** This is the accepted version of the paper. Please cite the published version. ** 'Pushing Through' in Plato's Sophist: A New Reading of the Parity Assumption1 ABSTRACT At a crucial juncture in Plato's Sophist, when the interlocutors have reached their deepest confusion about being and not-being, the Eleatic Visitor proclaims that there is yet hope. Insofar as they clarify one, he maintains, they will equally clarify the other. But what justifies the Visitor's seemingly oracular prediction? A new interpretation explains how the Visitor's hope is in fact warranted by the peculiar aporia they find themselves in. The passage describes a broader pattern of 'exploring both sides' that lends insight into Plato's aporetic method. 1 A Pattern of Exploring Both Sides 2 The Context: Being and Not-Being as Exhaustive Alternatives 3 A Warranted Sense of Hope Plato's Sophist is puzzling. It is ostensibly about defining the sophist yet, after numerous attempts, embarks on a lengthy tangent about being and not-being. Past interpreters have mined the initial definitions for insight into the method of division,2 while those who focus on the central discussion of being and not-being tend to be concerned with what we can learn about Plato's metaphysics and philosophy of language.3 But there are important methodological and epistemological lessons to be drawn from the way in which the 1 I am very grateful for the feedback I have received on several drafts of this paper. Thanks to Emily Kress, Huw Duffy, George Rudebusch, and William Altman for comments on earlier drafts and to the participants of the Dublin Workshop on the Aporetic Tradition at Trinity College, the Reasoning and Inquiry in Ancient Philosophy Workshop at the University of Chicago, the Ancient Philosophy Works In Progress group at New York University, and the Society for Ancient Greek Philosophy. Many thanks to Susan Sauvé Meyer and to two anonymous referees as well for a thoroughly helpful process that significantly improved the paper. And special thanks to Rachel Barney, David Charles, Ken Winkler, and Verity Harte for their advice and encouragement starting from the project's early stages. 2 For recent examples, see Devin Henry's "A Sharp Eye For Kinds: Plato on Collection and Division", and two papers in David Charles ed. Definition in Greek Philosophy: Lesley Brown's "Definition and Division in Plato's Sophist" and Mary Louise Gill's "Division and Definition in Plato's Sophist and Statesman". 3 For example, Blake Hestir's Plato on the Metaphysical Foundation of Meaning and Truth, Paolo Crivelli's Plato's Account of Falsehood: A Study of the Sophist, and Allan Silverman's The Dialectic of Essence: A Study of Plato's Metaphysics. 2 discussion of being and not-being proceeds. I will argue that Plato draws attention to these insights with a key claim, the so-called 'Parity Assumption'. As it turns out, this claim can only be properly understood when we see how it is justified by the method of the preceding discussion. A consistent methodological focus, then, is at least one respect in which the dialogue is more unified than it may at first seem. The dialogue's main speaker, the Eleatic Visitor, kicks off the apparent digression into being and not-being by raising a puzzle: their seventh attempt at defining the sophist has relied on her ability to make things appear and seem which in fact are not. She also makes real statements that are nevertheless not true (236c9–237a1). But these observations appear to assume that not-being, in a way, is. In doing so they raise the very specter that the great Parmenides, a fellow Eleatic, vehemently warned against (237a2–b3). Hence the problem: the current definition of the sophist runs afoul of Parmenides' injunction against claiming that not-being is. Yet, if we follow Parmenides' advice, then the sophist will once again elude our grasp. The interlocutors decide to examine this claim more closely along with contrasting claims about being. This spawns a series of additional problems. But before those problems are eventually resolved and just when they appear most damaging, the Visitor makes a striking announcement that has received less attention than it deserves. His announcement, the Parity Assumption, suggests that the interlocutors should hold out hope despite their present confusion. Their problems concerning both being and not-being will be resolved together; in clarifying one they will also clarify the other. G.E.L. Owen recognized the importance of the announcement and was the first to label it the 'Parity Assumption'.4 But neither he nor any interpreter since has explained what justifies this seemingly oracular prediction.5 I will argue that the Parity Assumption is not in fact an 4 Owen 1970, 229–31. The next statement from 251a1–3 is equally important, however, so I will consider this as part of the Parity Assumption as well. 5 There has been surprisingly little discussion of the claim since Owen. All Bluck says in his commentary is: "the solution will be similar in both cases" (1975, 106). McCabe, too, follows Owen's interpretation (McCabe 1994, 207). Thomas distinguishes between a strong and a weak version of this type of reading: on the strong version a given solution must clarify one just as much as the other, on the weak version that solution must clarify both sides to some degree, but can do so to different degrees. She endorses the weak version (2008, 651). While Crivelli generally pays very close attention to the arguments in the surrounding context in his 2012 book, he 3 assumption as has been supposed; it is a well-motivated expectation that arises out of the very structure of Plato's aporetic method. In fact, the Visitor himself calls it an expectation rather than an assumption: The Parity Assumption6 V. Then indeed let this stand as containing a serious source of puzzlement; and since both being and not-being alike have had their share of puzzlement, already at this point there is an expectation that insofar as one of the two shows up as either more obscure or clearer, the other too shows up similarly. And if in turn we are not able to see either one of them, we will in this way push the account through both at the same time, however we are able to do so most appropriately. (250e5–251a3)7 Taken as a mere assumption, the Parity Assumption provides only a forward-looking prediction about the joint illumination of being and not-being in the positive resolution to follow. I will offer a new reading, however, that shows how it has something quite important to tell us about the preceding discussion as well. The passage contains Plato's self-conscious description of a method that I call 'exploring both sides' as it is employed throughout the discussion of being and not-being. Exploring both sides is a method that Plato introduces most explicitly in the Parmenides, when he has Parmenides recommend exploring the consequences of both a does not even mention the Parity Assumption. The greatest exception is Notomi's article 'Plato on What is Not', which contains an in-depth discussion of the claim (though he prefers the term 'joint illumination'). He helpfully emphasizes the importance of the end of the passage from 251a1–3 and points out an affinity to the method employed at 251dff. (2007b, 268), but like those before him still suggests that the same solution will feature in resolving both the problems with being and those with not-being (2007b, 262). I will take Notomi's lead in emphasizing the final lines of the passage as well as connections to the immediate context, but will suggest a different reading of its main force. 6 Despite its being misleading, I will keep the traditional label so as not to bias the case in favor of my view. I simply ask the reader to keep in mind that, on my reading, the Parity Assumption is not in fact an assumption. See §3 below for a more detailed discussion of my translation along with the Greek text. 7 All translations are my own, based on the most recent OCT Greek edition of the relevant text or Diels-Kranz in the case of Parmenides' fragments. 4 hypothesis and its contradictory (135d7–136a2).8 Owen recognizes that the Parity Assumption has "obvious affinities" with this recommendation but does not pursue the lead any further (1970, 231). Yet this connection reveals something very interesting about the structure of the conversation in the Sophist. The Eleatic Visitor employs this technique of systematically considering a series of exclusive and exhaustive claims throughout the discussion of being and not-being. This procedure leads to a serious impasse at the center of the dialogue, but also opens the way for the positive resolution. I will argue that this structure is what justifies the Parity Assumption, which draws our attention to this very feature of the discussion. I will focus on two sets of puzzling questions about the Parity Assumption that my account can help us to answer. First, what is the best way to understand the expectation for the joint illumination of being and not-being, and why is it said to follow from their present aporia? On the standard interpretation, it is simply assumed that joint illumination will proceed by the solution to one set of problems (either those with being or those with notbeing) helping to resolve the other set of problems as well. On this view, the focus is on clarifying being and not-being as separate notions or concepts. I will argue, however, that being and not-being are understood at this point of the dialogue as involving exclusive and exhaustive claims about reality.9 The expectation is that understanding the truth or falsity of each claim will go hand in hand (since they are exclusive and exhaustive, one must be understood to be true, the other false). On my view, this expectation does in fact follow from the very structure of exploring both sides in the preceding inquiry. It cannot simply be, as implicitly assumed by Owen and others, that the Visitor knows where the conversation is going or thinks that some general principle about opposites will do the trick.10 The following two questions are closely related on my reading as well: why is the Parity Assumption announced where it is, and why did the interlocutors even bother to 8 For the suggestion that Plato employs this method specifically for testing first principles, see Vassilis Karasmanis's "Dialectic and the Second Part of Plato's Parmenides". 9 The claims in question are 'not-being is' and 'being is'. See below for a defense of my reading as well as an explanation of why they are initially taken to be exclusive and exhaustive, a mistake corrected in the positive resolution of the dialogue. 10 Thanks to Whiney Schwab for helping me see the dialectical importance of this contrast for my view. 5 discuss claims about being in the first place? After all, it was only the claim 'not-being is' that created difficulties for defining the sophist. The standard interpretation is hard-pressed to give a satisfying explanation. Someone like Owen might suggest that, since the proper understanding of being is related to that of not-being, it is worth trying one's luck with being after they have reached a dead end with not-being. But in that case the appropriate time to announce the Parity Assumption would be when they initially encounter problems with 'notbeing is', not after they have already examined related claims about being. Again, I will argue that my new interpretation of the Parity Assumption fares much better. The Visitor recommends the examination of being as part of exploring both sides, informed by their Parmenidean heritage of seeing the claims 'being is' and 'not-being is' as two exclusive and exhaustive routes of inquiry. The Visitor waits to announce the Parity Assumption since it is only after the interlocutors have reached what I call a 'well-motivated aporia' produced by exploring both sides that they are justified in expecting joint illumination. The key to a proper understanding of the Parity Assumption will be to see how it is justified by the method of the preceding conversation. Other interpretations cannot account for what else might warrant the Visitor's otherwise baffling claim. Thus my focus is first and foremost on the proper interpretation of the Parity Assumption itself. I cannot do full justice to all of the complexities of the Sophist here, but I will discuss the structure of the preceding conversation since, on my reading, that very structure is what motivates the Parity Assumption. Therefore my interpretation of the actual method employed will provide independent support for my interpretation of the Parity Assumption along with its main justification. It will be worthwhile to first get a better sense of the pattern of Exploring Both Sides that the Parity Assumption describes on this new reading. This will be the focus of §1. In §2 I address the second set of questions concerning the timing of the Parity Assumption, in part by emphasizing the Parmenidean heritage that is explicitly invoked. I then turn to a conservative analysis of the Greek text in §3 that helps answer the first set of questions concerning the Parity Assumption's main force and scope. This all goes to explain how the Parity Assumption is more than a mere prediction and how it is in fact justified by the preceding discussion. 6 §1: A Pattern of Exploring Both Sides As mentioned above, exploring both sides is a method that Plato introduces most explicitly in the Parmenides but employs throughout the Sophist as well. It is especially useful in the Sophist for its ability to produce a well-motivated aporia and to encourage further inquiry when the investigation might have otherwise ended prematurely. A straightforward example of exploring both sides is Parmenides' display in the Parmenides (136e5–166c5). Parmenides considers two exclusive and exhaustive claims: first that there is one, then that there is not one. In each case he explores the consequences of the claim in question with an eye towards which one is true.11 As I intend the label 'exploring both sides', the criteria for identifying an instance of the method are as follows: The pattern of exploring both sides involves: (a) a set of what are at least taken to be exclusive and exhaustive claims (b) an independent consideration of each claim (c) an aim of establishing which claim is true Condition (a) requires that the claims considered are taken to be exclusive and exhaustive. In that case the claims must be understood propositionally, but I use the term 'claim' advisedly. In the discussion leading up to the Parity Assumption, the interlocutors treat the available options as something akin to what we would call a proposition but without the same precision. Because they do not clearly distinguish between concepts and propositions in this portion of the dialogue, nor between sentences and their metaphysical correlates, the 11 At 135c5–137b5 Parmenides explicitly recommends the very method he goes on to employ, and he makes clear that the method is aimed at discovering the truth. He begins by asking Socrates what he will do about philosophy (135c5) and continues with following exhortation: "Lift yourself up then and train more by what seems to be useless and is called prattle by the Many. [Do this] while you are still young: if you don't, the truth will escape you" (135d3–6). After a detailed description of exploring both sides he again stresses that it is necessary "if you, practicing properly, are going to thoroughly see the truth" (136c4–5). Zeno underlines the point as well, adding that "without this wandering, detailed excursion through all things it is impossible to have understanding while hitting upon the truth" (136e1–3). Vasilis Karasmanis draws attention to the basic structure of this method (2012), which I describe in greater detail as the method of exploring both sides, and as distinct from Plato's other hypothetical method(s), in my manuscript 'A Long Lost Relative in the Parmenides? Plato's Family of Hypothetical Methods'. 7 term 'proposition' runs the risk of importing distinctions that are not present, and perhaps even intentionally absent. This is an important point because it underlines a central difference between my interpretation and the standard interpretation.12 Note that condition (a) only requires that they are taken to be exclusive and exhaustive claims; as long as they are treated as such the method can lead to epistemic progress. On my view, this is in fact what happens with the alternative claims 'being is' and 'not-being is'. The interlocutors initially treat them as both exclusive and exhaustive as they take Parmenides to have done, but come to realize in the end that this was a mistake. According to condition (b), each alternative claim must be considered in turn. Thus a simple disjunctive syllogism as represented by the following procedure will not count as a case of exploring both sides: 1. A or B 2. assume A 3. show that C follows 4. but, independently, not-C 5. infer not-A 12 I understand the subject of the Parity Assumption as what are taken to be two exclusive and exhaustive claims ('not-being is' and 'being is') rather than simple concepts or notions. That is to say, on my view, the subjects of joint illumination are such that they can stand in an exclusive and exhaustive relationship where one is viable while the other is not (as with the claims 'there is one' and 'there is not one' in the Parmenides). This is not to rule out the idea that the interlocutors are thinking of the concepts of being and not-being as intimately related to the claims 'being is' and 'not-being is' at this point in the dialogue. Nor is it to rule out that Plato elsewhere distinguishes more clearly between concepts and propositions. In fact, I believe that an essential part of the dialogue's positive resolution is to distinguish more clearly between several related claims about being and not-being and the notions themselves in the so-called 'communion of kinds' passage (251c8–259e7) as I will argue below. Only then do the interlocutors clearly distinguish the kind 'not-being' from the combination of the kind 'not-being' with the kind 'being' (the metaphysical correlate of the claim 'not-being is') or the combination of the kind 'being' with 'not-being' in relation to some third kind (e.g. the metaphysical correlate of the claim 'being is not change'). This is no small development: one might initially think that the metaphysical correlate of 'not-being is' should simply be the kind 'not-being' rather than its combination with another kind. These problems are especially acute when it comes to forms of the verb 'to be'; I discuss these issues as they appear in the Sophist as well as their Parmenidean background in sections 2 & 3 below. 8 6. conclude B [disjunctive syllogism] An argument of this form does mention what are taken to be exclusive and exhaustive claims (A and B) but does not consider them independently, therefore does not meet condition (b). This condition highlights one important way in which exploring both sides can encourage further inquiry. In the Parmenides, for example, Socrates finds himself in trouble after Parmenides reveals a series of objections against his hypothesis concerning the existence of forms. Socrates appears about ready to give up, but Plato then has Parmenides make a curious move; he points out that someone who denies the existence of forms will be vulnerable to serious objections as well (Parmenides 135b5–c2). If they had stopped after the reductio of the first option, then Socrates might have thought he had good reason to abandon the project based on a simple disjunctive syllogism as represented above. But now they have a reductio against both sides, one for the claim that forms exist and one for the denial of that claim. A defeatist attitude no longer makes sense: further inquiry is needed to figure out which way to go. This situation, where there are serious problems for each of a set of exclusive and exhaustive claims, I will call a 'well-motivated aporia'. Below is a simple example with two claims (again, A and B). Note that steps 1–4 are identical to the disjunctive syllogism above, but in this case the inference 'not-A' is not drawn after step 4. This is because in this case steps 1–4 are part of a broader procedure for inquiring into whether A or B is true; 'not-A' would imply 'B' by disjunctive syllogism, but the inference is not yet drawn because the other side is yet to be explored. There may, after all, be a mistake somewhere in these first four steps. Steps 5–7 serve as a check on what has been found in 1–4 and are inconclusive: they license the inference 'not-B', but it conflicts with the available inference that follows from the previous steps. Thus no firm conclusion can yet be drawn and there is a well-motivated aporia: 1. A or B 2. assume A 3. show that C follows 4. but, independently, not-C 5. assume B 6. show that D follows 9 7. but, independently, not-D 8. aporia [well-motivated aporia] There is good reason to follow up a simple reductio with exploring the other side since one may unwittingly be in such a situation. And a well-motivated aporia itself calls for further inquiry, either by resolving the problems on either side or by what the Parity Assumption calls 'pushing the account through', revisiting the status of the alternative claims. It may be, for instance, that the initial assumption that A and B are exclusive and exhaustive is mistaken. The third condition for exploring both sides relates to the aim of the argument. For example, an argument by cases will meet the first two conditions but not the third: 1. A or B 2. assume A 3. show that C follows 4. assume B 5. show that C follows 6. conclude C [argument by cases] In an argument by cases, the goal is to show that some conclusion (C in this case) follows no matter which alternative (A or B) is true. In exploring both sides, the motivation is to establish which alternative is true rather than some other conclusion that follows. A simple case of exploring both sides might look like this: 1. A or B 2. assume A 3. show that C follows 4. but, independently, not-C 5. assume B 6. show that D follows 7. and, independently, D (or, at the very least, there is no support for not-D) 8. all things considered, conclude B [exploring both sides] Note that steps 1–8 once again represent a process of inquiry rather than a simple demonstration or deduction. The conclusion, B, follows from 1–4 alone via disjunctive syllogism. Yet the whole idea of exploring both sides is to provide a check on such an inference; there could, after all, be serious problems on the other side as well. In this case, 10 exploring the consequences of B does not lead to additional problems and to a wellmotivated aporia. Steps 5–7 on their own do not license the conclusion deductively but, all things considered, B is the most reasonable conclusion at this stage of the inquiry. Exploring both sides does not guarantee the truth of the conclusion since there is always a possibility that something went wrong along the way. Here the fact that the other side does not appear to have any problematic consequences, however, lends further support for B. There is a consistent pattern of exploring both sides in the discussion of being and not-being in the Sophist. More often than not it proceeds by first creating and then responding to a well-motivated aporia. A clear example arises in the so-called 'Battle Between Gods and Giants', part of the puzzle-setting section focused on being (245e6–249d5). The positions of the materialist Giants and the immaterialist Friends of Forms are eventually put in terms of change and rest, and the Visitor helpfully sums up one central argument as follows (their claims are initially taken to be exhaustive, but this is later revealed to be a mistake): V. It follows then, Theaetetus, that if things are changeless13 then there is nowhere any nous14 for anything about anything. T. Exactly. V. And further, if in turn we agree that all things are borne and changing, also according to this argument we will remove this very same thing15 from the things that are. (249b5–10) The Visitor begins this short passage by drawing a corollary from the preceding discussion, namely the contrapositive of the foregoing conclusion that if there is nous then there is change (248e7–b4). He uses the same verb that Plato's character Parmenides used to describe the consequences that follow from a hypothesis (συ#βαίνω; Parmenides 136a1, Sophist 249b5). After highlighting how there can be no nous without change, he looks to the other side and 13 Omitting the extra ')άντων' in Duke et. al. along with Burnet and the manuscripts. 14 I have left the Greek term 'νοῦς' transliterated since it is not obvious what the precise English equivalent is in this context. The term standardly refers to the virtue of intelligence or reasoning; Stephen Menn suggests the translation 'reason' in a helpful discussion of the term (1995, 14–18). In this context, however, it is not clear whether there being nous refers to forms having nous, individual souls having nous, the world itself containing some kind of rational order, or even its having nous in a world-soul as in the Timaeus. For present purposes, this issue will not affect our understanding of the argumentative pattern here. 15 i.e. nous. 11 suggests that there can equally be no nous if all things change. In what follows the interlocutors independently follow out this line of reasoning (249b11–c9). The two alternative claims are 'all things are changeless' and 'all things change'. It is clear that condition (b) is met since each claim is considered independently. The following lines make clear that it meets conditions (a) and (c) as well. The Visitor emphasizes how they must "fight with every argument" ()αντὶ λόγῳ #αχετέον) against someone who does away with nous, how a philosopher must not accept these consequences, and how they must be like a child asking for 'both' change and rest in response (249c6–d5). The first two points show that the interlocutors take the lack of nous to be a reductio rather than a positive consequence derived through argument by cases. The closing analogy to a children's wish shows that they take the options to be exhaustive (even though this is a mistake that will soon be corrected). The interlocutors take themselves to be at an impasse whose resolution requires somehow moving beyond the confines of what is rationally acceptable, like a child insisting on two incompatible desires.16 This application of exploring both sides, then, leads to a well-motivated aporia. While exploring both sides in this case does not immediately open the door to a positive resolution, it does help them identify where they went wrong. They soon come to realize that there is a third alternative of some change and some rest. Their initial mistake of treating 'all things are changeless' and 'all things change' as both exclusive and exhaustive highlights a central lesson of the dialogue.17 16 Gill also draws attention to this passage, which she calls the 'children's plea'. On her view the point is to emphasize that a proper ontology needs to countenance not only stable entities and changing entities, but entities which exhibit both change and stability (2012, 18, 98–9, 205, 229–30). This is consistent with my reading, though I take the emphasis to be on the fact that the claims as presented are not exhaustive, rather than their not being exclusive. 17 The distinction between opposites that are exhaustive and those that are not is explicitly set out and explained later on in the case of something being small as opposed to it being not-large (257b1–c4). See n.32 below for an elaboration of this point. 12 This is just one small-scale example of the pattern of exploring both sides that the Parity Assumption draws attention to.18 Another can be found in the positive resolution. By this time, the interlocutors have learned their lesson and set out three genuinely exclusive and exhaustive claims. Unlike before, only two claims run into problems. The third remains as the beginning of a solution to their previous difficulties. The Visitor and Theaetetus set up this final application of exploring both sides as follows: V. Well then, so that our speech may be directed towards everyone who has ever discussed being or anything whatsoever, let the present issues be addressed to them, as well as to as many others with whom we were previously discussing, in the form of a question. T. What sort of issues, exactly? V. Should we neither apply being to motion and rest nor anything whatsoever to anything else, but rather in this way posit these things in our accounts as unmixed and incapable of participating in one another? Or should we draw all of them into the same [account] as capable of partaking of one another? Or [should we say that] some are and others aren't? Which of these, Theaetetus, will we say they would ever choose? T. I at least am not able to answer on their behalf on these issues. V. Why then don't you answer one at a time, examining the consequences in each case? T. That's a good idea. (251c8–e7) Here the space of possibilities is divided into three alternative claims, either everything combines with everything else, nothing combines at all, or some things do while others do not. The claims are exclusive as implied by the Greek interrogative 'poteron' ()ότερον)19 and are genuinely exhaustive as well.20 The Visitor explicitly suggests that they explore each one independently, as they in fact do in the following conversation. They find that there are 18 See the appendix for a diagram representing this pattern of exploring both sides throughout the discussion of being and not-being as I see it. It includes this application of the method in the Battle Between Gods and Giants (under the heading 'type ontologies' as well as the other applications mentioned below in the order that they appear in the dialogue. 19 This word standardly introduces an alternative question as it does at the beginning of the Visitor's second speech quoted above, but is often best left untranslated as I have done in this case. 20 Hestir also notes that these are exclusive and exhaustive options (2016, 148). 13 unacceptable consequences for the first two claims, 'all things combine' and 'no things combine', but make positive progress in following out the consequences of the third, this time using not only the same verb but the same exact phrase for following out the consequences used in the Parmenides (σκο)εῖν τὰ συ#βαίνοντα, Parmenides 135e9–136a1, Sophist 251e5–6). From the beginning this is portrayed as a choice between three options, and they are clearly interested in which claim is true. Thus the general pattern of exploring both sides is realized here as well. Not only does this argument meet the criteria for exploring both sides as defined above, but it also portrays itself as the continuation of a discussion begun earlier in the dialogue. The Visitor explicitly refers back to those "with whom we were previously discussing" and alludes to previous positions discussed.21 Similarly, in discussing change and rest he recommends that they do so "just as we questioned those others before" referring back to the discussion with the hot and cold dualists (249e6–250a7). There too the interlocutors explore what are taken to be exclusive and exhaustive claims, with the pluralists on one side and monists on the other. After reaching an impasse with count-ontologies they 'push through' by formulating the claims based on the type or quality of beings rather than their number.22 On my interpretation, the Parity Assumption describes this very pattern of creating and responding to a well-motivated aporia and emphasizes the option of 'pushing through'. The well-motivated aporia at the level of being and not-being is what justifies the Visitor in making the Parity Assumption. In response, the communion of kinds passage represents them 'pushing through' with a new set of alternative claims. 21 For example, those who "apply being to motion and rest", the focus of their inquiry just a few pages earlier. 22 Again, see the appendix for a diagram that lays out the structure of the successive applications of exploring both sides. The type-ontologies are the Giants' position that only what has touch and impact is (246a10–b1) and the Friends' position that true being is knowable and bodiless forms (246b6–8), later summarized as 'all things change' and 'all things are changeless' as discussed above. Lesley Brown points out how the Visitor splits the positions about being into countvs. type-ontologies (1998, 185). The first time we get a hint of this dichotomy, as Brown notes, is at 242c4–6 (τὰ ὄντα ... )όσα τε καὶ )οῖά ἐστιν) and it is emphasized again when they transition to the discussion of type ontologies at 245d12–246a2 (τοὺς δὲ ἄλλως λέγοντας αὖ θεατέον). 14 §2 The Context: Being and Not-Being as Exhaustive Alternatives Now that we have the structure of exploring both sides in front of us I will argue that this structure is in fact what is being described in the Parity Assumption. I will begin with the second set of questions from the introduction: Why is the Parity Assumption announced so late in the discussion of being and not-being? And why did the interlocutors even bother to discuss being in the first place? After all, it was only a claim about not-being that caused difficulties for defining the sophist. As far as the standard account is concerned, the Parity Assumption could have just as easily been announced immediately after the interlocutors encounter problems with 'not-being is'. In fact, this is what one should expect on the standard interpretation of the Parity Assumption; if the reason for discussing being is to get clear on not-being, then shouldn't the Visitor announce this before the discussion of being? On my view, the Parity Assumption is not made earlier because only after they encounter problems with being have the interlocutors, especially Theaetetus, realized that there is a well-motivated aporia that needs to be dealt with. After finding unacceptable consequences on the side of not-being, someone like Theaetetus might think they are in the clear; assuming that the route of being is straightforwardly acceptable, they should simply reject not-being by reductio and stick with what they know. Only after Theaetetus has explored the other side and realized that he is in equal, if not greater confusion about being is there a deep problem that needs to be addressed. This highlights an important difference between the standard interpretation and my interpretation about what it means for one side or the other to be clear. On the standard interpretation, the relevant sense of illumination or being clear is properly understanding a concept such as being or not-being. On the flip side, a concept is unclear when there are problems with understanding the concept (as there turn out to be for both being and notbeing). The progression of the discussion on the standard view is as follows: (1) the interlocutors find problems with and are thus unclear about not-being, (2) the interlocutors find problems with and are thus unclear about being, (3) the Parity Assumption announces that clarifying one with clarify the other. On my interpretation, however, the interlocutors are discussing what they take to be exclusive and exhaustive claims: a view of reality that includes not-being, characterized by the claim 'not-being is', and one that does away with 15 not-being, sticking with the claim 'being is'.23 Unlike a concept, a claim is unclear when one is unsure whether to accept or reject it. That is to say, it is clear either when one is sure that it should be accepted or when one is clear that it should be rejected. On my view, then, the progression of the conversation is somewhat different: (1') the interlocutors find problems with 'not-being is' but, assuming that there are not analogous problems with 'being is', are initially clear that they should reject the former claim and accept the latter; (2') the interlocutors nevertheless a) explore the other side, b) find that there are in fact problems with this alternative claim as well, and c) are thus in a well-motivated aporia, uncertain about whether to accept or reject either claim; (3') the Parity Assumption announces that clarifying whether or not to accept one claim will clarify whether or not to accept the other. This explains why the announcement of joint illumination in the Parity Assumption comes after (2): this is the first time they fully come to realize the lack of clarity in their present position. In the next section we will see exactly why the structure of their well-motivated aporia justifies an expectation for joint illumination. First, a closer look at the preceding discussion confirms that the discussion of being and not-being uses the method of exploring both sides to create a well-motivated aporia. Conditions (b) and (c) from the previous section are clearly met: claims about being and claims about not-being are examined independently and with a direct interest in the claims themselves. Condition (a) is less obvious: do the interlocutors really take these claims to be exclusive and exhaustive? The progression of the discussion and the explicit Eleatic background show that they do. The Eleatic background in the Sophist is hard to miss. The Visitor is introduced as coming from Elea and as a follower of his fellow Eleatics Parmenides and Zeno (216a3). He then kicks off the discussion that leads to the Parity Assumption by directly quoting Parmenides' poem: V. This account has dared to assume that not-being is; for falsity would not have come about in any other way. The great Parmenides, son, maintained steadfastly starting from when we were children and through to the end, speaking on each occasion both in prose and in meter: For this won't ever be tamed, he says, that not-being is 23 See n.28 below for more detail on what is entailed by each of these claims. 16 rather you must withhold your thought from this route of inquiry It is testified then by him, and if tested in due measure the account itself most of all should make it clear. Let's look at this then first, unless you somehow disagree. T. As far as I'm concerned, posit what you like. As for the argument, examine yourself where it goes through best and lead me down that route. (237a2–b6) Here the Visitor draws attention to their own implicit assumption that not-being is, one that the ensuing aporiai will reveal as problematic.24 He underlines the point by bringing in Parmenides' injunction against the position and with it the context of Parmenides' poem itself. At least on one interpretation of Parmenides' poem, Parmenides sets out two exclusive and exhaustive 'routes of inquiry' (ὁδός διζήσιος, fr. 2.2, 6.3, 7.2)25 related to being and not-being respectively.26 The metaphor of a physical 'route' (ὁδός) fits best with thinking of these in terms of exclusive and exhaustive claims where there is a forced choice between one route or the other.27 And the very same language is vividly repeated in the Sophist. In the above quote, after the Visitor recites Parmenides' injunction to stay away from the "route" 24 This highlights another striking parallel with the Parmenides, further supporting the idea that the method of exploring both sides is relevant to the Sophist as well. The Visitor uses the same language of hypothesis here found in the description of exploring both sides in Plato's Parmenides (ὑ)οτίθη#ι, 135e9, 136a2). Furthermore, the Parmenides explicitly recommends applying the method to this very position when he elaborates on the method a few lines later: "And the same account applies to dissimilarity and to change and rest and generation and destruction and to being itself and not-being" (Parmenides 136b4–6). Here he specifically mentions notbeing along with a list of other 'greatest kinds' also discussed in the Sophist (254d4ff). Given the procedure as recommended in the Parmenides, one of the hypotheses addressed would be 'not-being is'. 25 The relevant line of fr. 7 is in fact quoted at Sophist 258d3. 26 On one standard interpretation, the first route is explored primarily in the first two thirds of fragment 8 (though also in fragments 3, 4, and 6) and the second route primarily in the last third of fragment 8 and 9–15 (though also in fragment 6). See also the end of the first fragment for the injunction to learn the opinions of mortals in addition to the truth about reality. 27 Alexander Mourelatos is explicit that he understands the two routes as exclusive and exhaustive in his The Route of Parmenides (1970, 71). In Chapter 2 and Appendix 2 he argues that each route should be understood as a "sentence frame" of the form '__ is __' and '__ is not __' respectively. Cf. n.28 below. 17 of saying that not-being is (ὁδοῦ, 237a9), Theaetetus asks him to "lead me down this route" (ὁδόν, 237b6). Later, after the Visitor indicates that he might be switching sides, he uses the same language to refer to the other route: V. Come then, with what beginning should someone begin a daring argument? For I think, boy, that we must absolutely take the following route. T. [A route] of what sort? V. First to review the things now seeming to be clear, lest we may somehow be in confusion about these things but recklessly agree with each other that we are in the right. T. Tell me more clearly what you mean. V. Parmenides seems to me to converse with us carelessly, as well as everyone who ever yet hastened toward a judgment of determining with respect to the things that are how many and what sort they are. T. How so? (242b6–c7) Again, the Visitor suggests they "take the following route" (ὁδόν, 242b7), now referring to the alternative claim that being is.28 Furthermore, just before this the Visitor maintains that the only way out of their problems is either to agree with or to refute Parmenides' account 28 To be more precise, the interlocutors focus on corollaries of the claim 'being is' that aspire to give a complete characterization of reality excluding not-being. These claims consistently take the form 'being is __' or '__ is' with 'being' occasionally replaced with some equivalent. For example: "the all is hot and cold or some two things such as this" (243d8–9); "the all is more than one" (244b3); "the all is one" (244b6); "being is some two things or only one" (245e1–2); "only that which yields some impact and touch is" (246a11–b1); "true being is some knowable and bodiless Forms" (246b7–8); "the beings are nothing other than capacity" (247e4); "no beings change" (249b5); "all things are borne and changing" (249b8–9); "the all rests" (249d1); "being changes in every way" (249d2); "both [change and rest] are" (250a11–12). Compare this with Mourelatos' interpretation of Parmenides using the sentence frame '__ is __' mentioned in the previous note. This is analogous to the situation with not-being: there the claim 'not-being is' is thought to be required for the possibility of false appearance and false speech, which can only be accurately described with claims of the form '__ is not __' (e.g. "what he said is not true", or "even though it appears to be, the second line is not any longer than the first"). 18 (241d5–e6).29 This very dichotomy of two 'routes of inquiry' occupies the background of the entire discussion leading up to the Parity Assumption.30 On the one side is the claim 'not-being is', as well as what are taken to be its corollaries: that falsity is possible and that being is not. On the other side is the claim 'being is', as well as its perceived corollaries: that falsity is impossible and that not-being is not. The former characterizes reality as including not-being, which is seen as the only way to accommodate falsity and claims of the form '__ is not __'. The latter follows Parmenides in excluding not-being from a complete characterization of reality, initially taken to exclude all falsity and only allow for claims of the form '__ is __' (though the interlocutors will later see this as a false dichotomy). These claims are in fact a main focus throughout the discussion leading up to the Parity Assumption, even when it may seem as if they are talking about the meaning of the concepts 'being' and 'not-being' as assumed by the standard interpretation. For instance, Theaetetus describes their task in the discussion of being as "to track down being first, what in the world those talking about it think they are indicating" (243d3–5), but in the discussion that ensues they focus on metaphysical theses about the number and type of things that exist. Similarly, they ask the dualists in particular what they mean by 'being' in statements such as 'being is two' (243e2), but in answering this question focus on the truth or falsity of the position itself (cf. 243d8–9 & 245e1–2). In the discussion of not-being, too, they go back and forth between talk of not-being and of related claims. As we have seen, it is the hypothesis 'not-being is' that kicks off the discussion in the first place. The Visitor describes their discussion as 'the refutation of notbeing' (τὸν τοῦ #ὴ ὄντος ἔλεγχον, 239b2–3), only to later emphasize the same claim as before when he says: "the many-headed sophist has forced us to agree against our will that in a way not-being is" (... τὸ #ὴ ὂν ... εἶναί )ως, 240c4–5).31 29 Palmer's considered view in Plato's Reception of Parmenides is that Plato takes this to be a sophistic appropriation of Parmenides. But even if it is not Plato's own preferred interpretation it still plays a central role here. 30 See also 240e1–2, where 'not being is not' and 'not being is' are portrayed as alternative claims as introduced by the Greek interrogative ')ότερον'. 31 The position is similarly emphasized at 237c7–8, 238a8–9, 238c5–6, 239b7–10, 240e1–241a1, 241b1–3, 241d6–7, 246a1–2, 254d1–2, 256d11–e5, 258b7–261b3 and even in the Statesman (284a7–8). In many of these latter instances the related position 'being is not' is also emphasized. 19 This all goes to show that condition (a) is indeed met; the interlocutors take themselves to be dealing with two exclusive and exhaustive claims. Yet one might still wonder: if it is important for understanding the method here that the interlocutors are engaged with what they take to be exclusive and exhaustive claims, why all the confusion? Why do they not acknowledge more clearly and explicitly what they are up to? First, on my interpretation the Parity Assumption does in fact acknowledge the structure of their inquiry in a self-conscious fashion, as does the Visitor's claim about needing to discuss being to avoid mistakenly thinking that they are in the clear (quoted on p.17 above). But it is also important to emphasize that what is depicted in the Sophist is a circuitous process of inquiry, one that that explores various positions rather than straightforwardly laying out a single view. Along the way, the interlocutors develop more precise ways of speaking. The confusion in the discussion of being and not-being is part of the point: it shows how certain misconceptions can cause problems and how a proper inquiry can reveal and resolve them. The idea that 'being is' and 'not-being is' are exclusive and exhaustive claims is one of these very misconceptions. Plato has Socrates highlight the possibility of this type of misconception with his opening premonition that the Visitor is "some elenctic god coming to observe and refute us as careless in our way of speaking" (216b5–6).32 32 There are many examples of an initial lack of regimentation early in the discussion that is corrected by the end of the dialogue. For instance, the interlocutors frequently confuse the difference between contraries and contradictories before the issue is clarified at 257b1–c4. In the first definition of the Sophist they mistakenly infer from the fact that he is not a layman that he is a complete expert (221d1–6). The same mistake is made even more explicitly at 240b5 and again at d6–8 where the Visitor says that not-true is the contrary (ἐναντίον) of true, only later to assert that negation does not signify a contrary (ἐναντίον, 257b9). The very same mistake leads to the final aporia just before the Parity Assumption, where they assume that not changing implies rest and not resting implies change, leaving out the possibility that something may neither change nor rest (250c12– d3). In the discussion with the monists and pluralists, the interlocutors rather haphazardly contrast the position 'being is one' with 'being is two', leaving out other pluralist positions (see e.g. 245d12–e1). The distinction between finite and infinite pluralities is only made later on at 252b1–6 and is important because the argument against the dualists will not work against someone who posits an infinite plurality. Another salient example comes in the fifth definition of the sophist, where the final distinction is between those who argue on either side for pleasure and those who do so for profit. The latter is identified as sophistry, whereas the former is called 'prattle' ('ἀδολεσχική'). This division again is not exhaustive, as there may very well be other aims rather 20 The Visitor himself is explicit that he is wary of giving a straightforward display of his views. Socrates leadingly asks him whether he would like to go through the issue on his own or via question and answer "just like I did with Parmenides when he used question and answer, going through quite fine arguments when I was young and he was much older" (217c1–7). Socrates recommends the young Theaetetus, thus recreating the dynamic of the conversation with Parmenides that he alludes to (as depicted in Plato's Parmenides, another hint that the methodology of exploring both sides is indeed relevant to the Sophist). The Visitor agrees and says he would be ashamed to give the impression of offering a display (ἐ)ίδειξιν, 217e2). Instead, he consistently describes their conversation using the language of inquiry.33 This is not to say it is a joint inquiry between equals: the differences in age, experience, and position are significant.34 But there is nevertheless a clear emphasis on the epistemic progress being made by the interlocutors coming to realize their own ignorance and then overcoming it.35 than pleasure or profit. Interestingly, the very same word for prattle is used in the Parmenides to describe how exploring both sides is seen by the many (ἀδολεσχία, 135d5). This is yet another important methodological connection with the Parmenides that suggests we should be on the lookout for exploring both sides in the Sophist as well. 33 Starting at this very point, the Visitor and Theaetetus talk of examining (σκέ)το#αι/σκε)τέον/σκέψις: 35 occurrences), searching (ζητέω/ζήτησις: 17 occurrences), testing (βασανίζω: 2 occurrences), and hunting (θηρεύω/δυσθηρευτός: 5 occurrences; #εταδιώκω/#εταθέω: 3 occurrences; διερευνάω: 3 occurrences). The only use of 'ἐ)ίδειξις' is the one just quoted, characterizing what the Visitor hopes to avoid. The cognate 'ἐ)ιδείκνυ#ι' is used twice to describe the sophist's practice (230b7 & 234b9) and only once to refer to the Visitor and Theaetetus' discussion when they display their results at the end (265a1). 34 Theaetetus is portrayed as a young man who is likely encountering many of these arguments for the first time, whereas the Visitor has been through similar arguments before (217b5–9). For example, the Visitor realizes their confusion about being before Theaetetus does (249e2–5). Later in the dialogue the possibility of their talking past one another is made particularly salient when the Visitor and Theaetetus realize that they have different interpretations of Theaetetus' answer to a question (261d6–262b3). 35 For these reasons, I find it slightly misleading when Frede, Brown, and Hestir claim that the Sophist is atypical in its relation to Plato's own views. Frede calls the Sophist "the most dogmatic of all of Plato's dialogues" (1996, 135) and Brown calls it "markedly didactic" (2008, 438), both suggesting in their respective pieces that we can be more confident that Plato's own views are to be found in the Visitor's words (see also Hestir 2016, 107). I 21 The modest epistemic progress of first realizing what one doesn't know is explicitly highlighted throughout the discussion and is one of the motivating factors behind exploring both sides. After encountering the problems with not-being and some cautious repositioning on the Visitor's part,36 he opens the discussion of being "to review the things now seeming to be clear, lest we may somehow be in confusion about these things but recklessly agree with each other that we are in the right" (242b10–c2, also quoted on p.17 above).37 This trope of unwittingly being in ignorance is familiar from elsewhere in Plato, but also from earlier in the discussion of the so-called 'noble sophist' (229c1–6, 230b4–5). Being refuted so as to realize one's own puzzlement is there characterized as a purification of no small importance (230d7–e4). Here the Visitor merely flags the possibility that they are in such a position, but he suggests this more emphatically after the first aporia about change and rest: V. Oh blessed one, don't you notice that we are now in the greatest ignorance about [being],38 though appearing to ourselves to have something to say? agree that the dialogue takes a strikingly different approach from many of Plato's elenctic works in the way that it begins and ends, but it is important not to lose sight of the thoroughly elenctic and aporetic nature of the initial discussion of being and not-being in particular. Through exploring both sides, the interlocutors offer refutations of what are taken to be exclusive and exhaustive claims that lead to well-motivated aporiai. This shows that the language of inquiry highlighted above is not a mere pretense, but is still consistent with the idea that the positive solution contains views about false statement that the author himself wishes to endorse. 36 The Visitor asks Theaetetus' lenience on three counts. First he asks that Theaetetus welcome even the slightest improvement of their present impasse (241c7–10), second that he not take the Visitor to be a parricide by taking on Parmenides' account in their own self-defense (241d1–242a4), and finally that he not take the Visitor as crazy for turning back and forth at every step (242a5–b5). All three requests make good sense on my interpretation where the interlocutors are about to embark on a project of exploring both sides, one that will require taking both sides seriously as well as testing them rigorously, and that will require patience with what may be only incremental improvements. 37 Again, this makes little sense as a motivation for discussing being on the standard interpretation. On this view, the reason is to clarify not-being, not to confirm whether they are clear about being. But, as I have suggested, checking to see whether an apparent reductio is in fact just one half of a well-motivated aporia is in fact part of exploring both sides. On my view, then, the Visitor's avowed motivation makes perfect sense. 38 Literally the text reads 'it' (αὐτοῦ), but the pronoun refers to 'being' (τὸ ὄν) at 249d7. 22 T. I think we have something to say; I don't entirely understand how, in turn, it has escaped our notice that we are in this state. (249e2–5) Theaetetus here is somewhat hesitant to embrace the thought that they are in fact in such confusion about being. Yet after one final attempt at making sense of the claim 'both change and rest are', Theaetetus finally admits that they may be even more puzzled about being than about not-being (250e1–4). The Parity Assumption comes immediately afterwards, warranted by the interlocutors' full realization of the problems with each of their alternative claims. The overarching strategy of the discussion of being and not-being, then, is to raise problems with the seemingly clear side of being in order to motivate the resolution of the difficulties with not-being as well. Up to this point exploring both sides has made modest epistemic progress by helping the interlocutors see that they are confused even where they thought they were in the clear. And only at this point, when they have explored both sides and found problems with each, can the Visitor genuinely express the hope of the Parity Assumption. §3: A Warranted Sense of Hope Now we can address the first two questions about the Parity Assumption: what is the best way to understand the prediction of joint illumination, and why is it said to follow from their present aporia? Rather than seeing it as a mere assumption, understanding the claim as a genuine expectation warranted by the structure of exploring both sides will help answer these questions. It will also resolve a series of key interpretive puzzles that have been overlooked by the standard account. The central advantage of my interpretation is that it explains these features of the Parity Assumption, most importantly its justification based on the preceding discussion, that the standard interpretation is hard-pressed to accommodate. The Visitor announces the Parity Assumption just after Theaetetus admits that they might be in even greater confusion about being than about not-being. It is worth going over my translation once again along with the Greek for a more detailed understanding of what the announcement really entails: The Parity Assumption Ξ. Τοῦτο #ὲν τοίνυν ἐνταῦθα κείσθω διη)ορη#ένον* ἐ)ειδὴ δὲ ἐξ ἴσου τό τε ὂν καὶ τὸ #ὴ ὂν ἀ)ορίας #ετειλήφατον, νῦν ἐλ)ὶς ἤδη καθά)ερ ἂν αὐτῶν θάτερον εἴτε ἀ#υδρότερον 23 εἴτε σαφέστερον ἀναφαίνηται, καὶ θάτερον οὕτως ἀναφαίνεσθαι* καὶ ἐὰν αὖ #ηδέτερον ἰδεῖν δυνώ#εθα, τὸν γοῦν λόγον ὅ)ῃ)ερ ἂν οἷοί τε ὦ#εν εὐ)ρε)έστατα διωσό#εθα39 οὕτως ἀ#φοῖν ἅ#α. V. Then indeed let this stand as containing a serious source of puzzlement; and since both being and not-being alike have had their share of puzzlement, already at this point40 there is an expectation that insofar as one of the two shows up as either more obscure or clearer,41 the other too shows up similarly. And if in turn we are not able to see either one of them, we will in this way push the account through both at the same time, however we are able to do so most appropriately.42 (250e5–251a3) Three interpretive issues arise when giving a translation of the text, each of which provides a constraint on an adequate reading. The first is how to understand the language of clarity and obscurity, that is the talk of the way that something might "show up" (ἀναφαίνω), of its being "clearer" (σαφέστερον) or "more obscure" (ἀ#υδρότερον), and of the possibility of not being able to see (ἰδεῖν). The second is how to understand the present tense of the verbs meaning 'show up' in the Greek, which implies that they will do so simultaneously. The third is how to translate the final clause, which Duke et. al. emend in order to fit better with the standard interpretation established by Owen. My interpretation provides a preferable explanation for each of these otherwise puzzling aspects of the passage. When it comes to the language of clarity and obscurity, past interpreters have taken the word 'show up' (ἀναφαίνω) in a positive manner to mean 'come to light'. They then read 'clearer' and 'more obscure' adverbially, indicating different degrees to which something might come to light. This appears to be Notomi's reading, for instance, when he translates: "if one of these will turn up, whether faintly or clearly, the other will also turn up in this way" (2007b, 258) and similarly Owen "if one of them can be made out to a greater or less degree 39 Printing 'διωσό#εθα' with the manuscripts and with Burnet rather than the emendation 'διακριβωσό#εθα' of Duke et. al. See below for details. 40 Taking 'νῦν' and 'ἤδη' together (cf. ἤδη II in the LSJ). 41 Taking 'ἀ#υδρότερον' and 'σαφέστερον' as predicate nominatives with 'ἀναφαίνεσθαι' (cf. ἀναφαίνω II.2 in the LSJ). 42 Taking 'ἐυ)ρε)έστατα' adverbially (cf. Symposium 198d6). 24 of clarity the other can be made out to the same degree" (1970, 229).43 Yet my translation stays closer to Plato's use of these terms. 'Show up' does not have the positive valence of something becoming clear and unproblematic as 'coming to light' does; in fact, it can describe an appearance that is deeply obscure and problematic.44 On the other hand, 'clearer' clearly has a positive valence and 'more obscure' a negative one.45 Thus the two comparatives, rather than qualifying the degree with which something might come to light, suggest it becoming either clear and unproblematic in a positive way or obscure and problematic in a negative way. As a result, they are best translated as predicate nominatives rather than adverbs, hence my translation: "if one of the two shows up as either more obscure or clearer, the other too shows up similarly."46 On Owen and Notomi's reading the passage only says something about when one of the two sides becomes clearer. But if we stick with the standard meanings of the 43 While Notomi's translation is less explicit on this point than Owen's, it is clear from a later paraphrase that this is how he understands it: "if one of the two is made clear, the other becomes clear as well" (260). 44 The clearest evidence for this point is just a few lines above, where being is said to have 'shown up' (ἀνα)έφανται) outside of both change and rest even though this is the 'most impossible of all things' (250c9– d4). Another clear case where there is no such positive valence is Republic 487b7. There Adeimantus is objecting to an argument Socrates has just made by saying that people often feel that, despite agreeing to a series of questions, they have been led astray little by little until "the opposite of what they said before shows up" (ἐναντίον τοῖς )ρώτοις ἀναφαίνεσθαι). This appearance contains a contradiction and so the word must not have a positive valence here. The word is used three times elsewhere in the Sophist. Twice it simply refers to where the sophist showed up in one of the divisions (224d2, 231d8) and once to the way in which not-being appeared in the positive solution (260b8). None of these have an explicitly positive valence either. 45 Elsewhere in Plato the word 'obscure' (ἀ#υδρός) has a strongly negative valence. In Republic X Socrates suggests that something not being that which is, but being like it, will turn out to be an 'obscure' matter (597a10). In the Timaeus the receptacle is introduced as an 'obscure' and difficult kind (49a3). And in the Theaetetus, wax in the soul that becomes 'obscured' as a result of being too soft gives rise to indistinct perceptions (195a). It is implausible to understand the word adverbially here to mean 'clarify more obscurely' as others have. 46 While I prefer the predicate nominative construction, my interpretation is still consistent with taking the comparatives adverbially. In that case I would translate: "insofar as one of the two shows up in either a more obscure or a clearer manner..." 25 terminology in question, it also says something about when one side becomes more obscure. But why would there be a parity in both their clarity and their obscurity? This suggestion makes perfect sense given the background I have argued for, where we are considering what are taken to be exclusive and exhaustive claims that are clear to the extent that one should be accepted or rejected. Two exclusive and exhaustive claims have a special relation to one another: if you are clear about accepting one you should be equally clear about rejecting the other. And if you are unclear about whether to accept or reject one, you should be equally unclear about whether to accept or reject the other. There will indeed be this dual sense of parity when dealing with such claims: either a clear sense that one claim is to be accepted will be accompanied with a clear sense that the other should be rejected, or there will be a wellmotivated aporia where there are significant reasons against either accepting or outright rejecting either side. This is precisely where the interlocutors find themselves at the time of the Parity Assumption: they are in a well-motivated aporia where they want to accept that not-being is in order to properly define the sophist, but have heeded Parmenides' warning and encountered serious problems. They also want to accept that being is but, to their surprise, have found equal if not greater problems on that side as well. What the Parity Assumption initially offers is hope that, just as they have observed both sides become unclear in tandem, the two will become clear in tandem as well. Further inquiry may still be worthwhile.47 47 I do not want to overstate my disagreements with the standard interpretation. My view is consistent with the view that one important aspect of the conversation is getting clear on the kinds 'being' and 'not-being'; this much is clear given the positive advances in the communion of kinds passage, not least the analysis of notbeing as difference. But what the standard interpretation misses is the consistent interest in different claims about being and not-being that are taken to be exclusive and exhaustive, an important structural feature of the conversation that justifies the Parity Assumption. Part of the positive work being done by the communion of kinds passage is precisely to distinguish between the kind itself (something akin to a concept) and its combination with other kinds (something akin to a proposition or state of affairs, the metaphysical correlate of a claim). A view that positively denies that exploring both sides plays any role here would have to explain away the instances of exploring both sides as discussed above (see also the diagram in the appendix) and give an alternate reading of the Parity Assumption that explains how the claim about simultaneous joint illumination or obfuscation is justified by what comes before. 26 This same observation resolves the second interpretive puzzle. On the standard reading, the point of the Parity Assumption is that the very solution to one set of problems will resolve the other set as well. But the present tense of the verb 'show up' in both of its occurrences ('ἀναφαίνηται' and 'ἀναφαίνεσθαι' in the Greek) is puzzling if this is what the Visitor means. The moods and tenses of the two verbs constitute a present-general conditional where the mutual clarification is implied to be simultaneous.48 But how is it, for instance, that clarifying the problems with being would simultaneously clarify those with notbeing? Heindorf emends the second occurrence of the present-tense verb to the future so that it constitutes a future-more-vivid conditional instead, more consistent with the idea of two separate clarifications.49 But the text as it stands makes perfectly good sense when read in light of the unique structure of exploring both sides. Reasons for accepting one of two exclusive and exhaustive claims are equally reasons for rejecting the other; the clarification of the other side will be automatic without any need for a separate application. Interpreters have also been tempted to emend when it comes to the final issue of what the visitor means by "pushing the account through". I have opted for the more conservative route of keeping the text as it stands rather than emending.50 On any construal 48 See Smyth 2336b. 49 The future, of course, would indicate future action in this context (Smyth 2326). Both present-general and future-more-vivid conditionals begin with 'ἐάν' + subjunctive in the protasis (or in this case, 'καθά)ερ ἄν' in place of 'ἐάν'; cf. καθά II in the LSJ). The only difference in form is that present-general conditionals use the present tense in the apodosis and future-more-vivid conditionals use the future (Smyth 2297, Goodwin 397). 50 I have given the same construal of the grammar as Notomi and Owen, originally suggested by Campbell. Campbell takes 'λόγον' as the direct object of 'διωσό#εθα' and reads 'ἀ#φοῖν', referring to the pair of being and not-being, as a genitive governed by the διαprefix. While 'διωθέω' often means 'fend off' (e.g. Herodotus Histories 8.3, Isocrates Antidosis 320) it can also mean 'push through' (Timaeus 68a1, Xenophon Cyropaedia 7.5.39, Hippocratic De morbis 2.30). In the latter cases the accusative direct object is the thing through which the subject is pushed, but there are other cases where the accusative direct object is the thing pushed with 'δία' + gen. to indicate the thing through which it is pushed. Campbell cites such a parallel in Polybius (Historiae 21.28.14) but there is a closer parallel in Xenophon: "οὐ διέωσαν διὰ τῆς κόρης τὰς χεῖρας" (Hellenica 2.1.8). The only issue is that 'δία' is repeated in these cases unlike in the Parity Assumption. While the prefix does tend to be repeated in prose (Smyth 1654) this is not always the case. For instance, in the Timaeus Plato uses the verb 'διαβιάζο#αι' with the genitive and without repeating the prefix to describe air being forced through the veins: "τῶν φλεβῶν 27 that retains the text as is, there is a question about what the Visitor might mean by the relatively rare verb I have translated 'push through' (διωθέω). Yet the Duke et. al. version avoids this question by changing the verb. In explaining their decision to emend, Robinson reports being so persuaded by Owen's interpretation of the previous lines that, even though he admits that the text is grammatically possible as it stands, he thinks it preferable to change the verb to 'make accurate' (διακριβόω) so that the Visitor essentially repeats what he said above (1999, 153–5). The more conservative option is preferable on purely paleographic grounds, and again makes perfectly good sense on my interpretation. On my reading, this final line describes what should happen if both sides remain obscure. After all, it is perfectly possible that the interlocutors will not be able to make progress by clarifying either side of their well-motivated aporia. Maybe what is needed is a new way of understanding the alternative claims in the first place; perhaps there is another claim that avoids the Scylla of one and the Charybdis51 of the other (as the interlocutors found with 'all things change' and 'all things rest'), or perhaps there is an entirely new way of dividing up the options (as in the transition from count ontologies to type ontologies). This is how I read the point about not being able to see: if joint illumination fails, if both sides remain 'more obscure', it is worth trying to push through to a new way of conceiving the alternative claims in the first place. This is precisely what the interlocutors do in the communion of kinds passage.52 διαβιαζό#ενον" (84d6). Another equally viable alternative would be to emphasize the middle voice of 'διωσό#εθα' and translate "we will push ourselves through the account of both" (thanks to Marko Malink for this suggestion). As for 'ἀ#φοῖν', Cornford cites the same word at 226a8 to support his translation 'with both elbows', but it certainly need not mean this as it clearly does not in the dialogue's three other cases (243e1, 246c6, 248b3). Alternatively, it could be taken as a dative of interest, hence 'for both' instead of 'of both' or 'through both'. While nothing here can decide the issue definitively, I prefer the latter reading since it fits best with the way in which the alternative claims are re-envisioned in the ensuing discussion. 51 Campbell, Owen, and Notomi all draw attention to this potential allusion. 52 This contains the most regimented application of exploring both sides in the Sophist (discussed on p.12 above). The interlocutors have learned their lesson and explore three alternative claims that are genuinely exclusive and exhaustive: all kinds combine with one another, no kinds combine with one another, or only some do. 28 One final point worth noticing, and one that is equally hard to account for on the standard interpretation, is that the Parity Assumption is said to follow since (ἐ)ειδή) they have been in aporia about being and not-being. The standard interpretation focuses only on the forward-looking implications of the Parity Assumption and lacks any resources to explain why this might be the case. But the preceding context does indeed justify an expectation for joint illumination. The interlocutors have reached a well-motivated aporia through exploring both sides, and the very structure of this aporia suggests that becoming clear on whether to accept or reject one claim will thereby clarify the other as well. The hope brought about by their well-motivated aporia is twofold. The fact that both sides became unclear in tandem, that in both cases they were unsure whether to accept or reject the relevant claims, lends further support for the idea that they are in fact exclusive and exhaustive. And if they are exclusive and exhaustive they will be clarified in tandem as well. This is a hope, not a guarantee, because the claims as presently construed may not allow for clarification. The need may arise to push through their initial division to a new way of understanding (as they in fact do).53 On behalf of the standard interpretation, however, one might worry that the labels 'being' and 'not-being' as used in the passage do not represent the right entities to be involved in a well-motivated aporia. If my interpretation were right, the worry goes, then why does the Visitor fail to specify at this point that the alternatives are 'not-being is' on the one side and 'being is' on the other (along with their corollaries)? I grant that the Visitor is not being as precise as he could be, though suggest that this is part of the point. We have already seen how the preceding discussion inherits a Parmenidean understanding of being and not-being as representing two exclusive and exhaustive routes of inquiry, an understanding that they ultimately reject. Owen himself makes another off-hand comment that supports this idea: he suggests that "historically, [the Parity Assumption] is the appropriate reply to Parmenides" (1970, 231). Owen does not elaborate any further, however my interpretation does explain 53 The Greek conjunction 'ἐ)ειδή' can also have a purely temporal sense and may alternatively be translated 'after'. Even if one reads the clause temporally we can still ask why the Visitor specifies that the expectation of parity comes only after their present impasse. My account of why the Parity Assumption is justified by the preceding context helps explain why the Visitor would explicitly draw attention to the timing here (in addition to the reasons offered in the previous section). 29 how to read this part of the Sophist as an appropriate response. Parmenides took being and not-being as alternative claims that are exclusive and exhaustive, but the process of exploring both sides shows this assumption to be mistaken. We also need to be wary of anachronism here. While it is not entirely uncomfortable for us to use 'being' and 'not-being' as shorthand for exclusive and exhaustive claims (however mistaken this may ultimately be), it may have been even less so for Plato's contemporaries.54 Nowhere in the Sophist, at least not up until the Parity Assumption, do the interlocutors clearly distinguish between concepts and propositions. And given the Parmenidean context the two might not have been so clearly separated. No clear distinction between concepts such as 'being' and propositions such as 'being is' is made in Parmenides' poem either; after all, he famously says: "for the same thing is for reasoning and for being" (fr. 3).55 Our interpretation should be guided by the way the discussion actually proceeds in the aporia that the Visitor refers to. As shown in the previous section, there the interlocutors go back and forth between talking about 'being' and 'not-being' and related positions about being and not-being, while the focus throughout remains on the positions themselves. If the relevant sense of parity were meant to involve the concepts or notions alone, then it is not clear how this would follow from their previous conversation as the Visitor claims it does.56 54 For a discussion of how Plato goes back and forth between discussing propositional and non-propositional entities as principles in the Republic, see Gail Fine's 'Knowledge and Belief in Republic V–VII' p.99 n.28. David Sedley discusses an excellent, related example of how Plato's conceptual geography differs from our own in 'Plato's Theory of Change at Phaedo 70-71'. He persuasively argues that Plato's understanding of 'ἐναντίος', often translated 'opposite', is neither what we would call a contrary nor a contradictory. Rather it is what he labels a 'converse contrary' (2012, 155ff). 55 Similar issues arise when interpreting the two routes in Parmenides' poem, each of which is described with a subjectless and predicateless use of the Greek verb 'to be': simply 'ἔστιν' and 'οὐκ ἔστιν' respectively (see fr. 2.3–5 and 8.2–16). Mourelatos argues that this bare 'is' collapses several uses of the copula that we would otherwise distinguish (1970, 58). He also suggests that Parmenides' use of the participle 'being' is derivative from this bare 'is', a use that Plato could be harkening back to here in the Parity Assumption (1970, 53). 56 Since 'being' (τὸ ὄν) is used interchangeably with other formulations such as 'the all' (τὸ )άν), the interlocutors are clearly not focused on establishing anything like the Fregean sense of 'being' (see especially 242c8–243a1, 244b6ff, and 249d1–2). Hestir also catalogues fifteen different senses of 'being' that are in play here, (2016, 139–40). 30 Finally, a proponent of the standard interpretation would need to offer alternative explanations in response to the main questions we have been discussing so far: what justifies the Parity Assumption? why is it announced precisely when it is? what is the use of discussing being in the first place, and why should the Visitor expect joint illumination and obfuscation? I have argued that the standard interpretation falls short of satisfactory answers here, and the fact that my interpretation has a straightforward explanation in each case lends further support for reading the passage as I have suggested. Conclusion All things considered, then, the Parity Assumption is best understood along the lines I have suggested. It assumes a background of exclusive and exhaustive claims where there are reasons both for and against on either side. It suggests that the interlocutors' well-motivated aporia offers a glimmer of hope: insofar as they get clearer on whether to accept or reject one side of the dilemma they will get clearer on whether to accept or reject the other side as well. And even if this fails they still have the option of 'pushing the account through'. This interpretation is fully consistent with a conservative translation of the passage and explains otherwise puzzling features of the wording. And when interpreted in this way it makes good sense of the surrounding discussion as well. The structure it draws attention to is a pattern of exploring both sides that repeatedly encourages further inquiry when the interlocutors may have otherwise been inclined to give up. The discussion of being and not-being begins with an awareness of their implicit commitment to the claim that not-being is and the attendant problems that Parmenides himself highlighted. Rather than simply treating this as a reductio, they decide to explore the other side and articulate an alternative characterization of what is that excludes not-being. This involves the method of exploring both sides on a smaller scale, first with count ontologies (monists vs. pluralists) after which they 'push through' to type ontologies (the Giants vs. the Friends of the Forms). In the latter case, the claims 'all things rest' and 'all things change' run into problems, requiring the interlocutors to 'push through' once again to a position of some change and some rest. But even this position runs into a dead end, at which point they announce that they are equally if not more confused about being. It is only at this moment, when they have realized their deep confusion, that the Parity Assumption is 31 announced. And afterwards, one final attempt at 'pushing through' in the communion of kinds passage finally helps them out of their well-motivated aporia.57 Thus the Parity Assumption is not a mere assumption or an oracular prediction. It is based on a genuine hope that they are entitled to even in the midst their present impasse. And 'hope' or 'expectation' is precisely the right word; there is no guarantee that they will find a way forward, nor even a guarantee that the way they have been conceiving the alternative claims will allow for it.58 But the inquiry so far has adopted the structure of exploring both sides, and that structure lends hope even in the face of a deep, well-motivated aporia. As we have seen, this is precisely the hope that the Visitor recommends in the Parity Assumption. At the level of the drama, this insight encourages the interlocutors to continue in what does indeed end with a successful resolution of the aporia. At a more general level Plato is drawing our attention to the very technique of exploring both sides that he employs in the composition of the Sophist. Even when an application of the method runs into problems it creates a well-motivated aporia, one that is structured so as to provide a way forward. And what better dialogue to emphasize this than one concerned with distinguishing the philosopher from the sophist? This is at least one lesson we can learn about Plato's methodology in the Sophist above and beyond the more obvious examples of collection and division. The entire dialogue shows methodological care and creativity that deserves our close attention. 57 Again, see the appendix for a diagrammatic representation of the way the discussion proceeds through exploring both sides. 58 Thanks to Katy Meadows for pointing out the important difference between a hope or expectation and a guarantee for the purposes of the Parity Assumption. 32 References Bluck, R. 1975. Plato's Sophist: A Commentary. Ed. G. Neal. New York. Brown, L. 1998. "Innovation and Continuity: The Battle of Gods and Giants". In Method in Ancient Philosophy. Ed. J. Gentzler. Oxford, 181–208. ---. 2008. "The Sophist on Statements, Predication, and Falsehood". In The Oxford Handbook of Plato. Ed. G. Fine. Oxford, 437–62. ---. 2010. "Definition and Division in Plato's Sophist". In Definition in Greek Philosophy. Ed. D. Charles. Oxford, 151–69. Campbell, L. 1867. The Sophistes and Politicus of Plato. Oxford, 1867. Cornford, F.M. 1935. Plato's Theory of Knowledge: The Theaetetus and the Sophist of Plato. London. Crivelli, P. 2012. Plato's Account of Falsehood: A Study of the Sophist. Cambridge. Diels, H. and W. Kranz. 1954. Die Fragmente Der Vorsokratiker, Griechisch Und Deutsch. Berlin. Diès, A., ed. 1963. Platon, Oeuvres Complètes: Le Sophiste. Vol. 8.3. Paris. Fine, G. 1990. "Knowledge and Belief in Republic V–VII". In Epistemology. Ed. S. Everson. Cambridge, 85–115. Frede, M. 1996. "The Literary Form of the Sophist". In Form and Argument in Late Plato. Ed. C. Gill & M.M. McCabe. Oxford, 135–51. Gill, M.L. 2010. "Division and Definition in Plato's Sophist and Statesman". In Definition in Greek Philosophy. Ed. D. Charles. Oxford, 172–201. ---. 2012. Philosophos: Plato's Missing Dialogue. Oxford. Henry, D. 2012. "A Sharp Eye for Kinds: Plato on Collection and Division". Oxford Studies in Ancient Philosophy 41, 229–55. Hestir, B. 2016. Plato on the Metaphysical Foundation of Meaning and Truth. Cambridge. Karasmanis, V. 2012. "Dialectic and the Second Part of Plato's Parmenides". In Presocratics and Plato: Festschrift at Delphi in Honor of Charles Kahn. Ed. C. Kahn, R. Patterson, V. Karasmanis, & A. Hermann. Las Vegas, 183–203. 33 Künne, W. 2005 "Die ‚Gigantomachie' in Platons Sophistes. Versuch Einer Analytischen Rekonstruktion". Archiv für Geschichte der Philosophie 86.3, 307–21. Leigh, F. 2010. "Being and Power in Plato's Sophist". Apeiron 43.1, 63–85. ---. 2012 "Restless Forms and Changeless Causes". Proceedings of the Aristotelian Society 112.2, 239–61. Menn, S. 1995. Plato on God as Nous. Carbondale. McCabe, M.M. 1994. Plato's Individuals. Princeton. Mourelatos, A. 1970. The Route of Parmenides. New Haven. Moravcsik, J. 1962. "Being and Meaning in the Sophist". Acta Philosophica Fennica 14, 23–78. Notomi, N. 1999. The Unity of Plato's Sophist: Between the Sophist and the Philosopher. Cambridge. ---. 2007a. "Plato Against Parmenides: Sophist 236d-242b". In Reading Ancient Texts: Essays in Honour of Denis O'Brien Volume I. Ed. S. Stern-Gillet & K. Corrigan. Leiden, 167–87. ---. 2007b. "Plato on What Is Not", in Maieusis: Essays in Ancient Philosophy in Honour of Myles Burnyeat. Ed. D. Scott. Oxford, 254–75. Owen, G.E.L. "Plato and Parmenides on the Timeless Present". The Monist 50.3, 317–40. ---. 1970. "Plato on Not-Being". In Plato. Ed. G. Vlastos. Garden city, 223–67. Reprinted in Logic, Science and Dialectic: Collected Papers in Greek Philosophy ed. M. Nussbaum. Leiden, 104–37. Palmer, J. 1999. Plato's Reception of Parmenides. Oxford. ---. 2009. Parmenides and Presocratic Philosophy. Oxford. Robinson, D. 1999. "Textual Notes on Plato's Sophist". The Classical Quarterly 49.1, 139–60. Rowe, C. 2015. Plato: Theaetetus and Sophist. Cambridge. Sedley, D. 2012. "Plato's Theory of Change at Phaedo 70-71", In Presocratics and Plato: Festschrift at Delphi in Honor of Charles Kahn. Ed. C. Kahn, R. Patterson, V. Karasmanis, & A. Hermann. Las Vegas, 147–63. 34 Silverman A. 2002. The Dialectic of Essence: A Study of Plato's Metaphysics. Princeton. Thomas, C. 2008. "Speaking of Something: Plato's Sophist and Plato's Beard". Canadian Journal of Philosophy 38.4, 631–67. Vlastos, G. 1981. "An Ambiguity in the Sophist". In Platonic Studies. 2nd print, with corrections. Princeton, 270–322. not-being is (corollaries: being is not, falsity is possible) [unacceptable consequences] x Discussion of Being and Not-Being (236d9–264b10) being is two (or more) being is one Pluralists Monists [unacceptable consequences] x [unacceptable consequences] x true being is knowable and bodiless forms (corollary: all things are changeless) only what has touch and impact is (corollary: all things change) Giants Friends of Forms both change and rest are Parity Assumption (250e5–251a4) no kinds combine with one another all kinds combine with one another some kinds combine, some do not (not-being understood as difference; in a way, not-being is and being is not) Count Ontologies (243d6–245e8) Type Ontologies (245e8–249d5) Final Aporia (249d6–251a4) (only change is) (only rest is) (compromise) A PATTERN OF EXPLORING BOTH SIDES IN THE SOPHIST Examination of Not-Being (236d9–242b5) Examination of Being (242b6–250e4) Positive Solution (251a5–264b10) being is (corollaries: notbeing is not, falsity is impossible) The interlocutors are motivated to assent to the claim 'not-being is' in order to allow that falsity is possible for defining the sophist. Yet they find that unacceptable consequences follow. They decide to explore what they take to be the only alternative, 'being is', to see whether or not any problems arise when giving a characterization of reality that excludes not-being. These claims take the form '_ is' or 'being is _'. They again employ the strategy of exploring both sides on the side of being, beginning with different count ontologies. Yet they find problems on either side. They 'push through' their initial set of alternatives to instead examine what they take to be exclusive and exhaustive type ontologies, though they find problems here as well. They realize that the previous options were not exhaustive and again 'push through' to explore a third alternative. But this also leads co unacceptable consequences and ultimately to a well-motivated aporia. The interlocutors do in fact 'push through' to a new way of understanding the alternatives with one final application of exploring both sides. This time one alternative clearly wins out over the others and explains some of their previous difficulties. [unacceptable consequences] x [unacceptable consequences] x [unacceptable consequences] x [unacceptable consequences] x [unacceptable consequences] x [unacceptable consequences] x [unacceptable consequences] x The Visitor announces that they have encountered a serious source of puzzlement, but that there is nevertheless an expectation for joint illumination. He suggests that even if they are not able to clarify either side they can still push through to a new understanding of the relevant alternatives. Communion of Kinds (251c8–259e7) (1) (2) (3) (4) (5) (6) (7)