§1.1: Helen

The argument of Helen clearly employs the pattern of using what is taken to be an exhaustive polylemma with an eye to establishing the same positive conclusion in each case.Footnote ⁹ This is an argument by cases, a species of the general pattern described above, where a positive conclusion is derived from each lemma. The argument spans the entire work, introducing the goal of exonerating Helen in (2) and announcing the successful completion of that goal in (21).

The main polylemmatic structure of the argument becomes clear in (5)–(6):

and again when the argument is summarized in (20):

As these two summaries make clear, the argument operates by articulating four possibilities and examining each one in turn. This is precisely what happens in the intervening fourteen sections. Gorgias first examines the case of divine compulsion (6), then force (7), speech (8–14) and love (15–19), showing that Helen is not to be blamed in each case. Thus it has the structure of a fourfold polylemma.

It is also clear that Gorgias presents the polylemma as an exhaustive one. The division must be exhaustive (that is, on the assumption that Helen did in fact go to Troy) for the argument to be valid, and Gorgias does treat it as a valid argument.Footnote ¹³ Gorgias begins by clearly laying out the aim of the argument in (2):

At the end he explicitly refers back to this goal as having been achieved:

These statements would not make sense unless, at least at some level, Gorgias takes himself to be giving a compelling argument. In so far as the argument is meant as an argument at all, then, we should read it as offering an exhaustive division.Footnote ¹⁵

Gorgias’ introductory and concluding statements also show how his aim is not to establish which of the four possibilities actually obtained, but rather to establish what follows from each: Helen is not to be blamed. Thus the argument of Helen also meets the second characteristic feature of this recurring pattern. I agree with Barney's (n. 15) reconstruction as follows (at 5):

1. (1) Helen went to Troy either because of fate and the gods (I here simplify ‘the will of fortune and the plan of the gods and the decree of necessity’) or because of force or because of persuasion by speech [logos] or because of erōs.

2. (2) If she went to Troy because of fate and the gods, Helen is not to blame.

3. (3) If she went to Troy because she was forced, Helen is not to blame.

4. (4) If she went to Troy because she was persuaded by logos, Helen is not to blame.

5. (5) If she went to Troy because of erōs, Helen is not to blame.

6. (6) Therefore, Helen is not to blame for going to Troy (from 1 + 2 + 3 + 4 + 5).

Furthermore, Helen briefly exhibits a third element that is found in Gorgias’ other works. When discussing the case of love, Gorgias makes another dilemmatic split: love is either the pleasing effect of a beautiful body or a god. But still, either way Helen is not to blame (19). This nesting of one polylemma within another appears time and again in Palamedes and in the first part of On Not-Being as well. I have included a visual diagram of the argument's structure in the Appendix for easy comparison with the arguments of Palamedes and On Not-Being.

§1.2: Palamedes

The same pattern of employing an exhaustive polylemma with a focus of deriving some desired conclusion in each case is even more prevalent in Palamedes. The same goes for the further pattern of nested polylemmata. One difference is that Palamedes is often focussed on deriving a negative consequence from each lemma rather than a positive one. When the polylemma is conditional on some other possibility obtaining, this then serves as a reductio of that possibility. The following is a simple example: suppose that if I had gone to the mountains I would have either walked, biked or taken a train. Now suppose that each option would have been impossible. On this basis, we can conclude that I must not have gone to the mountains. As opposed to the argument by cases in Helen, I will call this specific pattern a ‘conditional polylemmatic reductio’.

Being a defence speech, the implicit aim of Palamedes is to argue that Palamedes should not be sentenced to death. Gorgias has Palamedes undertake three different argumentative strategies throughout the speech to establish this main conclusion. The first is to establish that he is not guilty by showing that he could not have been both willing and able to commit the crime (6–21). The second is to undermine Odysseus’ trustworthiness as a witness (22–32). Finally, he argues that a summary judgment would be overly hasty in this case (33–6). For present purposes I will focus on the first strategy, which proceeds by a series of conditional polylemmatic reductiones.

The initial strategy can be further subdivided into two alternative sets of arguments, arguments for the claim (a) that Palamedes would not have been able, and arguments for the claim (b) that Palamedes would not have been willing. This much is implicit in the way in which Gorgias has Palamedes set it up:

Thus the first set of arguments for (a) have the following form:

1. (i) if Palamedes were guilty of the crime, then he must have been both willing and able,

2. (ii) but he would not have been able; [claim (a)]

3. (iii) therefore, he is not guilty.

And the second set of arguments for (b) have the related form:

1. (i) if Palamedes were guilty of the crime, then he must have been both willing and able,

2. (ii) but he would not have been willing; [claim (b)]

3. (iii) therefore, he is not guilty.

These arguments have a concessive structure that allows Palamedes to accommodate potential objections: he can grant his opponent that he was willing, for instance, but still show that even granting this he would not have been able. This technique appears in the structure of On Not-Being as well.

There are ten arguments for the conclusion that Palamedes would not have been able to commit treason (6–12, 21). They stand out for the nested polylemmatic reductio structure they create: Palamedes tends to split the space of possibilities into multiple options, rule out every option but one, then repeat by splitting the last option into more possibilities, etc. Even then he grants one of the previously ruled-out possibilities for the sake of argument and proceeds to give another nested polylemmatic reductio. Thus the overarching structure is a conditional polylemmatic reductio, the conclusion being that the initial premise (that Palamedes was able) is to be rejected.

The way in which the argument is introduced makes it clear that this is a reductio against the possibility of Palamedes committing treason:

The imperfect ἔδει is important. It extends the counterfactual reasoning begun in the previous section (again expressed with the imperfect).Footnote ¹⁶ But it is natural to ask: a first beginning would have needed to come about … if what? The suppressed premise must be ‘if it had been possible’.Footnote ¹⁷ Thus the implicit structure here is:

1. (i) if it had been possible for a Greek to do it, then XYZ would have been possible,

2. (ii) but XYZ would not have been possible;

3. (iii) therefore, it would not have been possible for a Greek to do it;

4. (iv) therefore, a fortiori, Palamedes would not have been able. [claim (a)]

Understanding the structure in this way also fits well with the series of potential optatives that follow in the ensuing argument.

As mentioned above, there are ten distinct arguments in this section that fill out the ‘XYZ’ in premises (i) and (ii) above in different ways. The first argument (6–7) fills them out as follows:

1. (a) if it had been possible for a Greek to do it, then it would have been possible for them to communicate with the Trojans;

2. (b) if communication was possible, it was possible either one-on-one or with a third interpreter;

3. (c) either way would not have been possible (since they do not speak the same language and an interpreter would have added another witness);

4. (d) therefore, communication would not have been possible [by (b)–(c)].

The ensuing arguments follow the same pattern (see the Appendix for a complete summary). They each take the form of conditional polylemmatic reductiones, with a series of nested polylemmatic divisions conditional on the treason being possible. Negative results in each case provide a reductio of that possibility.

An analogous structure can be found in the next part of Palamedes. Gorgias has Palamedes offer another polylemmatic reductio, this time for claim (b), namely that, even granting his ability to commit treason, he would not have been willing (13–19). It begins with a large polylemma as in Helen, with six options considered. And once again we see the same nesting of one polylemma within another as diagrammed in the Appendix. This general pattern, and more specifically the use of a nested polylemmatic reductio, resurfaces in the first part of On Not-Being.

§2.1: Sextus’ version: a nested polylemmatic reductio

Sextus’ version of the first part of On Not-Being contains a nested polylemmatic reductio much like that of the first two parts of Palamedes and their positive counterpart in Helen. This structural similarity is part of why Sextus is the more likely candidate for preserving the original argument's structure.Footnote ¹⁹

After an initial introduction that sets out the tripartite structure of the whole treatise, Sextus summarizes the argument of the first part as follows:

Here I have given a neutral translation by simply rendering τὸ ὄν as ‘being’, τὸ μὴ ὄν as ‘not-being’, and forms of the verb εἶναι with a simple ‘is’ (leaving any extra supplement implicit as it is in the Greek). The advantage of the translations ‘being’ and ‘not-being’ is that they preserve the participial form of the original, making it easier to distinguish this construction from finite uses of the verb.Footnote ²³ What is clear, and is most important for our purposes, is that this sets up the overarching structure of a conditional polylemmatic reductio, with three exhaustive options conditional on there being anything whatsoever (see the Appendix for a diagram of this structure). Thus the force of the reductio is to show that nothing whatsoever is.Footnote ²⁴

In the remainder of the first part as reported by Sextus, each of the three options is systematically refuted, thus completing the reductio as set out in the introductory section. Interestingly, the sequence of arguments against the claim that being is mimics the overarching structure of the first part, thus creating a structure of nested polylemmata as in Gorgias’ other works. Once again the structure is laid out explicitly:

The parallel with (66) is quite close. This creates a nested polylemmatic reductio, as can be seen in the argument-structure diagrams in the Appendix.

One of the most puzzling sections is the intervening reductio of the not-being option in (67). In §2.2 I will argue that the complications of this section help to explain how Anonymous might have misunderstood the overarching argumentative structure. For this reason, a closer look at (67) is in order. The main takeaway will be that the argument consistently requires understanding a wide-scope negation, though there is one intentional slippage at the beginning. The difference is important; the narrow-scope claim ‘not-being is not’ is not strictly warranted by the argument, which instead supports the wide-scope claim ‘it is not the case that not-being is’.Footnote ²⁵ The section runs as follows:

On the face of it there are two arguments; ‘and alternatively’ (καὶ ἄλλως) indicates a transition from one argument to another.Footnote ³¹ But there is a puzzle as to how exactly they relate to one another. The transition suggests that they are two arguments for the same conclusion, which is further supported by the similarity of structure in both arguments; both begin with the hypothesis ‘if not-being is’ and give a reductio against that hypothesis. Yet, they do not appear to state the same conclusion. The first conclusion is put in narrow-scope terms, ‘not-being is not’, and the second in wide-scope terms, ‘it's not the case that not-being is’.

Strictly speaking, both arguments appear to license only the wide-scope version of the claim.Footnote ³² Thus it is more plausible to read both as arguments for the same conclusion. But if this is right, then why the switch? The pattern of narrow-scope vs wide-scope claims throughout this part of the text gives us some traction.Footnote ³³ In general, explicitly narrow-scope claims are infrequent. The polylemmatic reductio structure licenses wide-scope claims, and explicitly wide-scope claims do indeed surface at crucial junctures in the argument.Footnote ³⁴ So why does (67) begin with the narrow-scope claim? The best explanation is that it is an intentional slippage used to set up the argument in (75).

In (75) the target is the conjunctive claim ‘both being and not-being are’. The reductio depends on the narrow-scope claim from (67), ‘not-being is not’:

The argument here simply assumes that the narrow-scope claim ‘not-being is not’ is already agreed upon.Footnote ³⁵ Yet, while it was indeed stated as the conclusion to the first argument of (67), only the wide-scope claim was warranted. This suggests that Sextus (either following Gorgias or on his own) equivocates between the narrow-scope and the wide-scope claims on purpose; he uses whichever version best fits his current needs (which is the strictly warranted wide-scope claim for most purposes, but the narrow-scope claim for this particular argument). The narrow-scope claim has indeed been mentioned, but technically has not been argued for. Further support would need to be given or it would have to be endorsed on its own for the argument in (75) to go through.Footnote ³⁶

Despite this sleight of hand, the arguments in (67) are by no means blatantly fallacious, and the text is actually quite careful with the scope of the negation. The structure is that of two alternative arguments for the conclusion that it is not the case that not-being is, and thus part of the overarching polylemmatic reductio. Yet, the structure along with the scope of the claims argued for is misinterpreted by Anonymous, which in part explains why he reorders the arguments in MXG, as I will argue below.

§2.2: The MXG version, first part rearranged?

MXG, too, reports a polylemmatic reductio, though one that is much less intricate than those surveyed so far. It also reports two separate arguments, whose counterparts in Sextus play a subsidiary role as part of the polylemmatic reductio instead (see the Appendix for a comparison of the two structures). Below I begin with a series of detailed observations about the similarities and the differences between the two versions, then offer a hypothesis that explains them.

Two unique features of the MXG version immediately stand out. First, Anonymous shows a keen interest in the provenance of Gorgias’ arguments. The first part of MXG begins as follows (979a13–15):

Unlike Sextus, Anonymous emphasizes that the argument of the first part involves borrowing opposed arguments from others. He continues to stress this point by identifying the origins of different arguments. After a brief summary of the part of the argument that borrows most heavily from others, Anonymous notes (979a22–4):

He goes on to give Gorgias’ original arguments. Next, he sets out the arguments borrowed from others, where he again mentions Melissus (979b22) and Zeno (979b25, 37) and adds ‘the so-called arguments of Leucippus’ (980a7). None of the arguments in this latter group is explicitly said to originate from Gorgias himself. The arguments as he reports them are divided between first those that are original to Gorgias, and later those that are not.

The second peculiar feature of MXG is that it offers a critique of the arguments that are original to Gorgias. Anonymous criticizes those arguments immediately after considering them, before moving on to those that are borrowed from others (he does not criticize the latter).

Despite these obvious differences, there are obvious similarities as well. Most of the arguments of the MXG version appear to have a close parallel in Sextus’ version.Footnote ³⁸ Below is a list of what I take to be the main arguments attributed to Gorgias’ On Not-Being by the MXG version, with references to each counterpart in Sextus:

1. (1) first original argument that nothing is (979a25–31)

   1. a. similar to the first argument against the claim that not-being is in Sextus (67) in that both are based on the hypothesis that not-being is not-being:

      1. i. MXG: ‘For if not-being is not-being, not-being would be no less than being’ (εἰ μὲν γὰρ τὸ μὴ εἶναι ἔστι μὴ εἶναι, οὐδὲν ἂν ἧττον τὸ μὴ ὂν τοῦ ὄντος εἴη)Footnote ³⁹

      2. ii. Sextus: ‘For if not-being is … in so far as it is not-being, it will in turn be’ (εἰ γὰρ τὸ μὴ ὂν ἔστιν … ἧι δὲ ἔστιFootnote ⁴⁰ μὴ ὄν, πάλιν ἔσται)

   2. b. similar to the second argument against the claim that not-being is in Sextus (67) in making the inference that being is not by a principle of opposites:

      1. i. MXG: ‘But still if not-being is, being, he says, is not, that is, the opposite’ (εἰ δ’ ὅμως τὸ μὴ εἶναι ἔστι, τὸ εἶναι, φησίν, οὐκ ἔστι, τὸ ἀντικείμενον)

      2. ii. Sextus: ‘if not-being is, being will not be: for these are opposite to one another’ (εἰ τὸ μὴ ὂν ἔστι, τὸ ὂν οὐκ ἔσται· ἐναντία γάρ ἐστι ταῦτα ἀλλήλοις)

2. (2) second original argument that nothing is (979a31–3)

   1. a. similar to the second argument against the conjunctive claim ‘both being and not-being are’ in Sextus (76) in that both rely on the hypothesis that being and not-being are the same:

      1. i. MXG: ‘nothing would be, unless being and not-being are the same, but if they are the same …’ (οὐδὲν ἂν εἴη, εἰ μὴ ταὐτόν ἐστιν εἶναί τε καὶ μὴ εἶναι. εἰ δὲ ταὐτό …)

      2. ii. Sextus: ‘if being is the same as not-being …’ (εἴπερ ταὐτόν ἐστι τῶι μὴ ὄντι τὸ ὄν …)

3. (3) argument against it being ungenerated (ἀγένητον, 979b21–6)

   1. a. Similar to Sextus’ argument against it being eternal (ἀίδιον, 68–70) in making the inference that it is unlimited (ἄπειρον in both cases), that it is neither in itself (ἐν αὑτῶι in both cases) or in another, and that it is nowhere (μηδαμοῦ MXG, οὐδαμοῦ Sextus).

4. (4) argument against it coming to be (γενόμενον, 979b26–33)

   1. a. Similar to Sextus’ argument against it being generated (γενητόν, 71) in using the same dilemmatic reductio structure, ruling out that it could come either from being or from not-being:Footnote ⁴¹

      1. i. MXG: ‘For nothing comes to be either from being or from not-being’ (γενέσθαι γοῦν οὐδὲν ἂν οὔτ’ ἐξ ὄντος οὔτ’ ἐκ μὴ ὄντος)

      2. ii. Sextus: ‘For if it has come to be, it has come to be either from being or from not-being’ (εἰ γὰρ γέγονεν, ἤτοι ἐξ ὄντος ἢ ἐκ μὴ ὄντος γέγονεν)

5. (5) argument against it being either one or many (979b35–980a1)

   1. a. Similar to Sextus’ argument against it being either one or many (73–4):

      1. i. MXG: ‘if it is neither one nor many, nothing would be’ (εἰ δὲ μήτε ἓν μήτε πολλά, οὐδὲν ἂν εἴη)

      2. ii. Sextus: ‘it is neither one nor many, as will be established: therefore, it is not the case that being is’ (οὔτε δὲ ἕν ἐστιν οὔτε πολλά, ὡς παρασταθήσεται· οὐκ ἄρα ἔστι τὸ ὄν)

While the parallels are clear, they also reveal how the overarching structure differs. The order in which arguments are offered, the implied connection between different arguments, and the stated conclusion of each one taken on its own all vary significantly.

These differences are most pronounced in the first two arguments attributed to Gorgias. The first argument in MXG has an affinity with the first argument in Sextus, but the second argument is in fact the second to last argument in Sextus’ version. In MXG, both are arguments for the main conclusion that nothing is.Footnote ⁴² In Sextus, however, neither is aimed at the main conclusion; each simply rules out one arm of an initial trilemma. The first is an argument against the possibility that not-being is and the second an argument against the possibility that both being and not-being are.Footnote ⁴³ On this version, Gorgias is not entitled to conclude that nothing is until he has also argued against the third possibility, that being is, which in fact occupies most of Sextus’ paraphrase. Anonymous takes these first two arguments to be parallel to those he classifies as borrowed from others and therefore redundant. Sextus takes them as complementary arguments that are essential for drawing Gorgias’ overarching conclusion.

There is a much closer similarity in the arguments that MXG classifies as borrowed from others, and they appear in the same order as in Sextus. But again there is a difference in the stated conclusions. Both versions preserve two alternative arguments for the same conclusion, one based on a division between generated and ungenerated, the other based on a division between one and many. In the MXG version, the conclusion of each is ‘nothing is’.Footnote ⁴⁴ But in Sextus the conclusion is ‘it's not the case that being is’. Once again, Anonymous understands these as alternative arguments for the main conclusion that nothing is, while Sextus understands them as alternative arguments for an intermediate conclusion, one that only licenses the main conclusion when taken in conjunction with two other limbs of a trilemma. Anonymous does not report this overarching trilemmatic structure, instead seeing three alternative arguments for the same conclusion.

Spatharas (n. 10), 294–8, 364 offers an explanation for this discrepancy in his commentary. He maintains that the MXG version is closer to the original and that Sextus rearranged the arguments to separate those that had to do with being and not-being from those that had to do with a combination of the two. ‘The effort on behalf of Sextus to present a smoother and more “logical” arrangement’, he says, ‘may be taken as a sign that MXG is closer to the original, Gorgianic arrangement’ (298). On the contrary, I propose that the opposite is true: Sextus’ version is closer to the original. This makes On Not-Being more consistent with the logical structure of Gorgias’ other works; appealing to intervention by Sextus is not necessary to explain the structure of a polylemmatic reductio. As we will see, my hypothesis also explains why MXG differs with evidence internal to the text itself: Anonymous’ explicit interest in provenance and a confusion concerning wide-scope vs narrow-scope negation.

Because Anonymous seems particularly interested in where Gorgias’ arguments come from, it makes sense that he might have reordered them so as to group together first the arguments that are Gorgias’ own and second those he borrowed from others. This would only require one small change: fronting Gorgias’ original but puzzling argument concerning the conjunctive claim that both being and not-being are. On my hypothesis, Anonymous moved it next to Gorgias’ other original but again rather puzzling argument against the claim that not-being is. In fact, this hypothesis makes good sense of a line that otherwise has puzzled commentators. Just after what MXG reports as Gorgias’ second original argument (which again, on my hypothesis, is transposed from the end of the argument) Anonymous says (979a33):

This line has caused problems for interpreters. Both Untersteiner and Buchheim follow Diels in emending ‘same’ (αὐτὸς) to ‘first’ (πρῶτος). Foss transposes ὁ and αὐτὸς, which may be what Dillon and Gergel have in mind when they translate: ‘Such, then, is his argument.’Footnote ⁴⁷ Cassin keeps the manuscript reading, though reads οὕτως with manuscript R. On Cassin's rather optimistic interpretation, Anonymous tells us that he is using the very same words, not only the same general sense, as Gorgias does in the original (445–7). Yet, I take this line to say that the second of the two arguments is the same in that it argues for the same conclusion as the first. It makes sense that Anonymous might have included this as a justification for moving the second argument here from its original location.

This is a mistake: Anonymous confuses what are really two separate limbs of a trilemma for two arguments for the same conclusion. His mistake in identifying the overall aim is enabled by mistakenly treating it as the narrow-scope rather than as the wide-scope conclusion. Anonymous thinks that Gorgias shows that nothing is by establishing the narrow-scope claim that each thing (not-being included) is not. When he asks ‘but if it is thus, why does it follow that all things are not rather than are?’,Footnote ⁴⁸ he betrays his narrow-scope understanding of the conclusion. He rightly points out that the narrow-scope claim ‘each thing is not’ is not warranted by the argument, but wrongly sees it as aimed at this narrow-scope claim rather than at the wide-scope claim ‘it is not the case that not-being is’ that it actually warrants. Anonymous jumps the gun by assuming that this argument alone is meant to license the overarching conclusion, a confusion further confirmed by the fact that he helps himself to the claim that being is (which Sextus acknowledges needs to be denied independently) in offering his criticism (979b10). This confusion about the scope of the negation enables his reordering of the original argumentative structure.

Thus the hypothesis that Sextus remains more faithful to the structure of the first part of Gorgias’ On Not-Being makes good sense of both texts as they have come down to us, especially as concerns the similarities and the differences observed above. Anonymous makes one small change in the order of the argumentation, moving what he takes to be Gorgias’ second original argument to the beginning out of an interest in grouping it with Gorgias’ other original contribution. Because he misunderstands the scope of the negation, he sees this as one of three independent arguments for the same conclusion, meaning that the order of presentation does not matter. Sextus, on the other hand, accurately sees the overarching trilemmatic structure and preserves the original ordering.

So why not think, along with Spatharas, that MXG more accurately preserves the structure of the original, that Anonymous’ criticisms are justified, and that Sextus cleaned up this structure himself? Of course, we cannot know for sure, and it is possible that Sextus was the one who rearranged the argument. Yet, it is equally possible that it was this nuanced structure of the original, at least in part, that drew Sextus to Gorgias’ argument in the first place. Furthermore, it seems equally likely that Anonymous could have changed the argument to suit his own preferences. Mansfeld points out how Anonymous frequently uses Agrippa's first trope of disagreement, ἀπὸ τῆς διαφωνίας, throughout the treatise, and how Anonymous’ interpretation of the first part of Gorgias’ argument puts much emphasis on this same trope.Footnote ⁴⁹ But it could equally be that Anonymous was misled by his own argumentative technique and, seeing something similar in Gorgias, read it as Gorgias’ main technique. Since these ‘bias towards philosophical predilection’ arguments can cut either way, they should carry little weight in deciding which structural features are or are not Gorgias’ own. More weight should be given to the greater resemblance of Sextus’ argument to Gorgias’ nested polylemmatic reductiones in other works and to the evidence internal to MXG that suggests a misunderstanding in the scope of the negation fuelled by an interest in provenance.