§5#2Ὁ δὲ παρὰ τὸ ἑπόμενον ἔλεγχος διὰ τὸ οἴεσθαι ἀντιστρέφειν τὴν ἀκολούθησιν.
refutation depending on the consequent occurs because of the belief that the consequence is convertible.
Ὅταν γὰρ τοῦδε ὄντος ἐξ ἀνάγκης τοδὶ ᾖ, καὶ τοῦδε ὄντος οἴονται καὶ θάτερον εἶναι ἐξ ἀνάγκης.
For when, if this is, that of necessity is, they think that if that is, the other also of necessity is.
Ὅθεν καὶ αἱ περὶ τὴν δόξαν ἐκ τῆς αἰσθήσεως ἀπάται γίνονται.
From this also arise the illusions in opinions derived from sensation.
Πολλάκις γὰρ τὴν χολὴν μέλι ὑπέλαβον διὰ τὸ ἕπεσθαι τὸ ξανθὸν χρῶμα τῷ μέλιτι· καὶ ἐπεὶ συμβαίνει τὴν γῆν ὕσαντος γίνεσθαι διάβροχον, κἂν ᾖ διάβροχος, ὑπολαμβάνομεν ὗσαι. Τὸ δ᾿ οὐκ ἀναγκαῖον.
For people often suppose bile to be honey because the yellow color accompanies honey; and since it happens that the earth becomes wet when it has rained, even if it is wet, we suppose that it has rained.But this is not necessary.
Ἔν τε τοῖς ῥητορικοῖς αἱ κατὰ τὸ σημεῖον ἀποδείξεις ἐκ τῶν ἑπομένων εἰσίν.
And in rhetoric, proofs from signs are from consequents.
Βουλόμενοι γὰρ δεῖξαι ὅτι μοιχός, τὸ ἑπόμενον ἔλαβον, ὅτι καλλωπιστὴς ἢ ὅτι νύκτωρ ὁρᾶται πλανώμενος.
For wishing to show that someone is an adulterer, they take the consequent, that he is a dandy or that he is seen wandering at night.
Πολλοῖς δὲ ταῦτα μὲν ὑπάρχει, τὸ δὲ κατηγορούμενον οὐχ ὑπάρχει.
But to many people these belong, while the predicate does not belong.
Ὁμοίως δὲ καὶ ἐν τοῖς συλλογιστικοῖς, οἷον ὁ Μελίσσου λόγος ὅτι ἄπειρον τὸ ἅπαν, λαβὼν τὸ μὲν ἅπαν ἀγένητον (ἐκ γὰρ μὴ ὄντος οὐδὲν ἂν γενέσθαι), τὸ δὲ γενόμενον ἐξ ἀρχῆς γενέσθαι. Εἰ μὴ οὖν γέγονεν, ἀρχὴν οὐκ ἔχει τὸ πᾶν, ὥστ᾿ ἄπειρον.
Likewise also in syllogistic arguments, for example the argument of Melissus that the universe is infinite, having assumed that the universe is ungenerated (for from non-being nothing could come to be), and that what has come to be has come to be from a beginning.If then it has not come to be, the universe has no beginning, so that it is infinite.
Οὐκ ἀνάγκη δὲ τοῦτο συμβαίνειν· οὐ γὰρ εἰ τὸ γενόμενον ἅπαν ἀρχὴν ἔχει, καὶ εἴ τι ἀρχὴν ἔχει, γέγονεν, ὥσπερ οὐδ᾿ εἰ ὁ πυρέττων θερμός, καὶ τὸν θερμὸν ἀνάγκη πυρέττειν. Ὁ δὲ παρὰ τὸ μὴ αἴτιον ὡς αἴτιον, ὅταν προσληφθῇ τὸ ἀναίτιον ὡς παρ᾿ ἐκεῖνο γινομένου τοῦ ἐλέγχου.
But this does not necessarily follow; for it is not the case that if everything that has come to be has a beginning, everything that has a beginning has also come to be, just as it is not the case that if one who has a fever is hot, a hot person must also have a fever.The fallacy depending on treating as cause what is not a cause occurs when the non-cause is added as if the refutation occurred because of it.
Συμβαίνει δὲ τὸ τοιοῦτον ἐν τοῖς εἰς τὸ ἀδύνατον συλλογισμοῖς· ἐν τούτοις γὰρ ἀναγκαῖον ἀναιρεῖν τι τῶν κειμένων.
This sort of thing happens in reductio ad impossibile arguments; for in these it is necessary to refute some of the premises.
Ἐὰν οὖν ἐγκαταριθμηθῇ ἐν τοῖς ἀναγκαίοις ἐρωτήμασι πρὸς τὸ συμβαῖνον ἀδύνατον, δόξει παρὰ τοῦτο γίνεσθαι πολλάκις ὁ ἔλεγχος, οἷον ὅτι οὐκ ἔστι ψυχὴ καὶ ζωὴ ταὐτόν· εἰ γὰρ φθορᾷ γένεσις ἐναντίον, καὶ τῇ τινὶ φθορᾷ ἔσται τις γένεσις ἐναντίον·
If then the non-cause is counted among the necessary questions for the resulting impossibility, the refutation will often seem to occur because of this, as for example, to prove that "soul and life are not the same." "For if generation is contrary to destruction, a particular generation will be contrary to a particular destruction.
ὁ δὲ θάνατος φθορά τις καὶ ἐναντίον ζωῇ, ὥστε γένεσις ἡ ζωὴ καὶ τὸ ζῆν γίνεσθαι·
But death is a particular destruction and contrary to life; hence life is generation and to live is to be generated.
τοῦτο δ᾿ ἀδύνατον· οὐκ ἄρα ταὐτὸν ἡ ψυχὴ καὶ ἡ ζωή. Οὐ δὴ συλλελόγισται·
But this is impossible; therefore soul and life are not the same."Indeed, this has not been reasoned.
συμβαίνει γάρ, κἂν μή τις ταὐτὸ φῇ τὴν ζωὴν τῇ ψυχῇ, τὸ ἀδύνατον, ἀλλὰ μόνον ἐναντίον ζωὴν μὲν θανάτῳ ὄντι φθορᾷ, φθορᾷ δὲ γένεσιν.
For the impossibility occurs even if one does not say that life is the same as soul, but only that life is contrary to death, which is a destruction, and destruction contrary to generation.
Ἀσυλλόγιστοι μὲν οὖν ἁπλῶς οὐκ εἰσὶν οἱ τοιοῦτοι λόγοι, πρὸς δὲ τὸ προκείμενον ἀσυλλόγιστοι.
Therefore, such arguments are not simply non-syllogistic, but they are non-syllogistic in relation to the proposition.
Καὶ λανθάνει πολλάκις οὐχ ἧττον αὐτοὺς τοὺς ἐρωτῶντας τὸ τοιοῦτον. Οἱ μὲν οὖν παρὰ τὸ ἑπόμενον καὶ παρὰ τὸ μὴ αἴτιον λόγοι τοιοῦτοί εἰσιν· οἱ δὲ παρὰ τὸ τὰ δύο ἐρωτήματα ἓν ποιεῖν, ὅταν λανθάνῃ πλείω ὄντα καὶ ὡς ἑνὸς ὄντος ἀποδοθῇ ἀπόκρισις μία.
And this often escapes the notice of the questioners themselves no less.The arguments depending on the consequent and on treating as cause what is not a cause are of this kind; while those depending on making two questions into one occur when it escapes notice that they are more than one, and a single answer is given as if there were only one.
Ἐπ᾿ ἐνίων μὲν οὖν ῥᾴδιον ἰδεῖν ὅτι πλείω καὶ ὅτι οὐ δοτέον ἀπόκρισιν, οἷον πότερον ἡ γῆ θάλαττά ἐστιν ἢ ὁ οὐρανός; ἐπ᾿ ἐνίων δ᾿ ἧττον, καὶ ὡς ἑνὸς ὄντος ἢ ὁμολογοῦσι τῷ μὴ ἀποκρίνεσθαι τὸ ἐρωτώμενον, ἢ ἐλέγχεσθαι φαίνονται, οἷον ἆρ᾿ οὗτος καὶ οὗτός ἐστιν ἄνθρωπος; ὥστ᾿ ἄν τις τύπτῃ τοῦτον καὶ τοῦτον, ἄνθρωπον ἀλλ᾿ οὐκ ἀνθρώπους τυπτήσει. Ἢ πάλιν, ὧν τὰ μέν ἐστιν ἀγαθὰ τὰ δ᾿ οὐκ ἀγαθά, πάντα ἀγαθὰ ἢ οὐκ ἀγαθά; ὁπότερον γὰρ ἂν φῇ, ἔστι μὲν ὡς ἔλεγχον ἢ ψεῦδος φαινόμενον δόξειεν ἂν ποιεῖν· τὸ γὰρ φάναι τῶν μὴ ἀγαθῶν τι εἶναι ἀγαθὸν ἢ τῶν ἀγαθῶν μὴ ἀγαθὸν ψεῦδος.
In some cases, indeed, it is easy to see that they are more than one and that an answer should not be given, as for example, "Is the earth sea, or is the heaven?" But in some cases it is less so, and treating the question as one, they either agree by not answering what is asked, or they seem to be refuted, as for example, "Are this person and this person a man?" So that if one strikes this person and this person, he will strike a man and not men.Or again, of things of which some are good and others not good, "Are all good or not good?" For whichever he says, he would seem to produce either a apparent refutation or a falsehood; for to say that some of the non-good things are good, or of the good things not good, is false.
Ὁτὲ δὲ προσληφθέντων τινῶν κἂν ἔλεγχος γίνοιτο ἀληθινός, οἷον εἴ τις δοίη ὁμοίως ἓν καὶ πολλὰ λέγεσθαι λευκὰ καὶ γυμνὰ καὶ τυφλά.
But sometimes, when certain premises are added, even a true refutation would occur, as for example, if one should grant that one and many are similarly said to be white, naked, and blind.
Εἰ γὰρ τυφλὸν τὸ μὴ ἔχον ὄψιν πεφυκὸς δ᾿ ἔχειν, καὶ τυφλὰ ἔσται τὰ μὴ ἔχοντα ὄψιν πεφυκότα δ᾿ ἔχειν.
For if blind is that which does not have sight but is by nature suited to have it, then blind things will also be those which do not have sight but are by nature suited to have it.
Ὅταν οὖν τὸ μὲν ἔχῃ τὸ δὲ μὴ ἔχῃ, τὰ ἄμφω ἔσται ἢ ὁρῶντα ἢ τυφλά· ὅπερ ἀδύνατον.
When, therefore, one has it and the other does not, both will be either seeing or blind; which is impossible.