.2.25Ἀπαγωγὴ δʼ ἐστὶν ὅταν τῷ μὲν μέσῳ τὸ πρῶτον δῆλον ᾖ ὑπάρχον, τῷ δʼ ἐσχάτῳ τὸ μέσον ἄδηλον μέν, ὁμοίως δὲ πιστὸν ἢ μᾶλλον τοῦ συμπεράσματος· ἔτι ἂν ὀλίγα ᾖ τὰ μέσα τοῦ ἐσχάτουυ καὶ τοῦ μέσου· πάντως γὰρ ἐγγύτερον εἶναι συμβαίνει τῆς ἐπιστήμης.
Reduction occurs when the first term is clearly shown to belong to the middle, but the middle's belonging to the last term is unclear, yet equally credible as or more credible than the conclusion; further, if the middle terms between the last and the middle are few; for in all such cases it turns out to be closer to scientific knowledge.
οἷον ἔστω τὸ τὸ διδακτόν, ἐφʼ οὗ Β ἐπιστήμη, τὸ Γ δικαιοσύνη.
For example, let A be teachable, B be science, and Γ be justice.
ἡ μὲν οὖν ἐπιστήμη ὅτι διδακτόν, φανερόν· ἡ δʼ ἀρετὴ εἰ ἐπιστήμη, ἄδηλον.
That science, then, is teachable is clear; but whether virtue is science is unclear.
εἰ οὖν ὁμοίως ἢ μᾶλλον πιστὸν τὸ Β Γ τοῦ Α Γ, ἀπαγωγή ἐστιν· ἐγγύτερον γὰρ τοῦ ἐπίστασθαι διὰ τὸ προσειληφέναι τὴν Α Β ἐπιστήμην, πρότερον οὐκ ἔχοντας.
If, then, B-Γ is equally or more credible than A-Γ, it is a reduction; for we are closer to knowing because we have assumed the knowledge of A-B, which we did not have before.
ἢ πάλιν εἰ ὀλίγα τὰ μέσα τῶν Β Γ· καὶ γὰρ οὕτως ἐγγύτερον τοῦ εἰδέναι.
Or again, if the middle terms between B and Γ are few; for in this way too we are closer to knowing.
οἶον εἰ τὸ Δ εἴη τετραγωνίζεσθαι, τὸ δʼ ἐφʼ ᾧ εὐθύγραμμον, τὸ δʼ ἐφʼ ᾧ Ζ κύκλος· εἰ τοῦ Ε Ζ ἓν μόνον εἴη μέσον, τὸ μετὰ μηνίσκων ἴσον γίνεσθαι εὐθυγράμμῳ τὸν κύκλον, ἐγγὺς ἂν εἴη τοῦ εἰδέναι.
For example, if Δ is being squared, E is rectilinear figure, and Ζ is circle; if there were only one middle term between E and Ζ, namely "the circle becoming equal to a rectilinear figure by means of lunes," we would be close to knowing.
ὅταν δὲ μήτε πιστότερον ᾖ τὸ Β Γ τοῦ Α Γ μήτʼ ὀλίγα τὰ μέσα, οὐ λέγω ἀπαγωγήν.
But when B-Γ is neither more credible than A-Γ nor the middle terms are few, I do not call it a reduction.
οὐδʼ ὅταν ἄμεσον τὸ Β Γ· ἐπιστήμη γὰρ τὸ τοιοῦτον.
Nor when B-Γ is immediate; for such a thing is scientific knowledge.
§1.2.26Ἔνστασις δʼ ἐστὶ πρότασις προτάσει ἐναντία.
An objection is a premise contrary to a premise.
διαφέρει δὲ τῆς προτάσεως, ὅτι τὴν μὲν ἔνστασιν ἐνδέχεται εἶναι ἐπὶ μέρους, τὴν δὲ πρότασιν ἢ ὅλως οὐκ ἐνδέχεται ἢ οὐκ ἐν τοῖς καθόλου συλλογισμοῖς.
It differs from a premise because an objection can be particular, whereas a premise either cannot be so at all or at least not in universal syllogisms.
φέρεται δὲ ἡ ἔνστασις διχῶς καὶ 69b διὰ δύο σχημάτων, διχῶς μὲν ὅτι ἢ καθόλου ἢ ἐν μέρει πᾶσα ἔνστασις, ἐκ δύο δὲ σχημάτων ὅτι ἀντικείμεναι φέρονται τῇ προτάσει, τὰ δʼ ἀντικείμενα ἐν τῷ πρώτῳ καὶ τῷ τρίτῳ σχήματι περαίνονται μόνοις.
An objection is brought forward in two ways and 69b through two figures: in two ways because every objection is either universal or particular; through two figures because they are brought forward as opposed to the premise, and opposites are concluded only in the first and the third figures.
ὅταν γὰρ ἀξιώσῃ παντὶ ὑπάρχειν, ἐνιστάμεθα ἢ ὅτι οὐδενὶ ἢ ὅτι τινὶ οὐχ ὑπάρχει· τούτων δὲ τὸ μὲν μηδενὶ ἐκ τοῦ πρώτου σχήματος, τὸ δὲ τινὶ μὴ ἐκ τοῦ ἐσχάτου.
For when he claims that it belongs to all, we object either that it belongs to none or that it does not belong to some; and of these, the "to none" is from the first figure, and the "not to some" is from the last figure.
οἷον ἔστω τὸ Α μίαν εἶναι ἐπιστήμην, ἐφʼ ᾧ τὸ Β ἐναντία.
For example, let A be "being one science", and B be "contraries".
προτείναντος δὴ μίαν εἶναι τῶν ἐναντίων ἐπιστήμην, ἢ ὅτι ὅλως οὐχ ἡ αὐτὴ τῶν ἀντικειμένων ἐνίσταται, τὰ δʼ ἐναντία ἀντικείμενα, ὥστε γίνεται τὸ πρῶτον σχῆμα, ἢ ὅτι τοῦ γνωστοῦ καὶ ἀγνώστου οὐ μία· τοῦτο δὲ τὸ τρίτον· κατά γὰρ τοῦ Γ, τοῦ γνωστοῦ καὶ ἀγνώστου, τό μὲν ἐναντία εἶναι ἀληθές, τὸ δὲ μίαν αὐτῶν ἐπιστήμην εἶναι ψεῦδος.
If someone posits, then, that there is one science of contraries, an objection is made either that in general the science of opposites is not the same, and contraries are opposites, so that the first figure is formed; or that there is not one science of the knowable and the unknowable; and this is the third figure; for of Γ, the knowable and the unknowable, it is true that they are contraries, but false that there is one science of them.
πάλιν ἐπὶ τῆς στερητικῆς προτάσεως ὡσαύτως.
Again, in the case of a negative premise, it is the same.
ἀξιοῦντος γὰρ μὴ εἶναι μίαν τῶν ἐναντίων, ἢ ὅτι πάντων τῶν ἀντικειμένων ἢ ὅτι τινῶν ἐναντίων ἡ αὐτὴ λέγομεν, οἷον ὑγιεινοῦ καὶ νοσώδους· τὸ μὲν οὖν πάντων ἐκ τοῦ πρώτου, τὸ δὲ τινῶν ἐκ τοῦ τρίτου σχήματος.
For when he claims that there is not one science of contraries, we say either that the science of all opposites is the same, or that of some contraries it is the same, as for example of the healthy and the diseased; the "of all", then, is from the first figure, and the "of some" is from the third figure.
Ἁπλῶς γὰρ ἐν πᾶσι καθόλου μὲν ἐνιστάμενον ἀνάγκη πρὸς τὸ καθόλου τῶν προτεινομένων τὴν ἀντίφασιν εἰπεῖν, οἷον εἰ μὴ τὴν αὐτὴν ἀξιοῖ τῶν ἐναντίων, πάντων εἰπόντα τῶν ἀντικειμένων μίαν.
For simply in all cases, one who objects universally must state the contradiction in relation to the universal of the proposed terms, as for instance, if the opponent claims that the science of contraries is not the same, by stating that there is one science of all opposites.
οὕτω δʼ ἀνάγκη τὸ πρῶτον εἶναι σχῆμα· μέσον γὰρ γίνεται τὸ καθάλου πρός τὸ ἐξ ἀρχῆς.
In this way, it is necessary that the first figure is formed; for the universal becomes the middle term in relation to the original term.
ἐν μέρει δέ, πρὸς ὅ ἐστι καθόλου καθʼ οὗ λέγεται ἡ πρότασις, οἷον γνωστοῦ καὶ ἀγνώστου μὴ τὴν αὐτήν· τὰ γὰρ ἐναντία καθόλου πρὸς ταῦτα.
But in particular, [the objection is made] in relation to that of which the premise is stated universally, as for instance, stating that the science of the knowable and the unknowable is not the same; for contraries are universal in relation to these.
καὶ γίνεται τὸ τρίτον σχῆμα· μέσον γὰρ τὸ ἐν μέρει λαμβανόμενον, οἷον τὸ γνωστὸν καὶ τὸ ἄγνωστον.
And the third figure is formed; for that which is taken in part, as for instance the knowable and the unknowable, becomes the middle term.
ἐξ ὧν γὰρ ἔστι συλλογίσασθαι τοὐναντίον, ἐκ τούτων καὶ τὰς ἐνστάσεις ἐπιχειροῦμεν λέγειν.
For from the very premises from which it is possible to syllogize the contrary, from these we also attempt to state objections.
διὸ καὶ ἐκ μόνων τούτων τῶν σχημάτων φέρομεν· ἐν μόνοις γὰρ οἱ ἀντικείμενοι συλλογισμοί· διὰ γὰρ τοῦ μέσου οὐκ ἦν καταφατικῶς.
Therefore we bring them forward from these figures only; for in these alone are there opposing syllogisms, since through the middle (second) figure there was no affirmative syllogism.
ἔτι δὲ κἂν λόγου δέοιτο πλείονος ἡ διὰ τοῦ μέσου σχήματος, οἷον· εἰ μὴ δοίη τὸ τῷ Β ὑπάρχειν διὰ τό μὴ ἀκολουθεῖν αὐτῷ τὸ Γ. τοῦτο γὰρ διʼ ἄλλων προτάσεων δῆλον·
And furthermore, the objection through the middle (second) figure would require a longer argument; for example, if the opponent should not grant that B belongs [to A] because Γ does not follow B.
οὐ δεῖ δὲ εἰς ἄλλα ἐκτρέπεσθαι τὴν ἔνστασιν, ἀλλʼ εὐθὺς φανερὰν ἔχειν τὴν ἑτέραν πρότασιν.
For this is clear through other premises; but the objection should not turn aside to other things, but should immediately have the other premise manifest.
Ἐπισκεπτέον δὲ καὶ περὶ τῶν ἄλλων ἐνστάσεων, οἶον περὶ τῶν ἐκ τοῦ ἐναντίου καὶ τοῦ ὁμοίου καὶ τοῦ κατὰ δόξαν, καὶ εἰ τὴν ἐν μέρει ἐκ τοῦ πρώτου ἢ τὴν στερητικὴν ἐκ τοῦ μέσου 70a δυνατὸν λαβεῖν.
We must also examine the other kinds of objections, such as those from the contrary, from the similar, and from common opinion, and whether it is possible to take the particular objection from the first figure or the negative objection from the middle (second) figure. 70a