§26Τοῖς δὲ παρὰ τὸν ὁρισμὸν γινομένοις τοῦ ἐλέγχου, καθάπερ ὑπεγράφη πρότερον, ἀπαντητέον σκοποῦσι τὸ συμπέρασμα πρὸς τὴν ἀντίφασιν, ὅπως ἔσται τὸ αὐτὸ καὶ κατὰ τὸ αὐτὸ καὶ πρὸς τὸ αὐτὸ καὶ ὡσαύτως καὶ ἐν τῷ αὐτῷ χρόνῳ.
For those arguments which arise from the definition of a refutation, as was outlined before, one must meet them by examining the conclusion in relation to its contradiction, to see how it will be of the same thing, and in the same respect, and in relation to the same thing, and in the same way, and at the same time.
Ἐὰν δ᾿ ἐν ἀρχῇ προσέρηται, οὐχ ὁμολογητέον ὡς ἀδύνατον τὸ αὐτὸ εἶναι διπλάσιον καὶ μὴ διπλάσιον, ἀλλὰ φατέον, μὴ μέντοι ὡδί, ὥς ποτ᾿ ἦν τὸ ἐλέγχεσθαι διωμολογημένον.
And if one is asked at the very beginning, one must not admit that it is impossible for the same thing to be double and not double, but one must say that it is, "yet not in this way," just as what constitutes being refutation was once agreed upon.
Εἰσὶ δὲ πάντες οἵδ᾿ οἱ λόγοι παρὰ τὸ τοιοῦτο.
And all the following arguments depend on this sort of thing.
Ἆρ᾿ ὁ εἰδὼς ἕκαστον ὅτι ἕκαστον, οἶδε τὸ πρᾶγμα;
Does the person who knows each thing that it is each thing, know the matter?
Καὶ ὁ ἀγνοῶν ὡσαύτως;
And similarly for the one who does not know?
Εἰδὼς δέ τις τὸν Κορίσκον ὅτι Κορίσκος, ἀγνοοίη ἂν ὅτι μουσικός, ὥστε ταὐτὸ ἐπίσταται καὶ ἀγνοεῖ.
But someone who knows Coriscus that he is Coriscus, might not know that he is musical; so that he knows and does not know the same thing.
Ἆρα τὸ τετράπηχυ τοῦ τριπήχεος μεῖζον;
Is that which is four cubits long greater than that which is three cubits long?
Γένοιτο δ᾿ ἂν ἐκ τριπήχους τετράπηχυ κατὰ τὸ μῆκος· τὸ δὲ μεῖζον ἐλάττονος μεῖζον· αὐτὸ ἄρα αὑτοῦ μεῖζον καὶ ἔλαττον.
But from what is three cubits long there could come to be what is four cubits long in length; and what is greater is greater than what is less; therefore it is greater and less than itself.
§27Τοὺς δὲ παρὰ τὸ αἰτεῖσθαι καὶ λαμβάνειν τὸ ἐν ἀρχῇ πυνθανομένῳ μέν, ἂν ᾖ δῆλον, οὐ δοτέον, οὐδ᾿ ἂν ἔνδοξον ᾖ, λέγοντα τἀληθές.
As for those arguments which depend on begging and assuming the original point, if it is obvious to the questioner, one must not grant it, even if it is a reputable opinion, but speak the truth.
Ἂν δὲ λάθῃ, τὴν ἄγνοιαν διὰ τὴν μοχθηρίαν τῶν τοιούτων λόγων εἰς τὸν ἐρωτῶντα μεταστρεπτέον ὡς οὐ διειλεγμένον· ὁ γὰρ ἔλεγχος ἄνευ τοῦ ἐξ ἀρχῆς.
But if it escapes notice, one must shift the blame for the ignorance, owing to the badness of such arguments, onto the questioner, on the ground that he has not argued properly; for a refutation is without the original premise.
Εἶθ᾿ ὅτι ἐδόθη οὐχ ὡς τούτῳ χρησομένου, ἀλλ᾿ ὡς πρὸς τοῦτο συλλογιουμένου τοὐναντίον, ἢ ἐπὶ τῶν παρεξελέγχων.
Next, one must say that it was granted not for him to use it, but for him to reason to the contrary against it, or in the case of apparent refutations.
§28Καὶ τοὺς διὰ τοῦ παρεπομένου συμβιβάζοντας ἐπ᾿ αὐτοῦ τοῦ λόγου δεικτέον.
And those who draw conclusions by means of the consequence must be shown this in the argument itself.
Ἔστι δὲ διττὴ ἡ τῶν ἑπομένων ἀκολούθησις.
The consequence of accompanying things is of two kinds.
Ἢ γὰρ ὡς τῷ ἐν μέρει τὸ καθόλου, οἷον ἀνθρώπῳ ζῷον· ἀξιοῦται γάρ, εἰ τόδε μετὰ τοῦδε, καὶ τόδ᾿ εἶναι μετὰ τοῦδε.
For either it is as the universal follows the particular, as "animal" follows "man"; for it is assumed that if this is with that, that is also with this.
Ἢ κατὰ τὰς ἀντιθέσεις· εἰ γὰρ τόδε τῷδε ἀκολουθεῖ, τῷ ἀντικειμένῳ τὸ ἀντικείμενον.
Or it is according to opposites; for if this follows that, the opposite follows the opposite.
Παρ᾿ ὃ καὶ ὁ τοῦ Μελίσσου λόγος· εἰ γὰρ τὸ γεγονὸς ἔχει ἀρχήν, τὸ ἀγένητον ἀξιοῖ μὴ ἔχειν, ὥστ᾿ εἰ ἀγένητος ὁ οὐρανός, καὶ ἄπειρος.
On which also the argument of Melissus depends; for if "what has come to be" has a beginning, he assumes that "what has not come to be" does not have one, so that if the heaven has not come to be, it is also infinite.
Τὸ δ᾿ οὐκ ἔστιν· ἀνάπαλιν γὰρ ἡ ἀκολούθησις.
But this is not so; for the consequence is the other way around.
§29Ὅσοι τε παρὰ τὸ προστιθέναι τι συλλογίζονται, σκοπεῖν εἰ ἀφαιρουμένου συμβαίνει μηδὲν ἧττον τὸ ἀδύνατον.
And as for those who reason because of adding something, one must examine whether, when it is removed, the impossible conclusion nonetheless follows.
Κἄπειτα τοῦτο ἐμφανιστέον, καὶ λεκτέον ὡς ἔδωκεν οὐχ ὡς δοκοῦν ἀλλ᾿ ὡς πρὸς τὸν λόγον, ὁ δὲ κέχρηται οὐδὲν πρὸς τὸν λόγον.
And then one must make this clear, and say that the respondent granted it not because he believed it, but for the sake of the argument, whereas the questioner has used it for something not relevant to the argument at all.
§30Πρὸς δὲ τοὺς τὰ πλείω ἐρωτήματα ἓν ποιοῦντας εὐθὺς ἐν ἀρχῇ διοριστέον.
As for those who make multiple questions into one, one must distinguish them immediately at the very beginning.
Ἐρώτησις γὰρ μία πρὸς ἣν μία ἀπόκρισίς ἐστιν, ὥστ᾿ οὔτε πλείω καθ᾿ ἑνὸς οὔτε ἓν κατὰ πολλῶν, ἀλλ᾿ ἓν καθ᾿ ἑνὸς φατέον ἢ ἀποφατέον.
For a single question is one to which there is a single answer, so that one must not affirm or deny either several things of one, or one thing of many, but one thing of one.
Ὥσπερ δὲ ἐπὶ τῶν ὁμωνύμων ὁτὲ μὲν ἀμφοῖν ὁτὲ δ᾿ οὐδετέρῳ ὑπάρχει, ὥστε μὴ ἁπλοῦ ὄντος τοῦ ἐρωτήματος ἁπλῶς ἀποκρινομένοις οὐδὲν συμβαίνει πάσχειν, ὁμοίως καὶ ἐπὶ τούτων.
And just as in the case of homonyms, a property sometimes belongs to both and sometimes to neither, so that although the question is not simple, nothing prevents those who answer simply from suffering some consequence, similarly also in these cases.
Ὅταν μὲν οὖν τὰ πλείω τῷ ἑνὶ ἢ τὸ ἓν τοῖς πολλοῖς ὑπάρχῃ, τῷ ἁπλῶς δόντι καὶ ἁμαρτόντι ταύτην τὴν ἁμαρτίαν οὐδὲν ὑπεναντίωμα συμβαίνει· ὅταν δὲ τῷ μὲν τῷ δὲ μή, ἢ πλείω κατὰ πλειόνων, καὶ ἔστιν ὡς ὑπάρχει ἀμφότερα ἀμφοτέροις, ἔστι δ᾿ ὡς οὐχ ὑπάρχει πάλιν, ὥστε τοῦτ᾿ εὐλαβητέον.
Whenever, therefore, several properties belong to one thing, or one to many, no contradiction happens to the one who grants it simply and commits this error; but when a property belongs to one and not to the other, or several properties are predicated of several subjects, and there is a sense in which both belong to both, and again a sense in which they do not, one must beware of this.
Οἷον ἐν τοῖσδε τοῖς λόγοις.
As, for instance, in the following arguments.
Εἰ τὸ μέν ἐστιν ἀγαθὸν τὸ δὲ κακόν, ὅτι ταῦτα ἀληθὲς εἰπεῖν ἀγαθὸν καὶ κακὸν καὶ πάλιν μήτ᾿ ἀγαθὸν μήτε κακόν· οὐκ ἔστι γὰρ ἑκάτερον ἑκάτερον, ὥστε ταὐτὸ ἀγαθὸν καὶ κακὸν καὶ οὔτ᾿ ἀγαθὸν οὔτε κακόν.
If one thing is good and another is evil, that it is true to say of these that they are good and evil, and again that they are neither good nor evil; for each is not the other, so that the same thing is good and evil, and neither good nor evil.
Καὶ εἰ ἕκαστον αὐτὸ αὑτῷ ταὐτόν, καὶ ἄλλου ἕτερον· ἐπεὶ δ᾿ οὐκ ἄλλοις ταὐτὰ ἀλλ᾿ αὑτοῖς, καὶ ἕτερα αὑτῶν, ταὐτὰ ἑαυτοῖς ἕτερα καὶ ταὐτά.
And if each thing is the same as itself, and different from another; since they are the same not with other things but with themselves, and different from themselves, the things that are the same as themselves are different from and the same as themselves.
Ἔτι εἰ τὸ μὲν ἀγαθὸν κακὸν γίνεται, τὸ δὲ κακὸν ἀγαθόν ἐστιν, δύο γένοιτ᾿ ἄν.
Furthermore, if the good becomes evil, and the evil is good, they would become two.
Δυοῖν τε καὶ ἀνίσων ἑκάτερον αὐτὸ αὑτῷ ἴσον, ὥστε ἴσα καὶ ἄνισα αὐτὰ αὑτοῖς.
And of two unequal things, each is equal to itself, so that they are both equal and unequal to themselves.
Ἐμπίπτουσι μὲν οὖν οὗτοι καὶ εἰς ἄλλας λύσεις· καὶ γὰρ τὸ ἄμφω καὶ τὸ ἅπαντα πλείω σημαίνει· οὔκουν ταὐτόν, πλὴν ὄνομα, συμβαίνει φῆσαι καὶ ἀποφῆσαι· τοῦτο δ᾿ οὐκ ἦν ἔλεγχος.
These arguments, then, fall also under other solutions; for both "both" and "all" signify several things; therefore it does not happen that one affirms and denies the same thing, except in name; and this was not a refutation.
Ἀλλὰ φανερὸν ὅτι μὴ μιᾶς ἐρωτήσεως τῶν πλειόνων γινομένων, ἀλλ᾿ ἓν καθ᾿ ἑνὸς φάντος ἢ ἀποφάντος, οὐκ ἔσται τὸ ἀδύνατον.
But it is obvious that if one does not make a single question of several, but affirms or denies one thing of one, the impossible result will not happen.