Dividing Plato's Kinds

Phronesis 63 (2018) 392-407

brill.com/phro

Dividing Plato’s Kinds

Fernando Muniz Departamento de Filosofia, Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos, 6627, Pampulha, Belo Horizonte – MG – CEP 31270-901. Brazil [email protected]

George Rudebusch Philosophy Department, Northern Arizona University, 803 South Beaver Street Room 104, PO Box 6011, Flagstaff, Arizona 86011-6011. USA [email protected]

Abstract

A dilemma has stymied interpretations of the Stranger’s method of dividing kinds into subkinds in Plato’s Sophist and Statesman. The dilemma assumes that the kinds are either extensions (like sets) or intensions (like Platonic Forms). Now kinds divide like extensions, not intensions. But extensions cannot explain the distinct iden- tities of kinds that possess the very same members. We propose understanding a kind as like an animal body—the Stranger’s simile for division—possessing both an extension (in its members) and an intension (in its form). We find textual support in the Stranger’s paradigmatic four steps for collecting a subkind.

Keywords

Plato – division – kinds – forms – hiereion

1 Introduction

The Eleatic Visitor or Stranger (xenos) appears only in Plato’s Sophist and Statesman, where he uses a method of division to answer a question Socrates asks: ‘Do they [where the Stranger comes from] think that all these [Sophist, Statesman, and Philosopher] are one or two—or, just as the names are three,

2. Productive 1. 3. Expertise Exchange 4. Acquisitive Fighting 5. Conquest Inanimate Hunting Animate

6. On land 7. Animate Birds In water 8. By enclosures Fish 9. By night by torch By striking 10. By day Downward by barb Upward = Angling figure 1 Paradigmatic division of the angler did they divide also three kinds, one per name, and fasten a kind to each [name]?’1 ‘They hold them to be three,’ says the Stranger, ‘but to mark the boundaries between them’ is ‘a big job and not easy.’2 Nonetheless, the Stranger knows how to do it; at any rate, ‘he claims to have heard, well enough,’ how from his countrymen ‘and not to have forgotten.’3 He takes Theaetetus as interlocutor and illustrates the method with a ‘paradigm’ (paradeigma) that is ‘easy to know and of small importance but having an account no less than things of great importance’—the angler.4 And so the paradigmatic division begins, first of expertise into ‘productive’ expertise (poiētikēn, 219b11) and ‘acquisitive’ expertise (ktētikē, 219c7). The Stranger con- tinues as in Fig.1, in a division that proceeds from left to right according to the spatial metaphor the Stranger uses at 221b. The point of the division is to ‘uncover a path’ (atrapon … aneurēsei, Stat. 258c3) from kind to subkind, dividing again and again in order to define a

1 Πότερον ἓν πάντα ταῦτα ἐνόμιζον ἢ δύο, ἢ καθάπερ τὰ ὀνόματα τρία, τρία καὶ τὰ γένη διαιρούμενοι καθ’ ἓν ὄνομα [γένος] ἑκάστῳ προσῆπτον; Sph. 217a6-8. All translations ours unless noted. In this passage we retain the word γένος bracketed by Burnet. 2 Τρί’ ἡγοῦντο· καθ’ ἕκαστον μὴν διορίσασθαι … οὐ σμικρὸν οὐδὲ ῥᾴδιον ἔργον, Sph. 217b2-b3. 3 Διακηκοέναι γέ φησιν ἱκανῶς καὶ οὐκ ἀμνημονεῖν, Sph. 217b7-8. 4 Εὔγνωστον μὲν καὶ σμικρόν, λόγον δὲ μηδενὸς ἐλάττονα ἔχον τῶν μειζόνων, Sph. 218d8-e4.

Phronesis 63 (2018) 392-407 Downloaded from Brill.com09/25/2021 01:44:15PM via free access 394 Muniz and Rudebusch given expertise, here Angling. This division is the paradigm for the divisions the Stranger makes in order to answer Socrates’ question, ‘How many distinct kinds of thing are the Sophist, Statesman, and Philosopher?’ In the relevant dialogues, the Stranger ostensibly uses this method to define the Sophist and the Statesman (although there is no dialogue Philosopher doing the same for the Philosopher). It may be that the appearance of this new character and new paradigm mark a change in Plato’s ontology, in which he revised or replaced his Forms with divisible Kinds, or it may be that the new is compatible with his other writings on Forms. In either case, the understanding of Plato’s metaphysics or metaphysical development depends upon understanding the Stranger’s method of division. Unfortunately, as Cohen pointed out, ‘we don’t know what is being divided or what it is being divided into. And until we know these things, we don’t know very much about the method of division.’ Cohen demonstrated that there was no satisfactory account of what the Stranger’s kinds are, given the two available accounts of what the Stranger was dividing: a kind ‘may be an extensional entity, or it may be an intensional entity.’5 There is a worry about the terms Cohen used to set the dilemma.6 The worry is that it is words that possess Carnapian intensions and their Fregean counter- parts, senses. In contrast, in Plato’s dialogues non-linguistic objects, including kinds, possess or ‘have a share of’ forms. Therefore, to talk of a non-linguistic object having an intension appears to be confused or anachronistic. Moravcsik and Cohen raise this worry, for example, when the two list as examples of intensional entities ‘a natural property’ and ‘a [Platonic] Form’.7 Let us alleviate this worry. Moravcsik and Cohen follow Carnap in their use of the words ‘intension’ and ‘extension’. The first and longest chapter of Carnap’s Meaning and Necessity is titled ‘The Method of Extension and Intension’. Carnap, in informally presenting the plan of Meaning and Necessity, stated that the intension of a word corresponds to ‘the property which [the word] expresses’, a correspondence that Carnap took to be ‘in accord with customary conceptions’, including the Platonic conception of Forms.8 Now the

5 Both quotes from Cohen 1973, 181. 6 We thank hearers of presentations and readers of earlier drafts of this paper for this worry. Delcomminette 2000, 69, has different grounds for finding Cohen’s terminology ‘unsuitable’ (mal posé), which we do not address here. 7 Moravcsic 1973a, 172 and Cohen 1973, 181. 8 Carnap 1947, 1. George’s 1967 translation of Carnap 1928 used the same words, ‘intension’ and ‘extension’, in translating the following homage by Carnap to Frege: ‘Frege was the first who made precise the much-discussed and age-old (seit Jahrtausenden) distinction between intension and extension (Inhalt und Umfang) of a concept.’ Carnap’s reference to

PhronesisDownloaded 63from (2018) Brill.com09/25/2021 392-407 01:44:15PM via free access Dividing Plato’s Kinds 395 property or Form expressed by a word referring to an object is nothing but a property had by that object or a Form in which that object partakes. For example, the term ‘even number’ expresses the property or Form even number, the very property that all and only even numbers have or the very Form in which all and only even numbers partake. In recognizing that Forms and properties are two kinds of intensions or ‘intensional entities’, then, Moravcsik and Cohen accurately followed Carnap’s intended use of the word ‘intension.’ Moreover, Carnap’s account of intensions accurately interpreted Frege’s account of the ‘sense’ (Sinn) of a designating expression as containing a ‘mode of presentation’ (Art des Gegebenseins) of the object denoted.9 Frege related his intensional entity (the ‘sense’) to the object it presented (the ‘referent’) in the following passage: ‘Comprehensive knowledge of the referent would require us to be able to say immediately whether every given sense belongs to it (zu ihr gehöre). To such knowledge we never attain.’10 Notice that for Frege comprehensive knowledge does not require us to know, given some language, what senses attach to the words of that language, but rather to know of objects what senses ‘belong’ to them. Plato’s Forms, like Frege’s senses, belong to objects in such a way that comprehensive knowledge of those objects would require us to say what Forms those objects share. There is no confusion, therefore, in understanding Fregean senses and Carnapian intensions to belong to the objects, including the kinds, that they present. And Moravcsik and Cohen are not anachronistic in interpreting Platonic Forms to be one sort of intensional entity, along with shared properties, powers and features.

2 Kinds as Extensions

The extensional account of the Stranger’s method posits that a kind is a set and a subkind a subset. To illustrate, consider for example the step in the Stranger’s paradigm where he makes a division of expertise at fishing. Let Fishing (that is, Expertise at the Hunting of Fish: Fig. 1, Level 7) be the set that contains numer- ous expertises at Enclosure Fishing (say, fishing with nets, with baskets, with weirs) and at Strike Fishing (including torch fishing and fishing with barbs,

a distinction that is seit Jahrtausenden (literally, ‘thousands of years old’), shows that Carnap interprets Frege to have made precise the Platonic distinction between, say, the Form Even Number and particular even numbers. Likewise, Carnap intended his own semantics of the word ‘intension’ to interpret in a logically precise way talk of Platonic Forms as well as of properties. 9 Frege 1892, 26 (tr. Black 1948, 210). 10 Frege 1892, 27 (tr. Black 1948, 211).

Phronesis 63 (2018) 392-407 Downloaded from Brill.com09/25/2021 01:44:15PM via free access 396 Muniz and Rudebusch such as upon tridents or fishhooks). Then when the Stranger divides Fishing into Enclosure Fishing and Strike Fishing (Level 8), he is dividing the set of fishing expertises into two subsets of expertises. Such a model of division has the advantage of yielding an intuitive notion of division of kind into subkind just as a set is divided into subsets. But this model also has a flaw that appears when one reaches the target of a given search. To see the flaw, notice that Fishing by Day with Barbs (Fig. 1, Level 9) would be a set with two members, the one an expertise at striking downward from above with a spear, while the other is the target of the search, namely Angling, which is distinguished by striking upward from below with a hook on a line. Since on this model division is taking a subset, the ultimate division does not give us the Expertise Angling but rather the unit set containing Angling. As a remedy to the problem of the confusion of Angling with the unit set containing Angling, Cohen 1973 proposed that we take the members of a given kind not to be expertises but rather experts. For the same reason Wedin 1987 proposed another remedy, that we take the members of a given kind to be neither expertises nor experts but events of expertise. Quite apart from the unit/set problem, Moravcsik 1973a, 169-70 gives a general argument entailing that all merely extensional accounts fail as an interpretation of the Stranger’s kinds. The first premise is that in the Sophist the Stranger takes pains to establish that the kinds Motion, Rest and Being are ‘three’, (254d12), the kind Same is ‘fourth’ (255c5-7), and the kind Other is ‘fifth’ (255d9). The second premise is that, if the Stranger’s Same, Other and Being were sets, they would be but one set, since everything is a member of each of those ‘greatest’ kinds (megistōn, 254c3, also d4).11 Worse yet, the sameness of membership in Same, Other and Being is a matter of necessity, as the Stranger argues and as Theaetetus recognizes in his assent, ‘necessarily’ (anankaion, e.g. 256c7). If the Stranger’s kinds were sets, then Same, Other and Being would necessarily be one kind, not three. Thus kinds are not mere extensions. To illustrate, let us grant the Stranger the set S1 of all beings. Then let us specify set S2 as the set whose members are exactly those members of S1 that partake of sameness, and S3 as the set whose members are exactly those members of S1 that partake of otherness. It is possible to specify or collect the sets S1, S2 and S3 in different ways but, given the Stranger’s arguments, S1, S2 and

11 As the Stranger argues, ‘everything partakes of’ the Same (τὸ μετέχειν αὖ πάντ’ αὐτοῦ, Sph. 256a7-8). And ‘the nature of the Other operates in all the kinds so as to make each one other than Being’ (κατὰ πάντα γὰρ ἡ θατέρου φύσις ἕτερον ἀπεργαζομένη τοῦ ὄντος ἕκαστον, Sph. 256d12-e1). And all the kinds, ‘because they partake of Being, are and [are] beings’ (ὅτι μετέχει τοῦ ὄντος, εἶναί τε καὶ ὄντα, Sph. 256e3). Our version of Moravcsik’s argument elaborates his in various ways.

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S3 contain the very same members. It is a feature of sets that they are identified not by intensional properties such as the order of their members or the method of specifying their members, but solely by their extension: according to set theory’s axiom of extensionality, set X = set Y just in case X and Y have the same members. Thus, sets S1, S2 and S3 are one and the same, unlike the Stranger’s kinds Same, Other and Being, which are three. One way to state Moravcsik’s problem is that kinds do but extensions do not have the feature of intensional identity. It is possible for an extensionalist to escape this problem by proposing that the Stranger is equivocating, speaking of kinds as sets in the division passages, but speaking of kinds in some other way—perhaps as Forms—in the passages on the ‘greatest kinds’. But such an escape would be hard to fit to the text. For, even in the passage discussing the greatest kinds, the Stranger speaks of them as having parts, for example at 257d5 and 258a9. In any case, we take it that equivocation will be an inferior interpretive strategy if a non-equivocal option is to be found.

3 Kinds as Intensions

Because of the flaw in the extensional account, Moravcsik proposed instead an intensional account: ‘We take as our starting point that what is divided is in fact a single Form, and not a class … The claim that the Form is divided into parts is taken quite literally’ (1973a, 174). He developed a characterization of what division of intensions would be, defining two different notions of parts (1973a, 175). In a comment on the paper, Cohen 1973, 185-6 pointed out problems in that characterization. In the light of those criticisms, Moravcsik 1973b abandoned his first characterization and proposed a second. This second account consists of two axioms and a four-part division. The two axioms are about wholes: (A1) ‘A whole is more than the mere sum of parts;’ (A2) ‘Only wholes can have parts’ (1973b, 339). The four-part division is a classification of intensions meant to capture ‘the four types into which Plato classifies all intensions’ (1973b, 339). Every intension falls into one of the following four sets or ‘classes’. The first class contains anything that ‘is a whole, has parts, but is not itself a part’. These wholes are the highest named object in any division tree. These are the wholes ‘with which a division starts’. The second class contains anything that ‘is a whole, has parts, and is a part’. These are objects produced at the intermediate divisions. Each is part of a higher kind, but also itself divisible. The third class contains anything that ‘is a whole, has no parts, and is a part’. They are the lowest object in any division tree. The fourth class contains anything that ‘is not a whole, has

Phronesis 63 (2018) 392-407 Downloaded from Brill.com09/25/2021 01:44:15PM via free access 398 Muniz and Rudebusch no parts, but is a part’. Moravcsik intends this class to contain intensions ‘corresponding to which Plato will not postulate Forms’ (1973b, 340), such as the Stranger indicates in the Statesman (262c10-263a1) with the examples barbarian and every number except 10,000. Like his first account, Moravcsik’s second account runs into problems. For instance, the fourth class by definition does not have parts, and Moravcsik gives as an example not 10,000, which is a part of number, and indeed deter- mines as its extension every natural number both greater than and less than 10,000. But consider now the intension less than 10,000. Moravcsik’s model must deny that this intension is part of not 10,000, while affirming that not 10,000 is part of number. The word ‘part’ thus becomes obscure. Another problem arises for Moravcsik’s third class, which by definition contains wholes that have no parts, for example sophistry. But if human being can be divided into the parts Greek and barbarian, surely we can likewise divide sophistry into the parts Greek sophistry and barbarian sophistry. To deny this is again to make the word ‘part’ obscure. Yet another problem arises for Moravcsik’s second axiom, that only wholes can have parts. Moravcsik denies that the intension not 10,000 is a whole. But not 10,000 would seem to contain two parts, numbers less than 10,000 and numbers greater than 10,000. According to the second axiom (‘Only wholes can have parts’), then, not 10,000 would after all be a whole. In addition to these particular problems with Moravcsik’s second account, there is a general problem for any intensional model, a problem raised by Cohen:12

Intensional models … do not mesh very nicely with an intuitive understanding of the part of relation. One would have thought that while the class of men is a part of the class of animals, the intension animal is part of the intension man, and not the other way around. For ‘animal’ is part of the definition of ‘man’, while ‘man’ is not part of the definition of ‘animal’.

One way to state this problem is that kinds divide in a direction opposite to intensions. In the half century since Cohen raised this objection there have been no published replies.

12 Cohen 1973, 190. Brown 2010, 156 endorses Cohen’s problem. We follow Cohen’s conven- tion using italics to denote intensions (e.g. the intension productive expertise). We use initial capitals in naming kinds (e.g. the kind Productive Expertise), and we name linguistic expressions, English or Greek, by enclosing them in inverted commas (e.g. the substantives ‘productive expertise’ and ‘ποιητικὴ τέχνη’).

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4 The Stranger’s Simile

The 1973 exchange between Moravcsik and Cohen had the effect of producing a dilemma for interpreters that has remained unsolved for forty-five years. The first premise is the assumption that a kind is either a mere extension or else a mere intension. The second premise rules out mere extensions as not capturing one feature of kinds, their intensional identity. The third premise rules out mere intensions as not capturing another feature of kinds, their extensional division. We aim in this section to show how to escape the dilemma with a new interpretation of the method of division. The Stranger uses the simile of a body for a kind. When his target for division is the many expertises that have to do with ‘a city itself’ (polin autēn, Stat. 287b6), the Stranger says, ‘Let us divide them, like a hiereion, member by member.’13 A hiereion was a sacrificial animal body, and the step-by-step dismemberment was performed upon the body after killing it. In this simile what corresponds to a kind is the sacrificial body and what corresponds to the subkinds are the parts cut away at each step of the dismemberment. The Stranger’s hiereion simile echoes Socrates’ butcher metaphor for the division of a kind: ‘to cut through [it] by joints which it has by nature, trying not to shatter any part by using the technique of a bad butcher.’14 The hiereion simile is a way of understanding the method of division that escapes the dilemma. For a hiereion is a body that possesses both an intension and an extension. If kinds are like such bodies, the first premise of the dilemma is false: a kind is neither a mere extension nor a mere intension. Although our proposal that kinds are like bodies denies the first premise of the dilemma, we affirm the second and third premises of the dilemma as correctly indicating two features of kinds, intensional identity and extensional division. A hiereion, being an animal body, possesses an intensional identity. For example, the parts of an animal body need to be connected in a specific way. Imagine an artist who takes the very same parts, detaches and stitches them

13 Κατὰ μέλη τοίνυν αὐτὰς οἷον ἱερεῖον διαιρώμεθα, Stat. 287c3. Instead of the body of an animal, in the division of the ‘belief-mimic’ (δοξομιμητής) at Sph. 267e7-8 the Stranger uses the simile of the body of an artifact, namely the sidēros (σίδηρος), that is, any implement made of iron. Common to the animal and artifact similes is that both similes make kinds like bodies. 14 Διατέμνειν κατ’ ἄρθρα ᾗ πέφυκεν, καὶ μὴ ἐπιχειρεῖν καταγνύναι μέρος μηδέν, κακοῦ μαγείρου τρόπῳ χρώμενον, Phaedrus 265e1-3. Butchery in ancient Greece was predominantly or exclusively religious and therefore suggests a hiereion. See Berthiaume 1982, 62-70 and 79-93, and Eckroth 2007. Accordingly, Socrates’ metaphor, like the Stranger’s simile, also suggests a hiereion. In addition to the Phaedrus, Socrates also figuratively speaks of division as ‘dividing limbs (μέλη) and parts (μέρη)’ at Philebus 14e1, again suggesting a hiereion.

Phronesis 63 (2018) 392-407 Downloaded from Brill.com09/25/2021 01:44:15PM via free access 400 Muniz and Rudebusch together in an unnatural form, and calls it ‘Body 2’. Then the artist proceeds to detach and re-stitch them into yet another form, ‘Body 3’. The natural animal body and the two works of art all might contain and—depending on the stip- ulations of this rather horrible art—might even necessarily contain the very same body parts. Yet, the three bodies are distinct in virtue of their feature of intensional identity. Like these three bodies, the Stranger’s kinds Being, Same and Other are distinct in virtue of their intensional identity—for example, how those kinds are collected—although containing and even necessarily containing the same parts. In addition, a hiereion possesses the feature extensional division. It is able to divide, in virtue of its extension, into what we might call ‘subbodies’: head, torso and limbs (say). In contrast, the expression or logos ‘hiereion torso’ divides in the opposite direction, containing rather than being contained by the term or intension ‘hiereion’. The hiereion simile also captures the Stranger’s distinction between division into a subkind and into a mere part. As quoted above, Socrates pointed out that a skillful butcher will carve a hiereion at the joints, producing limbs and members, while an unskilled butcher’s hacking might fail and merely produce splinters and smashed bits of the hiereion. Those splinters and bits, although parts of the hiereion, fail to be limbs or members. The reason, surely, is that a limb or member, as a subbody, possesses a distinctive intension, appropriate to the division at hand, while the splinters and bits lack that intension. In this way, because kinds and subkinds possess intensions as well as extensions, the Stranger (at Stat. 262c10-263a1) can exhort Young Socrates to divide kinds ‘form by form’ (kat’ eidē) into subkinds as opposed to producing (by means of ‘linguistic expressions’, klēseis) mere parts that are not subkinds and do not correspond to the formal arrangement of the subject at hand. The hiereion simile thus escapes the dilemma. The simile therefore gives us a more charitable account of the Stranger’s method of division than merely extensional accounts, merely intensional accounts, or accounts that make the text inconsistent or vague. According to the simile, a kind (genos) is more inclusive than the first premise of the dilemma supposes. Such a kind possesses both an intension (a ‘form’, eidos) and an extension, namely, the many things collected in it. Division is kat’ eidē, which we translate ‘form by form’, or ‘according to form’.15 Division properly done—that is, according to form and

15 Brown 2010, 156 n. 14 proposes to translate ‘κατά᾽ in these contexts as into, in its ‘distributive sense’, instead of by or according to. This is a surprising claim, since Greek has the preposition ‘εἰς’ meaning into, and Plato uses it in a distributive sense with verbs of cutting and dividing, for example: ‘we put them into two forms opposite to each other’ (εἰς

PhronesisDownloaded 63from (2018) Brill.com09/25/2021 392-407 01:44:15PM via free access Dividing Plato’s Kinds 401 not according to mere linguistic expressions—produces parts that themselves are kinds. When we speak of cutting apart a hiereion, strictly speaking what is cut apart is the hiereion’s matter or extension, that is, the many things collected together in such a body. Likewise, when we speak of dividing a kind, what is strictly speaking divided is the extension of the kind, that is, the many things that are collected in it.

5 Four Steps to Collect a Kind

A successful interpretation needs to be faithful as well as charitable. The hiereion simile in the text is some support for the superior fidelity of our account, since merely extensional and merely intensional accounts do not fit the simile as well as our account. In this section we provide further textual support for the superior fidelity of our account, support we find in the Stranger’s paradigmatic division. We show that there the Stranger goes through four steps to collect a kind, and that our account of kinds better fits the paradigm than com- peting accounts.16

δύο δὲ αὐτὰ τίθεμεν ἐναντία ἀλλήλων εἴδη, Stat. 306c8); ‘after dividing this into twelve parts’ (διελομένους αὖ καὶ τοῦτο εἰς τὰ δώδεκα μέρη, Laws 848e4-5); and ‘dividing into two equal parts’ (διαιρούμενος εἰς ἴσα δύο μέρη, Laws 895e3). Even with the particular verb διατέμνειν that Brown cites, Aristotle uses the preposition ‘εἰς’ in order to express into (insects ‘divided not just into two parts, but into more [than two]’: διατεμνόμενα … οὐ μόνον εἰς δύο μέρη ἀλλὰ καὶ εἰς πλείω, De Respiratione 471b20-2). Brown 2010, 156 n. 14 argues that her proposed translation is ‘confirmed by’ a passage in the Phaedrus where Socrates describes ‘division’ (διαιρέσεων, 266b4) as the power κατ’ εἴδη … διατέμνειν κατ’ ἄρθρα ᾗ πέφυκεν (265e1-2). She translates this as the power ‘to divide into forms, following the objective articulation {literally: according to the joints}’, (153, her curly brackets). But her translation is forced. She gives no explanation why the preposition ‘κατά’ plus accusative at the first occurrence means into but at the second means following or according to. Nothing in the text signals such a change in meaning between the two prepositional phrases. In context, the second occurrence seems more naturally to stand in apposition to the first, continuing the meat- cutting metaphor already begun with the word ‘διατέμνειν’, with its primary meaning to cut through. She gives us no reason to reject a literal, univocal translation of the preposition ‘κατά’, giving: the power ‘according to forms, to cut through [a thing] according to joints which it has by nature’ like a skillful meat cutter. Thus the passage Brown cites as the sole evidence for her translation fails to give it significant confirmation. 16 There are other textual issues that remain unsolved by any current account. Perhaps the most important problem is that the Stranger uses intension words (like ‘εἶδος’) sometimes to refer to intensions but at other times to refer to kinds. The problem raised by these texts has led many interpreters to suppose that intension words like ‘εἶδος’ must change their meaning from other dialogues and become in these dialogues synonyms for kind words like ‘γένος’. We do not in this space present our solution, that ‘εἶδος’ preserves its meaning

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In the paradigmatic division to define the Angler, the Stranger begins with undefined references to ‘power’ and ‘expert’ (dunamin, technitēn, Sph. 219a5-6) and with Theaetetus’ hypothesis that the Angler is a kind of expert (219a7). On the grounds that there are ‘roughly two forms of all expertises’ (tōn ge technōn pasōn schedon eidē duo, 219a8), the Stranger proceeds to collect two kinds, Productive Expertise and Acquisitive Expertise (Fig. 1 above, Level 2). The Stranger collects Productive Expertise in four steps. The first step is to state a list: ‘farming, and whatever is an attendance for any living body, and whatever is an attendance for any composite or molded body—anything we call an artifact—and the imitative expertise.’17 The Stranger states this list in such a way that it is difficult to guess what relevant intension or ‘power’ is shared by each item on the list. Indeed, when the Stranger affirms about his list that ‘by one name we might most justly refer to all these things together’, Theaetetus is unable to see the relevant shared intension and asks, ‘How [might we most justly refer to them], and by what [name]?’18 Accordingly, we take it that the first step is to state an open-ended list, that is, an as yet uncol- lected plurality or extension. In the second step, the Stranger and Theaetetus agree upon the intension shared by the items on the list:

With respect to anything whatsoever, if it does not exist beforehand, but someone afterwards brings it into being, we say, I suppose, that the one who brings it into being makes and the thing being brought into being is made.—[We say so] rightly.19

For things that are farmed, for any living body that someone attends, for artifacts whether composite like fabric or molded like pottery, and even for imitation, there is something that a person brings into existence by the power to make. We interpret this power to make to be the relevant power shared by each of the items listed at the first step. Since such a power is an intension, we interpret the Stranger’s second step in general to state a relevant intension shared by the items on the list stated in the first step.

as an intension word. On our reading the Stranger sometimes uses intension words figuratively as metonyms rather than as literal synonyms for extension words. 17 Γεωργία μὲν καὶ ὅση περὶ τὸ θνητὸν πᾶν σῶμα θεραπεία, τό τε αὖ περὶ τὸ σύνθετον καὶ πλαστόν, ὃ δὴ σκεῦος ὠνομάκαμεν, ἥ τε μιμητική, Sph. 219a10-b1. 18 Σύμπαντα ταῦτα δικαιότατ’ ἂν ἑνὶ προσαγορεύοιτ’ ἂν ὀνόματι.—Πῶς καὶ τίνι; Sph. 219b1-3. 19 Πᾶν ὅπερ ἂν μὴ πρότερόν τις ὂν ὕστερον εἰς οὐσίαν ἄγῃ, τὸν μὲν ἄγοντα ποιεῖν, τὸ δὲ ἀγόμενον ποιεῖσθαί πού φαμεν.—Ὀρθῶς, Sph. 219b4-7.

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The Stranger in the third step elicits from Theaetetus that ‘the things we just now went through held their power, all together, in this’ (i.e. in making).20 Interpreters tend to ignore this third step, although the Stranger immediately restates it—‘after bringing them under a head with [their power]’ (sunkephalaiōsamenoi, 219b11)—as a condition for the fourth step in which the kind is named.21 We take it that the kind is collected by the end of the third step, since all that remains after the third step is to name it. We propose, then, that the third step is the moment at which a kind is collected. To be clear, it is not the moment in which a hierarchy of kinds and subkinds is displayed, nor even the moment in which a division takes place. The moment at which a kind is collected is like the moment in naïve set theory when a new set is formed using the axiom of specification. The axiom of specification produces a new set B, given a recognized set A, in terms of a predicate F which holds true or not of each item in set A. The axiom states: ‘To every set A and every predicate F(x), there corresponds a set B whose elements are exactly those elements x of A for which F(x) holds true.’22 Like the Axiom of Specification, the Stranger’s third step operates upon some objects that have been listed at the first step, with a power—corresponding to the predicate F(x)—that was identified at the second step, to produce a kind by bringing the objects listed under a head with that power. There is a metaphysical question how the Axiom of Specification permits the creation of a one from some plurality of things.23 In a corresponding way, when the third step somehow collects into a one the many items listed in the first step with the power stated in the second step, one might ask how the one has been gathered from many.24 But we do not need to consider such metaphysical issues for the task at hand. Our thesis in this section requires us only to show that the hiereion account is more faithful to the text than the com- peting accounts. According to the merely extensional interpretation, the kind Productive Expertise is the set containing anything that farms or nurtures living bodies, anything that produces composite bodies, anything that produces

20 Τὰ δέ γε νυνδὴ διήλθομεν ἅπαντα εἶχεν εἰς τοῦτο τὴν αὑτῶν δύναμιν, Sph. 219b8-10. (Burnet reads: Τὰ δέ γε νυνδὴ <ἃ> διήλθομεν ἅπαντα: our translation allows the pronoun to be implicit.) We take the antecedent of the pronoun ‘τοῦτο’ to be the infinitive ‘ποιεῖν’, ‘to make’, at b5. 21 ‘After bringing them under a head with [their power], let us call them “Productive Expertise”,’ Ποιητικὴν τοίνυν αὐτὰ συγκεφαλαιωσάμενοι προσείπωμεν, 219b11-12. 22 See, for example, the presentation in Halmos 1960, 5-6. 23 See Varzi 2016 for an overview of the mysteries of set theory that inspired twentieth-century mereologists. 24 Socrates asks related questions in the Philebus. See Muniz and Rudebusch 2004.

Phronesis 63 (2018) 392-407 Downloaded from Brill.com09/25/2021 01:44:15PM via free access 404 Muniz and Rudebusch molded bodies, and anything that produces representations or imitations (as listed at 219a10-b1). Accordingly, the extensional model ought to predict that the Stranger would name this kind immediately after his first step—which he does not. Again, if we were to interpret the kind Productive Expertise as the intension productive expertise, we ought to predict that the Stranger would name this kind immediately after he identifies this intension in the second step—which he does not. The Stranger requires a third step, bringing the extension under a head with an intension. On our account, the third step is necessary to the process of collecting a kind, since a kind possesses both an intension and an extension, like a body. And, on our account, the completion of the third step is sufficient for taking the fourth step of naming the resulting kind. We propose that any satisfactory interpretation of the Stranger’s kinds must give an account of all four steps, as ours does. It is true that, in the Stranger’s dozens of collections, it is rare for him explicitly to go through all four paradigmatic steps. But the only step that the Stranger ever explicitly describes as unnecessary is the fourth step of naming.25 Accordingly we take the Stranger usually to abbreviate the process of collecting subkinds by leaving implicit some steps. One way he abbreviates the process is to observe that a kind possesses two forms. For example, to divide the kind Acquisitive Expertise, he asks:

Aren’t there two forms of Acquisitive Expertise? The one a trading between those who are willing, done through gifts and wages and purchasing, while the remaining one—making use of conquest, whether by deeds or by words—as a whole would be coercive?26

25 The subkind of disputation that quibbles about contracts is not ‘worthy’ (ἄξιον) of a name, Sph. 225c3-4. And to give names to the two subkinds of the kind Expertise at Management of Footed Animals is ‘more involved than what is needed’ (περιπεπλεγμένον μᾶλλον τοῦ δέοντος, Stat. 265c3-4). Perhaps another example is ‘the [subkind Hunting] of Inanimate Things (τὸ μὲν τῶν ἀψύχων) (Fig. 1, Level 5), ‘which is nameless except at some parts’ (ἀνώνυμον ὂν πλὴν κατ’ ἔνια … ἄττα μέρη, Sph. 220a1-2). 26 At Fig. 1, Level 3. Κτητικῆς δὲ ἆρ’ οὐ δύο εἴδη; τὸ μὲν ἑκόντων πρὸς ἑκόντας μεταβλητικὸν ὂν διά τε δωρεῶν καὶ μισθώσεων καὶ ἀγοράσεων, τὸ δὲ λοιπόν, ἢ κατ’ ἔργα ἢ κατὰ λόγους χειρούμενον σύμπαν, χειρωτικὸν ἂν εἴη; Sph. 219d4-7. Other examples in the Sophist where a kind (expressed by a singular genitive) possesses δύο εἴδη (‘two forms’) are: 223c9 (Τῆς … ἀλλακτικῆς, ‘of the exchange [expertise]’), 227c7 (καθάρσεως, ‘of cleansing [expertise]’), 227d13 (κακίας, ‘of baseness’), 235d1 (τῆς μιμητικῆς, ‘of mimetic [expertise]’), 236c6, restated at 264c4 (τῆς εἰδωλοποιικῆς, ‘image-making [expertise]’), and 266e4 (Τῆς … εἰδωλουργικῆς ‘of copy-fashioning [expertise].’ Likewise members of a kind (expressed by a plural genitive)—instead of the kind itself—possess two forms at 219a8 (τῶν γε τεχνῶν πασῶν, ‘of all expertises’).

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In this passage, the feminine adjective ‘ktētikēs’ (‘acquisitive’) refers to an expertise (technēs), and its genitive case expresses its possession of the two forms. In this division the Stranger does not go through the four steps—first listing all the particular expertises at voluntary trading with gifts, wages, pur- chases etc.; second, identifying the power of voluntary trading shared by those expertises; third, bringing those particulars under a head with that power; fourth, naming the subkind—and then going through the same four steps for the other subkind. Instead he collects the first subkind by doing nothing more than describing its form as ‘a trading between those who are willing’ (in doing so calling to mind some of the items collected under that heading by referring to the trading form as ‘done through gifts and wages and purchasing’). And he collects the remaining subkind, Expertise at Acquisition through Conquest, by referring to its ‘coercive’ form ‘as a whole’, in effect collecting under that heading the various coercive expertises by describing that one form as ‘making use of conquest, whether by deeds or by words’. As we see it, the Stranger’s abbreviated collection aims to bring his interlocutor to apprehend the third step. If his audience can jump to that step, then the first two steps need not be explicit in order for him to produce an understanding of the given division.27

6 Conclusion

The Stranger’s method of division has been a mystery: no one has been able to say what the Stranger is collecting and dividing. We have proposed an interpretive and philosophical solution to this problem that is faithful to the Stranger’s hiereion simile and accounts for the Stranger’s paradigmatic four steps for collecting a subkind. On our reading, the third step collects a kind by bringing the items of an extension under a head with its shared intension. Such a kind, like a body, possesses both an intension and an extension. Since a body gets its identity from its intension while dividing in respect of its extension, our interpretation both fits the text where the Stranger distinguishes Being, Same

27 There are similar uses of the intension word εἶδος in the following abbreviated divisions. Of Expertise at Discrimination (διακριτική), ‘one [form] was to separate worse from better, the other [form was to separate] like from like’ (τὸ μὲν χεῖρον ἀπὸ βελτίονος ἀποχωρίζειν ἦν, τὸ δ’ ὅμοιον ἀφ’ ὁμοίου, Sph. 226d1-2). There are ‘many forms of [Expertise at] Cleansing’ (πολλὰ εἴδη καθάρσεων, 226e5-6). There are two forms ‘of Ignorance’ (ἀγνοίας), ‘the [form] not knowing but seeming to know’ (τὸ μὴ κατειδότα τι δοκεῖν εἰδέναι, 229c5) with the implied second form, not knowing but not seeming to know. And there are two forms of ‘Child-Rearing [Expertise]’ (παιδείας), ‘the admonitory form’ (τὸ νουθετητικὸν εἶδος, 230a8-9) and ‘the refuting [form]’ (τὸν ἔλεγχον, 230d6-7).

Phronesis 63 (2018) 392-407 Downloaded from Brill.com09/25/2021 01:44:15PM via free access 406 Muniz and Rudebusch and Other as three kinds and gives an accurate whole/part relation between kind and subkind. Our proposal opens a new avenue to finding a successful translation of the key terms ‘eidos’ (‘form’) and ‘genos’ (‘kind’) in the Stranger’s dialogues. Our solution promises to extend to Plato’s other dialogues, such as the Phaedrus and Philebus, where Socrates uses or refers to a method of division of genē (‘kinds’) according to eidē (‘forms’).28 And our proposal will make it possible better to evaluate interpretations of the philosophical value of the Stranger’s method of division and better to examine vexed questions such as how Plato may have revised his theory of Forms in his later dialogues— although such avenues, extensions, evaluations and examinations are beyond the scope of this paper.29

References

Berthiaume, G. (1982), Les rôles du mágeiros. Étude sur la boucherie, la cuisine et le sac- rifice dans la Grèce ancienne. Leiden. Black, M. (1948), Frege, ‘On Sense and Reference’, Philosophical Review 57: 209-30. [Translates Frege 1892.] Brown, L. (2010), ‘Definition and Division in Plato’s Sophist’ in D. Charles (ed.), Definition in Greek Philosophy (Oxford), 151-71.

28 And to the Timaeus. When Timaeus speaks of the intelligible creature that is a model for this visible cosmos, he describes it as a whole containing all other intelligible creatures ‘one by one and kind by kind as its parts … just as this [visible] cosmos is made up of us and all visible creatures’ (καθ’ ἓν καὶ κατὰ γένη μόρια … καθάπερ ὅδε ὁ κόσμος ἡμᾶς ὅσα τε ἄλλα θρέμματα συνέστηκεν ὁρατά, 30c8-d1). There are problems, parallel to those for the Stranger’s kinds, in interpreting this intelligible living model as merely an extension or merely an intension. We would propose to interpret it as like a body, as we have interpreted the Stranger’s kinds. Accordingly the intelligible living model would be neither an extension nor an intension, but would comprise both, like a body. 29 We gratefully acknowledge support for this research from a 2014-15 CAPES grant from Brazil to Muniz and 2014-15 sabbatical support from Northern Arizona University to Rudebusch. We thank Sylvain Delcomminette, Mary Louise Gill, Verity Harte, and Eric Brown, each leading a multi-day workshop with us on the method of division, and we thank the other workshop participants, Rachana Kamtekar and Marta Heckel. We thank organizers and audiences at presentations to the Universidade de Campinas, the University of Arizona, the University of California, Berkeley, and Northern Arizona University, also to MarkFest: A Conference in Honor of Mark McPherran and to the First Annual Philosophy Desert Workshop, with particular thanks to Christine Thomas for commenting there. We thank Paolo Crivelli, Matthew Patrick Fahy, David Liebesman, Christopher Rowe, and Will Starr for conversation or correspondence, and George Boys-Stones, Barbara Hall, Sarah Jansen, Brianna Zgurich, Hayden Niehus, John Proios, Evan Rodriguez, Jona Vance, and anony- mous referees for reading and commenting on earlier drafts.

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