The διακριτικὴ τέχνη (the art of separating or discriminating), from which the sixth definition of the Sophist starts (226b1–231b9), is puzzling. Prima facie the art of separating does not fit the initial division of art between ποιητικὴ τέχνη (production) and κτητικὴ τέχνη (acquisition) at 219a8–c9.Footnote ² Therefore, scholars generally agree that, although mutually exclusive, ποιητική and κτητική are not exhaustive and leave room for a third species of art, διακριτικὴ τέχνη, on a par with ποιητική and κτητική.Footnote ³ However, I argue that textual evidence suggests otherwise.

Later during the sixth division (at 226e8–227a1) we indeed learn that medicine (ἰατρική) is a species of purification (καθαρτική), which itself is a species of διακριτική. But medicine, whether it is conceived as removing evil from the body or helping the body to recover health, is certainly a form of care (θεραπεία) for the body (see, for instance, the expression τὰς ὑπὸ τῶν ἰατρῶν θεραπείας at Pl. Prt. 354a5).Footnote ⁴ Now, the art of caring is cited among the examples of production at the beginning of the Sophist (at 219a10–b2). Therefore, medicine, a part of διακριτική and a kind of care, seems productive. Moreover, another part of διακριτική, the art of carding (ξαντική), is clearly treated as productive in the Statesman (= Plt.) (the Stranger speaks of the ἔργα of carding at Plt. 282e4). Finally, at Plt. 282b1–c10, the Stranger uses the couple διακριτική/συγκριτική (the art of combining) for dividing wool-working (ταλασιουργική), a productive art (cf. ποίησιν, Plt. 282a7). Since, as these texts suggest, parts of διακριτική are productive, διακριτική cannot be a third species of art on a par with ποιητική and κτητική. Rather, διακριτική is intertwined with ποιητική.Footnote ⁵

Does it mean that (not only parts of but) διακριτικὴ τέχνη itself is productive? We cannot rule out that Plato completely disregards the initial division between ποιητική and κτητική in the sixth definition of the Sophist,Footnote ⁶ and that διακριτικὴ τέχνη could be both productive and something else, acquisitive for instance.Footnote ⁷ However, the exhaustive and exclusive division of art between ποιητική and κτητική is never questioned in the dialogue (it is even repeated at 265a4–5), which might indicate that it remains valid throughout the Sophist. It is also more charitable to provide Plato with a consistent account of the divisions of art in the Sophist than having him changing his mind in the course of the dialogue. Another possibility, which preserves the initial division of arts into productive and acquisitive, is that the couple διακριτική/συγκριτική creates a transversal cut among all arts.Footnote ⁸ Besides being productive or acquisitive, a given art would then either separate or combine. Nevertheless, it is doubtful that every acquisitive art either separates or combines something: in which category would the angler and the wrestler fall, for instance? By contrast, the productive arts mentioned at the beginning of the Sophist (219a10–b1) are easily divided according to the couple διακριτική/συγκριτική: farming or tillage (γεωργία) is there explicitly associated with the care for mortal bodies (περὶ τὸ θνητὸν πᾶν σῶμα θεραπεία), which, as we saw, has a διακριτικὴ τέχνη as one of its parts (medicine);Footnote ⁹ on the other hand, imitation (μιμητική) and the creation of utensils (σκευή) must imply a combination or a composition of some sort (see for the creation of utensils τὸ σύνθετον at 219a11 that clearly matches the συγκριτικὴ τέχνη introduced in the Statesman). Taking the cut between διακριτική/συγκριτική as internal to the productive arts seems therefore the best way to maintain the initial division into acquisitive and productive arts.

Admitting that the starting point of the sixth definition is productive, why did Plato not tell us? Perhaps he did, in an indirect way.Footnote ¹⁰ Recall that the Stranger introduces the sixth division by the following saying: ‘when one can't catch [a beast] with one [sc. hand]’; Theaetetus immediately completes the saying as follows: ‘… one must use both’ (ΞΕ. … οὐ τῇ ἑτέρᾳ ληπτόν; ΘΕΑΙ. οὐκοῦν ἀμφοῖν χρή, 226a7–8). I interpret the two ‘hands’ as representing the two parts of art that have been initially distinguished: productive and acquisitive. Before the sixth division, the first five divisions took their starting points in different parts of the acquisitive art.Footnote ¹¹ So only one ‘hand’ has been used. By insisting just before the sixth division that one must now also use the other ‘hand’, I take it that Theaetetus and the Stranger agree that they must switch from the acquisitive art that has guided the enquiry until now to the art that has been left aside so far: the productive art. In that way, they indeed use ‘both hands’ for capturing the beast. As such, the occurrence of this saying does not constitute proof, but, once it is seen through the lens of the accumulated evidence from the Sophist and the Statesman gathered above, this apparently innocuous saying becomes a subtle and discrete way for Plato to announce to his reader the necessity to switch to a division of the productive art.Footnote ¹²