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 exten- sion (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, © koninklijke brill nv, leiden, 2018 | doi:10.1163/15685284-12341355Downloaded from Brill.com09/25/2021 01:44:15PM via free access Dividing Plato’s Kinds 393 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 ‘para- digm’ (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 meta- physical 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 num- ber, 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 lan- guage, 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, there- fore, 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 inten- sional 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.