⁴ The extreme version of this tendency is Diels–Kranz's decision not even to print MXG. A more recent example on the other side is Mansfeld, J., ‘Historical and philosophical aspects of Gorgias’ “On What Is Not”’, reprinted in Studies in the Historiography of Greek Philosophy (Assen, 1990), 97–125Google Scholar. Mansfeld cites a number of recent scholars who, like himself, consider MXG to be more reliable (at 97 with endnote 4 at 120). As a result, he only refers to Sextus ‘for some points of detail’ (at 98). Mourelatos (n. 2), 136 largely follows suit calling MXG ‘unquestionably’ the better source for the second part of the treatise. He does quote from Sextus but again only to supplement his findings from MXG; even with regard to passages that are preserved only by Sextus he is less than enthusiastic, stating merely that ‘it is perhaps not impossible to recover behind that Hellenistic encrustation a recognizably Gorgianic thought’ (Mourelatos [n. 2], 158). Likewise, Caston, V., ‘Gorgias on thought and its objects’, in Graham, D.W. and Caston, V. (edd.), Presocratic Philosophy: Essays in Honour of Alexander Mourelatos (Aldershot, 2002), 205–32Google Scholar is largely dismissive of the evidence from Sextus, and relies on it only tentatively and infrequently (e.g. at 222, 224, 229). Gagarin (n. 3), 38 also notes that MXG is the current favourite among translators.

⁵ Much of the language Sextus uses is only attested in authors much later than Gorgias himself, whereas the language of MXG is consistent with other works of the fourth and fifth centuries b.c.e. See Kerferd, G.B., ‘Gorgias on nature or that which is not’, Phronesis 1 (1955), 3–25, at 14CrossRefGoogle Scholar; Calogero, G., Studi sull'Eleatismo (Florence, 1977 ²), 158 n. 4Google Scholar; and Diels, H., Aristotelis qui fertur de Melisso Xenophane Gorgia libellus (Berlin, 1900), 10Google Scholar. For a case-study concerning the third part of the treatise see Gaines, R.N., ‘Knowledge and discourse in Gorgias's “On the non-existent or on nature”’, Philosophy & Rhetoric 30 (1997), 1–12Google Scholar.

⁶ Kerferd (n. 5) goes to great lengths to argue that MXG preserves the same argument as Sextus does in the first part, though I will argue that they do differ in at least one crucial respect. Caston (n. 4) and Mourelatos (n. 2) give detailed analyses of the second and third part respectively but set the first part aside.

⁷ I will follow Mansfeld, J., ‘De Melisso Xenophane Gorgia: Pyrrhonizing Aristotelianism’, RhM 131 (1988), 239–76Google Scholar in referring to the author of MXG as ‘Anonymous’. Anonymous is standardly referred to with a masculine pronoun; while it is mere conjecture that the author would have been male, this is unfortunately all too likely given the long history of sexism.

⁸ By ‘polylemma’ I simply mean a division into two or more possibilities, which can be represented as a disjunction with two or more disjuncts.

⁹ For an argument to fit the pattern discussed here, the polylemma need only be taken to be exhaustive. The argument will only be sound, however, if the polylemma truly is exhaustive. I will suggest that the relevant polylemma in Helen is portrayed as exhaustive and taken to be so for the sake of the argument, though this is ultimately a mistake (perhaps even a self-conscious one on Gorgias’ part).

¹⁰ See Gagarin, M. and Woodruff, P., ‘The sophists’, in Curd, P. and Graham, D.W. (edd.), The Oxford Handbook of Presocratic Philosophy (Oxford, 2008), 365–82Google Scholar for translating εἰκός with a normative valence. In general, they recommend ‘reasonable’ as an English translation, which Spatharas adopts for this case in D.G. Spatharas, ‘Gorgias: an edition of the extant texts and fragments with commentary and introduction’ (Diss., University of Glasgow, 2001). Yet, here ‘reasonable’ is misleading, since Gorgias is not enumerating cases that would make Helen's action rational. For this reason, ‘likely’ is better in this instance.

¹¹ I am including the medieval conjecture accepted by most modern commentators. The text as it is transmitted does not mention the fourth possibility, but Gorgias transitions to it in (15) in a way that suggests it was understood to have already been mentioned, stating simply: ‘and I will go through the fourth cause with the fourth argument’ (τὴν δὲ τετάρτην αἰτίαν τῶι τετάρτωι λόγωι διέξειμι). Here is the logical place for that to have happened. It also fits well with the mention of this option in the final summary quoted immediately below.

¹² All translations are my own and based off of the Greek text of DK with more recent texts and translations consulted in addition. The following were particularly useful. Those including all of Gorgias’ works are Spatharas’ commentary (n. 10 above); Graham, D.W. (ed.), The Texts of Early Greek Philosophy: The Complete Fragments and Selected Testimonies of the Major Presocratics (Cambridge, 2010), 740–50Google Scholar; Buchheim, T. (ed.), Reden, Fragmente und Testimonien (Hamburg, 1989 ²), 39–64Google Scholar; and Untersteiner, M., Sofisti: testimonianze e frammenti (Florence, 1949), 36–74Google Scholar. In addition, Cassin, B., Si Parménide: le traité anonyme De Melisso, Xenophane, Gorgia (Lille, 1980)Google Scholar and Diels (n. 5) contain the MXG version of On Not-Being. For Helen, MacDowell, D., Encomium of Helen (Bristol, 1982)Google Scholar was also consulted, as were the translations of Dillon, J.M. and Gergel, T., The Greek Sophists (New York, 2009)Google Scholar and Gagarin, M. and Woodruff, P., Early Greek Political Thought from Homer to the Sophists (Cambridge, 1995)CrossRefGoogle Scholar.

¹³ Cf. Barnes, J., The Presocratic Philosophers (New York, 1982), 416Google Scholar. I will distinguish strictly exhaustive polylemmata, which cover all possibilities, from polylemmata that are conditional on some other possibility obtaining. Most of the polylemmata used by Gorgias are conditional in this sense.

¹⁴ Following MacDowell's reconstruction of the text (cf. ‘Gorgias, Alkidamas, Cripps and Palatine manuscripts’: [n. 12], 120–1). The manuscripts read ἢ rather than καὶ.

¹⁵ While we are meant to initially take the argument as exhaustive, the fact that the argument appears to generalize such that no one is ever to blame, and that Gorgias ends by calling it an amusement (παίγνιον), may indicate that we are meant to question whether it really did cover all of the relevant possibilities in the first place. For further discussion of this point, see Barney, R., ‘Gorgias’ Encomium of Helen’, in Schliesser, E. (ed.), Ten Neglected Classics of Philosophy (Oxford, 2016), 1–25Google Scholar.

¹⁶ As Smyth notes under ‘Present and Past Unreal Conditions’: ‘the imperfect refers to present time or (sometimes) to a continued or habitual past act or state’ (Smyth, H.W., A Greek Grammar for Colleges [New York, 1920], §2304Google Scholar). The imperfect here is the appropriate tense for Palamedes’ state of inability that is presumed to be continuous from that past time up through the present moment of his speech.

¹⁷ This fits best with the imperfect and with the structure of the ensuing argument of Palamedes. If the suppressed premise were instead ‘if it had happened …’, as suggested in Long, A.A., ‘Methods of argument in Gorgias’ Palamedes’, in Voudouris, K.I. (ed.), Η ΑΡΧΑΙΑ ΣΟΦΙΣΤΙΚΗ, The Sophistic Movement (Athens, 1984), 233–41Google Scholar, then it is difficult to see how the ensuing argument would work. It could have the structure: (i) if it had happened then XYZ would have happened, (ii) but XYZ could not have happened, (iii) therefore it did not happen, but in this case the conclusion would be that it did not happen, not that Palamedes would not have been able, which is the expressed aim. Càffaro, L., Encomio di Elena; Apologia di Palamede (Florence, 1997)Google Scholar suggests that the initial hypothesis is ‘Palamede è un traditore’ (‘Palamedes is a traitor’), which cannot be right for the same reason that the argument would no longer be aimed at the explicit conclusion that Palamedes was not able. This conclusion is explicit not only in the way in which the argument is introduced but also in the way in which it ends (12): ‘Thus it would have in fact been entirely impossible for me to do any of these things in any way’ (πάντως ἄρα καὶ πάντηι πάντα πράττειν ἀδύνατον ἦν μοι).

¹⁸ The correspondence is only rough, and partly influenced by the natural impulse to try to identify arguments from each version with one another. Still, there are clear cases of arguments that appear in only one of the two paraphrases, for instance Sextus (75–6) and MXG 980a3–8. For an outline of the similarities and the differences between the arguments in the first part, see pp. 98–99 below.

¹⁹ One might worry that, even before addressing the structure, one needs to make better sense of the subject matter, more specifically whatever is denoted by τὸ ὄν, τὸ μὴ ὄν and εἶναι more generally. These are familiar challenges in interpreting the Eleatics as well, though in Gorgias’ case there is the extra complication that Sextus is possibly rephrasing Gorgias’ initial terminology. In the end, however, these issues will not affect the way in which one understands the underlying method indicated by Sextus’ paraphrase. For recent discussions of how best to understand the verb ‘to be’ in Greek philosophy, see Kahn, C.H., ‘A return to the theory of the verb be and the concept of being’, AncPhil 24 (2004), 381–405Google Scholar and Brown, L., verb, ‘The “to be” in Greek philosophy’, in Everson, S. (ed.), Language: Companion to Ancient Thought 3 (Cambridge, 1994), 212–36Google Scholar.

²⁰ I understand Sextus to be using the conclusion in the final clause here, ‘it is not the case that anything is’, interchangeably with the conclusion stated at the beginning of this section as well as the end of (76), ‘nothing is’.

²¹ Bekker's emendation here is well motivated. There is sign of a lacuna as ἔστι should read ἔστιν given that it is followed by a vowel. Furthermore, there is support for the missing τι in the formulation at the end of the section (οὐκ ἄρα ἔστι τι). Finally, the τι could have easily dropped out owing to haplography.

²² It is likely that τό has dropped out of the manuscripts since, when this option is picked up again in (75), it is stated with τό repeated: τό τε ὂν καὶ τὸ μὴ ὄν. The meaning here must be ‘being and not-being’, as I have translated, rather than ‘that which is and is not’, as the Greek without the second τό would suggest.

²³ Kerferd (n. 5), 14–16, 22 prefers the translations ‘that which is’ and ‘that which is not’, because they allow for a more indefinite reading of the subject in either case, allowing that any theoretical construct of previous thinkers could be substituted. I take it that Kerferd supposes ‘being’ and ‘not-being’, by contrast, to indicate definite concepts that do not allow this indefinite substitutable reading, though I do not think that we have clear concepts corresponding to the terms in English to preclude this reading. I intend to use ‘being’ and ‘not-being’ as placeholders that are ambiguous between the definite (single concept) and the indefinite (schema for inserting any construct) readings.

²⁴ One might worry, however, that the third option is redundant. This option immediately stands out as somewhat odd; the first two options appear to be contradictories, in which case they alone exhaust logical space. Surely they are at least contrary to one another, in which case we should know in advance that both cannot obtain at once. If they are neither contrary nor contradictory, then it becomes hard to see how the three options listed are meant to be exhaustive in the first place. It is possible that Sextus or even Gorgias recognizes the redundancy, as hinted at by the rather emphatic ‘he will prove even this’ (καὶ τοῦτο διδάξει) in (66) quoted above. Another suggestion mentioned by Graham (n. 12) is that the conjunctive case is a direct response to the Atomists, who thought that the world was made up of both atoms (being) and void (not-being). While this option is strange, and perhaps self-consciously so, the overarching structure of a conditional polylemmatic reductio is still quite clear.

²⁵ To see the difference, compare the claims ‘it is not the case that all roads are ploughed’ and ‘all roads are not-ploughed’. The latter is equivalent to ‘all roads are unploughed’ and is not consistent with there being any ploughed roads. The former, however, leaves open the possibility that some roads are ploughed while others are not.

²⁶ Here is the intentional slippage where the negation is narrow-scope (in the Greek, οὐκ clearly modifies ἔστιν rather than the whole clause).

²⁷ I have translated ἄτοπον literally as ‘out of place’, but the force in the Greek is stronger than that of the English: this is not merely to say that it would be strange or surprising but rather illogical or bizarre enough to warrant a reductio.

²⁸ The negation is ambiguous between a wide-scope reading and a narrow-scope reading; οὐκ could be modifying ἔστι (narrow-scope) or the whole clause (wide-scope). I have gone with the wide-scope translation strictly warranted by the argument, though again the ambiguity may be intentional.

²⁹ Here the negation is unambiguously wide-scope (οὐδέ modifies the whole clause).

³⁰ Manuscript N has τὸ before μὴ ὄν, in which case the more natural translation would be ‘in so far as not-being is’.

³¹ Another clear example of καὶ ἄλλως indicating an alternative argument for the same conclusion occurs at the beginning of (73).

³² Both arguments have the same reductio structure, and a reductio only warrants the wide-scope claim. Using the example from n. 25 above, if I run a reductio against the claim ‘all roads are ploughed’, then I have only established the truth of the wide-scope claim ‘it's not the case that all roads are ploughed’. Suppose, for instance, that the reductio depends on only the more accessible roads being ploughed, while the road to the mountains was skipped; in this case, some roads are ploughed and some are not, warranting the true claim ‘it is not the case that all roads are ploughed’ but making ‘all roads are not-ploughed’ false.

³³ It is unlikely to be a simple mistake since Gorgias appears to be sensitive to the distinction between narrow-scope and wide-scope claims in the ensuing argument. The second argument of (66) above dismisses the narrow-scope claim that ‘being is not’ as part of the reasoning behind denying the claim that ‘not-being is’. But the next argument embraces the wide-scope claim ‘it is not the case that being is’. To be consistent, Gorgias has to maintain that the narrow-scope claim ‘being is not’ is false and the wide-scope claim ‘it is not the case that being is’ is true. He has to be sensitive to the distinction to pull this off.

³⁴ For instance, at the end of (74) the first two prongs of the argument are summarized in explicitly wide-scope terms: ‘But indeed, for these reasons it is clear that neither is it the case that being is nor that not-being is’ (ἀλλὰ γὰρ ὅτι μὲν οὔτε τὸ ὂν ἔστιν οὔτε τὸ μὴ ὂν ἔστιν, ἐκ τούτων συμφανές). The first prong (it is not the case that not-being is) is precisely the argument that was made in (67). We then see the same summary in wide-scope terms at the very end of the argument of the first part in (76): ‘… from which it follows that nothing is. For if neither being is nor not-being nor both, and nothing is recognized beyond these, nothing is’ (οἷς ἕπεται τὸ μηδὲν εἶναι. εἰ γὰρ μήτε τὸ ὂν ἔστι μήτε τὸ μὴ ὂν μήτε ἀμφότερα, παρὰ δὲ ταῦτα οὐδὲν νοεῖται, οὐδὲν ἔστιν).

³⁵ As I understand it, the argument runs as follows:

1. (i)

   (i) Assume for reductio that being is and not-being is

2. (ii)

   (ii) Being and not-being are the same in so far as their being is concerned [by (i)]

3. (iii)

   (iii) Not-being is not [argued for in (67)]

4. (iv)

   (iv) If not-being is not, and being and not-being are the same in so far as their being is concerned, then being is not

5. (v)

   (v) Being is not [by (ii)–(iv)]

6. (vi)

   (vi) Neither being nor not-being is [by (iii), (v)]

7. (vii)

   (vii) Contradiction [by (i), (vi)]

8. (viii)

   (viii) Therefore, it is not the case that being is and not-being is [by reductio, (i)–(vii)]

³⁶ This is one way in which the argument in (75) is deficient, though it is not the only oddity. The lemma discussed here, ‘both being and not-being are’, already seems redundant (see n. 24 above).

³⁷ Understanding οὐδέν as implicit from the previous line (οὐκ εἶναί φησιν οὐδέν· εἰ δ’ ἔστιν, ἄγνωστον εἶναι …) with the same implicit structure.

³⁸ The clearest exception is the final argument in the MXG version that nothing is moved (980a1–8), which does not have a parallel in Sextus’ version.

³⁹ Alternatively, one might understand the final clause as carrying over the previous subject and containing a complete use of the copula rather than an incomplete use as I have translated it (and as found in Sextus). In this case the translation would be ‘[not-being] would be not-being no less than being’. Either way, however, the hypotheses and the reductio structure appear to be the same.

⁴⁰ Manuscript N has τὸ after ἔστι.

⁴¹ While both versions have the same structure, the reasons given against it coming from being are substantially different. I will set aside the question of which is more accurate to Gorgias’ original in substance for present purposes; it will not affect the similarities in structure.

⁴² οὐδὲν ἂν εἴη (979a30), οὐκ ἂν εἴη οὐδέν (979a31–2), μηδὲν εἶναι (979a34).

⁴³ These are the arguments detailed in the previous section.

⁴⁴ ἀδύνατον τι καὶ εἶναι (979b34), οὐδέν ἐστιν (980a1).

⁴⁵ Taking ἐκείνου as a genitive of connection or comparison (Smyth [n. 16], §§1417, 1431).

⁴⁶ Printing οὗτος with L. R has οὕτως.

⁴⁷ Foss, H.E., De Gorgia Leontino commentatio (Halle, 1828)Google Scholar; Dillon, J. and Gergel, T., The Greek Sophists (London and New York, 2003), 71Google Scholar.

⁴⁸ εἰ δὴ οὕτω, πότερον μᾶλλον ξυμβαίνει ἅπαντα μὴ εἶναι ἢ εἶναι; (979b8–9). Manuscript R reads as quoted, whereas manuscripts L reads: … ἅπαντα ἢ εἶναι, μὴ εἶναι.

⁴⁹ Mansfeld (n. 7), 239–76, at 249–53. I take this possibility that Anonymous rearranged the argument to fit one of his favourite tropes and the possibility that Sextus rearranged the argument to fit his logical proclivities to be a wash; we should look to other factors to decide which structure is more accurate, as I suggest below.

⁵⁰ See LSJ s.v. ἀρχή, 1.c. This use of ἀρχή is attested in Antiphon (5.73), one of Gorgias’ contemporaries.

⁵¹ οὐκ ἀληθῆ λέγειν διὰ δισσῶν ὑμῖν ἐπιδείξω τρόπων· οὔτε γὰρ βουληθεὶς ἐδυνάμην ἂν οὔτε δυνάμενος ἐβουλήθην ἔργοις ἐπιχειρεῖν τοιούτοις.

⁵² εἰ μὲν οὖν εἰμι σοφός, οὐχ ἥμαρτον· εἰ δ’ ἥμαρτον, οὐ σοφός εἰμι. οὐκοῦν δι’ ἀμφότερα ἂν εἴης ψευδής.

⁵³ εἰ ἀίδιόν ἐστι τὸ ὄν, οὐ γέγονεν, καὶ εἰ γέγονεν, οὐκ ἔστιν ἀίδιον. Spatharas (n. 10) notes the parallel between Palamedes (26) and Sextus (72) in his commentary at 301.

⁵⁴ εἰ γὰρ ἀμφότερα, οὐ ταὐτόν, καὶ εἰ ταὐτόν, οὐκ ἀμφότερα. A more conservative translation might be more accurate in this case even if a bit clunky: ‘for if “both”, then not “same”, and if “same”, then not “both”.’