Plato's Absolute and Relative Categories at Sophist 255c14 Beginning at Sophist 255c91 the Eleatic Stranger attempts a proof that 'being' (τὸ ὄν) and 'other' (τὸ θάτερον) are different very great kinds. The key step in this proof is to group beings (τῶν ὄντων) into those that are themselves in themselves (αὐτὰ καθ' αὑτά) and those that are in relation to others (πρὸς ἄλλα). Much effort has been made to understand this distinction between αὐτὰ καθ' αὑτά and πρὸς ἄλλα. The prevailing approach takes the former to name the class of 'absolute' terms and the latter to name the class of 'relative' terms,2 categories described in Diogenes Laertius' Life of Plato.3 Many, however, have argued that this category approach fails 1 For references, I follow the lineation of Duke, et al. 1995. However, they mislabel the key line, 255c14, as '15'. In Burnet 1900 and Diès 1925 it is line c13. 2 Since Plato is liable to employ words without regard for the use/mention distinction, and the singular-term/universal distinction, 'terms' covers individuals and properties, subjects and predicates. I adopt 'categories' simply to mean classes of terms that are exclusive and between them exhaust all terms. 3 Defenders of this category approach, who cite Diogenes in support, include Dancy 1999, 45-49 and Malcolm 2006, 277. Owen 1957, 107n27 took this view, but later rejected it. Heinaman 1983, 14 and de Vries 1988, 385 share the above approach, but do not mention Diogenes by name. The category approach is opposed by: Frede 1967, 1-99 and 1992, 397-424; Owen 1970, 223-67; Bostock 1984, 89-119 and Brown 1986, 49-70, all of whom take a semantic approach and hold that the αὐτὰ καθ' αὑτά and πρὸς ἄλλα distinction is between two senses or uses of the verb 'εἶναι'. I am in broad sympathy with the category approach, and my reading is a 2 because some terms, such as 'sameness', fit into neither class. In part I of this paper, I show that an alternative manuscript reading can preserve the general category approach, whilst allowing 'sameness' to fit into the scheme. Part II defends my alternative reading against the possible objection that certain terms do not fit into the new scheme. I conclude by noting an important similarity between Plato's and Aristotle's characterisations of relatives. I. The DL Category Reading and the Alternative Category Reading Those who favour the category approach often suggest that we understand the αὐτὰ καθ' αὑτά/πρὸς ἄλλα distinction of Sophist 255c14 in the light of the following Diogenes Laertius passage: Amongst beings (τῶν ὄντων), some are absolute (καθ' ἑαυτά), others are said in relation to something (πρός τι). Those said absolutely are all those which need (προσδεῖται) nothing to be added in expressing them (ἐν τῇ ἑρμηνείᾳ). Examples of these would be man, horse and the other animals... Those said in relation to something (πρός τι) are all those the expression of which need something, for example, larger than something, quicker than something, more beautiful and other such things. For the larger is larger than the smaller (ἐλάττονος) and the quicker is quicker than something (τινός) (Lives iii 108-9). version of it. I will not discuss the semantic approach, which has become less dominant over recent years. For a good overview of the literature on this distinction, see Malcolm 2006, 276. 3 Call this interpretation 'DL'.4 If we apply DL to Sophist 255c13-14, two mutually exclusive classes of beings are mentioned in Plato's text: the 'absolute' and the 'relative'. DL is taken to distinguish absolute from relative terms by saying that relative terms need some additional supplementation to decide their sense. They are therefore 'incomplete'. The examples given in the Diogenes Laertius passage are comparative adjectives: 'larger', 'quicker' and 'more beautiful'. In a typical case, 'Socrates is larger' must take a 'than Y' to determine its significance.5 As well as such syntactically incomplete terms, there are semantically incomplete terms like 'large': 'Socrates is large' may make a syntactic sentence, but one cannot assess the truth or falsehood of it without an additional 'for a Y' where 'Y' represents a kind term, for example.6 The contrasting examples of terms are 'man' and 'horse'. These do not 4 The above passage falls at the end of a long series of divisions (Lives iii 80109) which Diogenes reports Aristotle as saying were made by Plato (Lives iii 80). Diogenes does not refer to any particular Platonic texts, and the DL reading does not make the historical claim that Sophist 255c14 is the source for this distinction in Diogenes. Rather the DL reading uses the distinction is an interpretive tool for looking at the Sophist. 5 Note that the Greek comparative, unlike the English, can be used as syntactically complete to mean that an item has a property only to a limited extent: in Greek, 'Socrates is larger' could mean 'Socrates is somewhat large'. However, it is clear that this is not the sense of the comparative here, since Diogenes specifies that 'the larger is larger than the smaller' and that 'the quicker is quicker than something' (Lives iii 109 3-4). 6 For this view see Owen 1957, 108-9; Dancy 1999, 49-53 and Malcolm 2004, 284. Even though all the examples in DL are syntactically as well as semantically 4 require further supplementation to be meaningful: they are complete. But since incompleteness is the mark of relative terms, we should take these other terms, including 'man' and 'horse', as complete and we can call them 'absolute'. As well as exclusive, DL takes the distinction at Sophist 255c13-14 to be exhaustive. Plato's αὐτὰ καθ' αὑτά and πρὸς ἄλλα are interpreted as having the same extension as the 'absolute' and 'relative' classes of terms distinguished at DL iii 108-9. The latter distinction is exhaustive since Diogenes uses the 'τὰ μέν...τὰ δέ...' construction throughout this series of divisions (iii 80-109), to indicate an exhaustive division of a given genus into species. Particularly similar to 108-9 is 107-8, where that construction is used to distinguish the 'divisible' (τὰ μέν μεριστά) from the 'indivisible' (τὰ δὲ ἀμέριστα), which is obviously an exclusive and exhaustive contrast. Moreover, in Lives iii 109, the 'absolute' and 'relative' categories have proved to be identical with the classes of what we may call 'complete' and 'incomplete' terms. Since every term is either complete or incomplete, the distinction between αὐτὰ καθ' αὑτά and πρὸς ἄλλα is also exhaustive. For these reasons, the DL reading takes αὐτὰ καθ' αὑτά and πρὸς ἄλλα to be exclusive and exhaustive categories. Exhaustivity is targeted by the standard objection to the DL reading.7 'πρὸς ἄλλα' means 'in relation to other things'. Therefore, any term that 'πρὸς ἄλλα' incomplete, they take DL to indicate semantic, not syntactic incompleteness, which is not unreasonable: Diogenes' claimed source for Plato's view, Aristotle (DL iii 80), slides readily from syntictically incomplete examples (e.g. τὸ μεῖζον at Cat. 6a38) to semantically incomplete ones (e.g. ἕξις, διάθεσις, αἴσθησις, ἐπιστήμη and θέσις at Cat. 6b1-3). 7 Frede 1967, 17; Owen 1970, 256; Malcolm 2006, 278. 5 correctly describes cannot relate a thing to itself. This entails that if X and Y are related by a πρὸς ἄλλα term, then X and Y are numerically distinct. Call this kind of relative 'aliorelative'.8 The Sophist passage says that 'other' (255d1-7) is a πρὸς ἄλλα term and it is indeed an excellent example of an aliorelative. 'Other' is a relative under the DL reading, because 'X is other' entails that X is other than some Y. Moreover, 'other' is aliorelative, because if X is other than Y, then X and Y are, for that very reason, non-identical. Now, the objectors say, where do we place 'same'? It cannot simply be ignored. It is one of the five 'very great kinds', and it features prominently in the discussion from 254e2 onwards: in particular, the proof that precedes ours picks out 'same' explicitly (255b8-c8). But if, as scholars have urged,9 we take seriously the logical implications of πρὸς ἄλλα, then 'same' will not fall into either category. 'Same' cannot be in the class of πρὸς ἄλλα terms, because if X is the same as Y, they are not numerically distinct. But 'same' is relational, in the sense that 'same' is an incomplete term: 'X is the same' must be completed with an 'as Y'. So 'same' does not fit into the category of αὐτὰ καθ' αὑτά either. Thus the division of terms in this 8 This is an old term for what are now known as 'irreflexive relations'. I adopt the old term with a new meaning, so as to avoid simply assuming that Plato has a modern understanding of relations. Usually, an irreflexive relation is thought of thus: € ∀x¬Rxx . That is, if anything bears an irreflexive relation, it does not bear it to itself. If it is possible for x to bear the relation to itself, the relation is known as 'nonreflexive'. But since Plato does not clearly recognise 'individuals' and 'relations', I wish to allow 'relative' and 'aliorelative' to range over both. 9 Frede 1967, 17; Owen 1970 256; Malcolm 2006, 282. 6 passage is not exhaustive. Since the categories are supposed to be exhaustive under the DL reading, it is argued that the reading must be rejected. To save the DL reading, we would need a logical class of terms that accommodates both 'other' and 'same'. The natural move for the DL interpretation is to understand πρὸς ἄλλα as describing not only aliorelatives, but all relative terms, perhaps in line with DL iii 108 7: that is, to take πρὸς ἄλλα as equivalent to πρός τι ('in relation to something'), which would include aliorelatives, such as 'other', as well as non-aliorelative terms, such as 'the same'. Bostock and Dancy suggest such a move.10 But this reply fails to take seriously the sense of πρὸς ἄλλα, and so fails to answer the objection as posed. Moreover, it is not clear that Diogenes understands πρός τι as wider than πρὸς ἄλλα: all Diogenes' examples of relatives are aliorelatives. We must, therefore, look elsewhere to find a class description of 'relatives' that will accommodate both 'other' and 'same'. Adopting an alternative reading, favoured by one major manuscript family, can do this. At 255c14, the B and D manuscripts read πρὸς ἄλληλα (in relation to each other), instead of πρὸς ἄλλα (in relation to others). As far as I am aware, no commentator or editor has suggested adopting the B and D reading.11 So before discussing the philosophical advantages of the alternative reading, let me make the palaeographical case for it. B and D belong to the same family of manuscripts, while T and W represent two separate manuscript families (Duke, et al. 1995, 384; Nicoll 1975, 41). So editors may prefer the T and W reading of πρὸς ἄλλα partly on the grounds that two independent readings that agree are more likely to be correct. 10 Bostock, 1984, 93 and Dancy 1999, 59. 11 Silverman 2002, 165n57 notes that the manuscripts differ, but makes nothing of this observation. 7 However, the B manuscript is reliable for the Sophist: of the eight cases where T and W share an error, the B manuscript shares the error in five cases but has the correct reading in three cases.12 So when it is the minority reading, B is often correct. Second, the error of reading πρὸς ἄλλα for πρὸς ἄλληλα at 255c14 could have crept into either the T or W tradition by the anticipation of a scribe: 'in itself' contrasts naturally with 'in relation to others' but less naturally with 'in relation to each other'. The eight errors shared by T and W in the text of the Sophist suggests some degree of contamination between the T and W traditions. So the error could then have been transmitted horizontally from one tradition to the other.13 Note also that πρὸς ἄλληλα is unlikely to be a casual scribal error. The relation that beings that are 'other' have to each other will again be described as πρὸς ἄλληλα at 258e1-2, and we should read that as consistent with 255c14, if possible. Thus, because of the general soundness of the B manuscript, the possibility of contamination between T and W and the ease of reading πρὸς ἄλλα in error, from a palaeographical standpoint, πρὸς ἄλληλα is at least as plausible a reading as πρὸς ἄλλα. 12 Those eight cases are 224a7; 225b1; 230c2; 233b5; 237c2; 252b9; 252d6 and 253a9. B is preferred over T and W at 224a7; 225b1; 237c2 by Duke et al. Burnet is even more likely to prefer B. 13A correcting hand on the B manuscript, B2 corrects from a source in W's family, but predates both W and T (Duke, et al. 1995, xi and 384). B2 does not correct B at 255c14 from πρὸς ἄλληλα to πρὸς ἄλλα. So it is possible that the archetype of W also read πρὸς ἄλληλα. This suggests an error introduced into the W tradition and transmitted to T. I admit that this argument is not probative, as B2 is not a very prolific corrector of the Sophist text. 8 Not only does the B and D reading make good palaeographical sense, it also makes linguistic sense. It is clear that the expression πρὸς ἄλληλα, when not contrasted with αὐτὰ καθ' αὑτά, can be used to describe the relationships that something has to other items (for example: Theaetetus 152d7, 156a8 and 182b5; Sophist 248b6 and 258b1). But Plato often uses the expression πρὸς ἄλληλα to describe a relation that things that are the same have to each other, especially things that are of the same kind (for example: Theaetetus 195c8-d1; Sophist 228c4, 253a2 and 253b9; Parmenides 136b1 and 158d2). Linguistically and palaeographically, πρὸς ἄλληλα is at least as plausible as πρὸς ἄλλα. Philosophically, πρὸς ἄλληλα is the more plausible reading, since it has a logic that will accommodate 'same' and 'other'. The logic implied by the reciprocal pronoun is what I will call a reciprocal relative. Under the DL view, X is a relative iff X is semantically incomplete, and becomes completed when a relation, R, to some appropriate Y is specified. The reciprocal account adds the characterisation that Y is similarly incomplete and also related to X. This is the sense in which X and Y reciprocate. So we can define 'reciprocal relatives' thus: X and Y are reciprocal relatives iff X bears the relation R to Y and Y bears the relation R-1 (inverse of R) to X. Inverse relations are defined as follows: where a relation, R, takes an item and links it to a second item, the inverse of the relation, R-1, takes the second item and links it back to the first.14 For example, if the relation is 'is larger than' then the inverse is 'is smaller than'; if the relation is 'is a parent of', then the inverse will be 'is an offspring of'. There are cases where a relation and its inverse are identical. If X is a neighbour of Y, then Y is a neighbour of X. We could say that X and Y are neighbours πρὸς ἄλληλα. 14 For further reflections on inverse relation see Williamson 1985, 249-262. 9 The B and D manuscript reading, supported by the notion of a reciprocal relative, allows both 'same' and 'other' to fit into one of the two categories. As it happens, the 'same' relation and its inverse are identical: if X is the same as Y, then Y is the same as X. But we can see that X and Y here conform to the definition of reciprocal relatives, so that sameness will fit into a class of πρὸς ἄλληλα terms: X and Y are the same πρὸς ἄλληλα. πρὸς ἄλληλα will also accommodate 'other'. Some subject X is other in so far as it is other than something else, Y, where X and Y are non-identical. If X is other than Y, Y is other than X. Again, these X and Y conform to the definition of reciprocal relatives. Hence, if we read πρὸς ἄλληλα, both 'same' and 'other' fit comfortably into the 'relatives' category of terms. By adopting the B and D manuscript reading we can undergird an alternative category reading. This reading differs slightly from the DL category reading. The DL reading suggests that the dichotomy between αὐτὰ καθ' αὑτά and πρὸς ἄλλα is between absolute and relative terms. Because of the logic of πρὸς ἄλλα, the relative terms would be read as aliorelative. The B and D manuscript reading also suggests that the dichotomy is between the absolute and relative terms. Like DL, the alternative category reading understands relative terms to be incomplete. But unlike DL, since it reads πρὸς ἄλληλα for πρὸς ἄλλα, the relative class of terms will be reciprocalrelatives. Thus, the alternative category reading is the claim that that there are two classes of terms: those that are complete, and those that come in pairs of incomplete, but reciprocating, terms. II. An Objection to the Alternative Category Reading The alternative category reading must overcome a version of the standard objection. There are pairs of relatives that fit neither into the αὐτὰ καθ' αὑτά class 10 of terms (because they are each incomplete), nor into that of 'reciprocal relatives', since we can use them without their reciprocal partner. An example would be the pair 'animal' and 'foot'. A 'foot' is always the foot of an animal, and is therefore, arguably, a relative.15 If so, 'foot' is aliorelative because nothing is ever the foot of itself. But an animal is not always (or perhaps ever) the animal of a foot. So there is no reciprocity between the pair. 'Foot' seems to be merely aliorelative. If classes of terms are to be categories, they must jointly exhaust all the terms there are. So, to be a category reading, the alternative reading must show that the αὐτὰ καθ' αὑτά and πρὸς ἄλληλα classes of terms are jointly exhaustive. And the existence of relatives that are merely aliorelative suggests that they are not. I have two responses to this objection. First, I will outline the reasons that Plato could have for holding that all relatives are reciprocal relatives, which would entail that there are no mere aliorelatives. Second, I will cite evidence from a passage in the Parmenides, one that the B and D reading makes parallel to Sophist 255c14, and where Plato is quite clear that all relatives come in reciprocal pairs. To ward off the objection that there are some mere aliorelatives, we must show that for Plato, if something is a relative of any kind, it is a reciprocal relative. This is accomplished by showing that being a relative entails having a reciprocating partner. A consequence of the definition of reciprocal relatives given above is that only a reciprocal pair of terms can feature in a certain exceptionlessly correct statement. This serves as a test for whether two terms are a reciprocal pair. To 15 Aristotle, at least, would count 'foot' as a relative. At Categories 8a13-27 he posits organic parts as relative to the whole organism, which creates problems for his definition. Categories 7a4-5, 7a16-17 and 7a201-2 also mention organic parts as relatives. 11 illustrate this, take the example of 'master' and 'slave'. We find both Plato (Parmenides 133c8 see below) and Aristotle (Categories 6b29) asserting that 'master' and 'slave' are a reciprocal pair.16 If X is a master, then X is a master of some Y. This shows that 'master' is a relative. But what kind of thing is Y? The reciprocating partner, Y, will bear the inverse of the relation 'is a master of' to X. That is to say, it will bear the 'is a slave of' relation to X. So Y will be a slave. Aristotle shows that for any relative term, we can create the other expression in the pair that reciprocates with the first (ὀνοματοποιεῖν, 'to name-make' Categories 7a5-7). This ability to create reciprocating partners is what guarantees that all relatives have one. To create a partner, he coins a new expression that describes the reciprocating partner in a reciprocal pair. For example, Aristotle says, take 'rudder' as a relative. Like 'foot', it is an aliorelative, as nothing can be a rudder of itself. Nevertheless, we can always make exceptionlessly correct statements involving the relative and its reciprocating partner, by coining the passive verbal noun 'ruddered' for the reciprocating partner of 'rudder'. Moreover, a rudder, X and a ruddered Y, will conform to the definition of reciprocal relatives, because if X is a rudder of Y, Y is ruddered by X. Or, as Aristotle puts it: 'A rudder is the rudder of a ruddered thing, and a ruddered thing is ruddered by a rudder' (Categories 7a14-15). This ability to coin expressions for the other item in a pair of reciprocal relatives guarantees that any relative has a reciprocating partner, including aliorelatives. This is, perhaps, why Aristotle thinks that all relatives are reciprocal relatives. 16 There is no sign in the Categories of Aristotle's view that the slave belongs to the master in a way that the master does not belong to the slave (Politics 1254a813). 12 But does Plato think the same way? We would have some good evidence that he does if we could show that Plato allows himself to coin new expressions for the reciprocating partner to give exceptionlessly correct statements involving the relative and its partner. In the context of the discussion of relatives in Republic IV, Plato says that we can do this with the relative 'knowledge'. 'Knowledge' is a standard example of a relative in Plato and Aristotle.17 To generate an exceptionless partner for 'knowledge' we would choose 'object of knowledge': If X knows Y, Y is an object of knowledge for X. 'Object of knowledge', then, just means 'whatever knowledge is of'. Plato suggests an indefinite reciprocating partner in Republic 438c6-9. Knowledge is of learning (τὰ μαθήματα) or 'whatever one ought to say that knowledge is of' (ὅτου δὴ δεῖ θεῖναι τὴν ἐπιστήμην). Even if Plato has not yet coined the single-expression reciprocating partner for 'knowledge' ('the knowable': see below), he, like Aristotle, does not make the reciprocating partner a hostage to natural language. This leaves Plato free to agree with Aristotle that all relatives have a reciprocating partner and so there are no mere aliorelatives, since for any aliorelatives one will be able to coin the term for a reciprocating partner. Thus, we are not forced to admit that there are some mere aliorelatives, and so are not forced to concede the objection that there are relatives that do not fit into the class of reciprocal relatives. The second response to the objection is that a parallel passage in Plato suggests that all relatives are reciprocal relatives. Once we read Sophist 255c14 with 17 Plato: Republic 438c-d; Parmenides 133c, where the partner is ἀλήθεια; Charmides 168b-c, where the partner for knowledge is also τὰ μάθηματα. Aristotle: Categories 6b34, where the partner is ἐπιστητόν. 13 the B and D manuscripts, we can see that the Parmenides draws a parallel distinction between πρὸς ἄλληλα and non-πρὸς ἄλληλα ways of being spoken of: Therefore, also, among the Ideas all those which are what they are (εἰσὶν αἵ εἰσιν) in relation to each other (πρὸς ἀλλήλας) have their relation to themselves, but not in relation to those things in our world. (133c8-d1) Once we adopt the B and D reading of Sophist 255c14, the linguistic similarity is sufficient for the Parmenides to be relevant to understanding the Sophist's αὐτὰ καθ' αὑτά/ πρὸς ἄλληλα distinction. The 'what they are' (αἵ εἰσιν cf. ὅπερ ἐστὶν at Sophist 255d7) and in relation to one another (πρὸς ἀλλήλας cf. πρὸς ἄλληλα Sophist 255c14) are parallel. The Parmenides passage is textual evidence that Plato thinks there are no mere aliorelatives. This time, Plato uses the examples of a master and a slave (Parmenides 138d8). If he did think that there were mere aliorelatives, 'master' would be a good example of one: Plato certainly thinks that no unified agent can be master of himself.18 So 'master' and, we could add, 'slave' are each aliorelative. But, in a move we would expect if he thought all relatives come in reciprocal pairs, Plato does not simply let the examples stand individually. They 'are what they are in relation to each other', i.e. it is impossible to be a 'master' without being master of a 'slave', and it is impossible to be a 'slave' without being the slave of a 'master'.19 Therefore, these 18 cf. Republic 431a where the definition of σωφροσύνη as self-mastery is dismissed on these grounds. 19 cf. Categories 7a31-7b9. In this passage, Aristotle points out that 'master' is the only proper correlative of 'slave'. 14 putative cases of aliorelatives are not mere aliorelatives. They are, in addition, reciprocal relatives. However, in the Parmenides, unlike in the Sophist, Plato mentions a pair of relatives that apparently do not reciprocate: 'knowledge' and 'truth' (Parmenides 134a3-4). On the face of it, 'knowledge' and 'truth' are not related as 'master' is to 'slave': although it is impossible to know without knowing truths, it is perfectly possible for there to be a truth that is not known. Put another way, the inverse of the 'is knowledge of' relation is the 'is an object of knowledge for' relation. The inverse of 'is knowledge of' has nothing to do with 'truth'. 'Knowledge' and 'truth' may be more akin to the 'foot' and 'animal' case, a case that appeared problematic for the alternative category-reading. To be a reciprocal pair, these should be 'knowledge' (ἡ ἐπιστήμη) and the 'knowable' (τὸ ἐπιστητόν), which are the terms Aristotle uses (Categories 6b34). Does this show that Plato does not have a view of relatives where all relatives are reciprocal relatives? I suggest that the counterexample which 'knowledge' and 'truth' present to the claim that all relatives are reciprocal is merely apparent. 'Truth' should be understood here as 'object of knowledge' or 'the knowable'. At Theaetetus 201d2-3, Theaetetus recalls the term 'ἐπιστητός' (knowable) as a surprising coinage by an anonymous third party. This suggests that Plato is uncomfortable with the term. It is likely that when he wrote the Republic and the Parmenides, dialogues perhaps slightly earlier than the Theaetetus, he was shy of using the neologism. As we saw, at Republic 438c3, Plato prefers to refer to the reciprocal partner of 'knowledge' as 'learning' (τὰ μαθήματα), and the use of 'truth' (and 'beings' at 134a8-b1) in the Parmenides, I suggest, is another example of Plato still feeling his way with the terminology, and avoiding 'ἐπιστητόν'. 15 Finally, the Parmenides argument does not require a more specific partner for 'knowledge', so Plato does not use one. The argument is supposed show that the Forms are unknowable. In so far as that is the aim of the argument, it focuses only on the term 'knowledge' and can leave its reciprocal partner less well specified: Parmenides needs only the claim that our knowledge cannot have an object that is in the realm of the Forms, and it does not matter whether the reciprocal partner of knowledge is 'truth', 'beings' or 'knowables'. Plato recognizes in this argument that 'knowledge' is a relative, and has a reciprocal partner, but, because nothing turns on what the partner is, he leaves it indefinite. III. Conclusion I began with the DL category reading, which made two main claims. First, that all relatives are incomplete terms. Second, that the categories of αὐτὰ καθ' αὑτά and πρὸς ἄλλα are exhaustive. The second claim was found to be incoherent when we tried to place 'same' in the scheme. I argued that we could save a category reading by dropping the πρὸς ἄλλα category in favour of the πρὸς ἄλληλα category suggested by the B and D manuscripts. The logic implied by the reciprocal pronoun, as we saw, accommodates 'same'. I was able to show, by appealing to both philosophical and textual considerations, that this reading is not vulnerable to the objection that there are some mere (i.e. non-reciprocal) aliorelatives. This left us with a position where, first, all relatives are incomplete, second the 'absolute' and 'relative' categories are exhaustive and third, all relatives come in reciprocal pairs. The latter is a view shared by Plato and Aristotle (e.g. at Categories 6b28-35). If this is the case, it prompts the question: what further similarities might there be between Plato's and Aristotle's conceptions of relatives? 16 BIBLIOGRAPHY Bostock, David. 1984. 'Plato on "is not"' Oxford Studies in Ancient Philosophy 2: 89119. Brown, Lesley. 1986. 'Being in the Sophist: A Syntactic Inquiry' Oxford Studies in Ancient Philosophy 4: 49-70. Burnet, John. 1900. Platonis Opera. vol. 1. Oxford: Oxford University Press. Dancy, R. M. 1999. 'The Categories of Being in Plato's Sophist 255c-e' Ancient Philosophy 19: 45-72. Diès, Auguste. 1925. Platon Oeuvres Complètes. vol. 3. Paris: Belles Lettres. Duke, E. A., Hicken, W. F., Nicoll, W. S., Robinson, B. D., and Strachan, J. C. 1995. Platonis Opera. vol. 1. Oxford: Oxford University Press. Frede, Michael. 1967. 'Prädikation und Existenzaussage' Hypomnemata 18: 1-99. Frede, Michael. 1992. 'Plato's Sophist on False Statements' in Kraut ed. 1992. Heinaman, Robert. 1983. 'Being in the Sophist' Archiv für Geschichte der Philosophie 65: 1-17. Kraut, Richard. 1992. The Cambridge Companion to Plato. Cambridge: Cambridge University Press. Malcolm, John. 2006. 'A Way Back for Sophist 255c12-13' Ancient Philosophy 26: 275-89. Nicoll, W. S. M. 1975. 'A Problem in the Textual Tradition of Plato's Politicus' The Classical Quarterly 25: 41-47. Owen, G.E.L. 1957. 'A Proof in the Peri Ideon' Journal of Hellenic Studies 77: 10311. Owen, G.E.L. 1970. 'Plato on Not-Being' in G. Vlastos ed. 1970. 17 Silverman, A. 2002. The Dialectic of Essence: A Study of Plato's Metaphysics. Princeton: Princeton University Press. Vlastos, Gregory. 1970. Plato I: Metaphysics and Epistemology. New York: Doubleday. de Vries, Willem. 1988. 'On Sophist 255B-E' History of Philosophy Quarterly 5: 385-394. Williamson, Timothy. 1985. 'Converse Relations' Philosophical Review 94 (2): 249262.