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σύνθεσις and διαίρεσις, ‘wrong (fallacious) combination, composition, and disjunction, separation, in reading or speaking’, which are here taken together as one form of fallacy, are two in de Soph. El. c. 4, 165 b 26, Ib. 166 a 22, and 33. The solution of them is given in c. 20, where “Euthydemus' argument” is also referred to, and thence no doubt transferred hither.

‘Another is, to pronounce in combination what is (properly, or is intended to be) separated, or the reverse, the combined as separate: for since it seems to be the same either way (when combined or separated, and it is in this appearance, and the advantage taken of it, that the fallacy lies), whichever of the two happens to be more serviceable, that must be done’. δεῖ does not here imply a moral obligation; it is not intended to recommend the practice; the only obligation is that which is imposed by the art; if you want to avail yourself of this unfair mode of reasoning (which I don't say I approve, I am only stating what the art requires), this is the way to proceed.

‘This is Euthydemus' argument. For instance to know that a trireme is in the Piraeus, because he knows each (of two things which are here omitted)’. This example, which is unintelligible as it stands here, has some further light (or obscurity) thrown on it by the form in which it occurs in de Soph. El. c. 20, 177 b 12, καὶ Εὐθυδήμου δὲ λόγος, ἆρ᾽ οἶδας σὺ νῦν οὔσας ἐν Πειραιεῖ τριήρεις ἐν Σικελίᾳ ὤν; but in both much is left to be supplied, the argument alluded to being supposed to be well known, and in every one's recollection. Schrader thus fills up the argument:—What you know, you know in the Piraeus—where the two disputants were standing—this is admitted: but you know also that there are triremes: this also is conceded, because the respondent knows that the Athenians have triremes somewhere; out at sea, or in Sicily, (referring to the expedition of 415 B.C.): whence the conclusion, you know that there are triremes in the Piraeus. The illicit combination (σύνθεσις) in this interpretation— though Schrader does not explain it further—must lie in the conjunction of the Piraeus with the knowledge of triremes, to which it does not belong in the respondent's interpretation of the question: and ἕκαστον will be ‘each of these two pieces of knowledge, the knowledge of what is known in the Piraeus, and of the triremes’. They are both known separately, Euthydemus illicitly combines them.

This seems to be a reasonable explanation of the example so far as it is given in the Rhetoric. But it seems quite certain that Aristotle is quoting identically the same argument in de Soph. El. The triremes and the Piraeus appear in both, and both are styled Εὐθυδήμου λόγος, the well-known argument of Euthydemus. Schrader, though he refers to the passage, takes no account of the words ἐν Σικελία ὤν, which it seems must have formed part of it. Victorius has endeavoured to combine both in his explanation of the fallacy—I am not at all sure that I understand it: I will therefore transcribe it in his own words verbatim et litteratim. “Tu scis te esse in Piraeo: quod concedebatur ipsi (the respondent), ac verum erat. Scis triremes Atheniensium esse in Sicilia (miserant enim eo classem ut eam insulam occuparent); id quoque non inficiabatur qui interrogatus erat. Tu scis igitur (aiebat ille) in Piraeo triremes esse, in Sicilia existens. Qua captione ipsum in Sicilia, scire triremes esse in Piraeo cogebatur; cum eo namque, scire in Piraeo, coniungebatur triremes esse: a quo remotum primo pronunciatum fuerat: ab illo vero, in Sicilia, cum quo copulatum editum primo fuerat, disiungebatur: atque ita efficiebatur ipsum, in Sicilia cum esset, scire in Piraeo triremes esse. Quod vero hic adiungit ἕκαστον γὰρ οἶδεν: separatim scilicet utrunque nosse intelligit, se in portu Atheniensium tunc esse: triremesque item in Sicilia. E quorum conglutinatione fallax ratio conflata, quae inde vocata est παρὰ σύνθεσιν.” By this must be meant, that the two statements, existence or knowledge in the Piraeus, and knowledge of triremes in Sicily, which ought to be kept separate, are combined in one statement, and hence the fallacy: true separately, they are not true together. Whether this is a satisfactory version of Euthydemus' fallacy I fear I must leave it to others to decide. My principal difficulty is as to the mode of transition from the Piraeus to Sicily in the two first propositions, which as far as I can see is not satisfactorily accounted for. What is there to connect the ‘knowing that you are in the Piraeus’, or ‘knowing in the Piraeus’, with knowing or being in Sicily? And yet there must be some connexion, apparent at least if not real, to make the fallacy plausible. This is nevertheless Alexander's solution of it. Comm. ad Top. 177 b 12, τὸν δὲ λόγον ἠρώτα Εὐθύδημος ἐν Πειραιεῖ τυγχάνων, ὅτε αἱ τῶν Ἀθηναίων τριήρεις εἰς Σικελίαν ἦλθον. ἔστι δὲ τοῦ σοφίσματος ἀγωγὴ τοιαύτη. “ἆρα γε σὺ νῦν ἐν Πειραιεῖ εἶ; ναί. ἆρ᾽ οἶδας ἐν Σικελίᾳ τριήρεις οὔσας; ναί. ἆρα οἶδας σὺ νῦν οὔσας ἐν Πειραιεῖ τριήρεις ἐν Σικελίᾳ ὤν;” παρὰ τὴν σύνθεσιν τὸ σοφίσμα. However this may be, at any rate, if Plato's dialogue is to be trusted, there is no kind of fallacy however silly, transparent, and contemptible, of which Euthydemus and his partner were incapable; and the weight of authority, notwithstanding the utter want of sense, must decide us to accept this explanation.

Of Euthydemus, and his brother and fellow-sophist Dionysodorus, contemporaries of Socrates, nearly all that we know is derived from Plato's Euthydemus. They had studied and taught the art military, and the forensic branch of Rhetoric, Euthyd. 273, C. D, before entering at an advanced age upon their present profession, viz. that of ἐριστική, the art of sophistical disputation, and of universal confutation, by which they undertook to reduce any opponent whatsoever to silence. Many examples of their mode of arguing are given in the Platonic dialogue, but Aristotle's instance does not appear among them. See also Grote's Plato, on Euthydemus, Vol. I., ch. xix. The fallacies are exemplified from the dialogue, p. 545 seq. And on Euthydemus and his brother, also Stallbaum's Disp. de Euth. Plat. prefixed to his edition of the dialogues, p. 10 seq. (Ed. I).

An example of illicit combination is given in the περὶ Ἑρμηνείας, the treatise on the proposition or elementary combination of words, c. 11, p. 20 b 35, ἀλλ᾽ οὐχί, εἰ σκυτεὺς καὶ ἀγαθός, καὶ σκυτεὺς ἀγαθός. εἰ γάρ, ὅτι ἑκάτερον ἀληθές, εἶναι δεῖ καὶ τὸ συνάμφω, πολλὰ καὶ ἄτοπα ἔσται.

‘Another example is that one that knows the letters, knows the whole verse; for the verse is the same thing (as the letters, or elements, of which it is composed)’. The reason given, τὸ ἔπος τὸ αὐτό ἐστιν, contains the fallacy. It assumes that the things combined are the same as they are separate; which is not true.

‘And (thirdly) to argue, that since twice a certain amount (of food or a drug) is unwholesome, so must also the single portion be: for it is absurd to suppose that if two things separately are good, they can when combined unite into one bad’. If the two parts together are unwholesome, neither of them can be wholesome separately, because the combination of two good things can never make one bad, This is a fallacious confutation; of a physician, may be, who is recommending the use of a drug. You say that your drug is wholesome: now you only administer a certain quantity. Suppose you were to double it, you would not say that it was wholesome then: but if the two parts together are unwholesome, how can either of them, the component elements being precisely the same in each, be wholesome? two wholesomes could never make an unwholesome. Here the undue combination of the double with the single part produces the fallacy (so Victorius).

‘Used thus, it serves for refutation, but in the following way for proof (this is, by inverting the preceding): because one good thing cannot be (made up of) two bad’. If the whole is good, then the two parts, which is not always true. ‘But the entire topic is fallacious’: in whichever way it is applied (Victorius).

‘And again, what Polycrates said in his encomium of Thrasybulus, that he put down thirty tyrants: for he puts them all together’. This again, which without further elucidation would not be altogether intelligible, is explained by two notices in Quintilian, III 6. 26, VII 4. 44.

As an illustration of the argument from number, he gives this, An Thrasybulo triginta praemia debeantur, qui tot tyrannos sustulerit? Whence it appears that Polycrates had argued that he deserved thirty rewards for his services, one for each tyrant that he had expelled; an illicit combination. Spalding ad loc. III. 6, “Hoc videtur postulasse Polycrates, qui dixit:” quoting this passage. On Polycrates see § 6, infra.

‘Or that in Theodectes' Orestes, for it is a fallacy of division: “It is just for her that slays her husband” to die, and for the son to avenge his father: and accordingly this is what has actually1 been done: (but this is a fallacy) for it may be that when the two are combined, (the sum-total) is no longer just’. Orestes, being the son of her that had slain her husband, was no longer the right person to take vengeance on his murderer. On the use of οὐκέτι, the opposite of ἤδη, ‘not now as before, in former cases’, see note on I 1. 7, ἤδη, οὔπω, οὐκέτι.

On Theodectes of Phaselis, see note on II 23. 3, and the reff. Also compare the topic of that section with this example from his Orestes, which in all probability is there also referred to. This passage of Aristotle is cited by Wagner, Fragm. Trag. Graec. III 122, without comment, as the sole remaining specimen of Theodectes' Orestes.

‘This may also be explained as the fallacy of omission; for the (person) by whom (the deed was done) is withdrawn’. Had it been stated ‘by whom’ the vengeance was inflicted, the injustice of it would have been apparent. It is stated generally, the particular circumstances which falsify the statement in this case being omitted. παρὰ τὴν ἔλλειψιν is explained in § 9, τὴν ἔλλειψιν τοῦ πότε καὶ πῶς, the omission of time and circumstances, which falls under the more general head of τὸ ἁπλῶς καὶ μὴ ἁπλῶς, § 10, an unqualified, instead of qualified statement. It occurs also in § 7.

1 A^{c} and three other MSS have οὐκοῦν καὶ ταῦτα καὶ πέπρακται. Spengel, ed. 1867, rightly puts the first in brackets and retains the second, which I have followed in the translation.

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