SOCRATES ON THE DEFINITION OF FIGURE IN THE MENO

Theodor Ebert (Erlangen University)

Plato’s Meno is, in its rst part (up to 79e), an attempt to nd a de ni- tion of virtue (). Meno, Socrates’ interlocutor, thinks that this is an easy task and provides Socrates with a list of virtues for several dif- ferent persons, for a man, a woman, a child, an old man, a free man and a slave (71e–72a). When Socrates has made it clear to Meno that such a list does not qualify as a de nition (72c6–d1), since it does not give a single explanation covering all the virtues, Meno comes up with a different proposal: virtue is the ability to rule over other men (73c9). This leads to an even more spectacular failure on Meno’s part: since such an ability can hardly be the virtue of a child or a slave (73d2–5), this de nition would be too narrow; yet it is also too broad, since ruling over people without justice would not count as virtue either (73d6–10). Meno accepts his defeat and declares that he is unable to nd a common explanation for all the virtues, as he is in other cases (74a11–b1). Socrates then explains to Meno that they are searching for the de - nition of a general concept and he proposes to his partner to do rst some preparatory work on an easier example, that of the de nition of a gure (μ) (74e11–75a9). When Meno declines to engage in this sort of inquiry and wants Socrates to do the job for him (75b1), Socrates is willing to do so, provided that afterwards Meno will tell him what he takes the de nition of virtue to be (75b2–6). Socrates then gives Meno the following de nition of gure: “Let gure be for us that thing which, alone of the things that are, always accompanies colour”. (75b9–11, tr. Sharples, slightly altered) The de ning formula in Greek is this: μ μ μ. Socrates adds that he would be quite happy if Meno would come up with a similar de nition of virtue. Sharples, the most recent commentator of the dialogue in the English-speaking world, has the following comment on this sentence: There are two possible interpretations of this, not mutually exclusive: (i) one cannot have a patch of colour which has no shape (Sharples’ 114 theodor ebert

rendering of μ—Th. E.), (ii) anything that has shape must have some colour. (i) is perhaps the more natural reading of Plato’s words; (ii) might have been expressed as ‘is always accompanied by colour’.1 To speak of “two possible interpretations” of this sentence while claim- ing that one of these “is perhaps the more natural reading of Plato’s words” seems to me misleading. For what we have here are in fact the two universally quanti ed propositions that make up any proper de - nition. To see this, it will be suf cient to put the de nition of man as a rational animal in the same format: let man be that creature which, alone of the things that are, always accompanies rationality. Or in short: only men are always rational animals. The two words ‘only’ and ‘always’ are used to express two propositions of the form “Every S is P”. First of all, “only men are rational animals” is equivalent to “every rational animal is a man”; secondly, “men are always rational animals” is a somewhat colloquial way of saying “every man is a rational animal”. So the job of the two words ‘only’ and ‘always’ is simply to render the de niendum and the de niens coextensive, which is a requirement any de nition should comply with. Now, the job of the Greek words corresponding to the English ‘only’ and ‘always’, i.e. μ and respectively, in stating a de nition is just the same. Hence, “only gures accompany colour” is equivalent to “every companion of colour is a gure” and “ gures always accom- pany colour” will be “every gure is a companion of colour”. The second sentence corresponds to Sharples’ (ii). His (i), which takes up the ‘only’ part of Socrates’ de nition, is a somewhat entangled way of stating “every companion of colour is a gure”, for to say that “one cannot have a patch of colour which has no shape” is equivalent to saying that “every patch of colour has a shape”. Hence, the two pos- sible interpretations that Sharples wants to nd in Socrates’ words correspond simply to the two propositions stating the coextensivity of the de niendum ‘ gure’ (shape) and the de niens ‘accompanies colour’ (is a companion of colour). Thus Socrates’ model de nition of gure should have made it clear to Meno that a proper de nition of virtue should comply with the formal requirement instantiated in the de nition of gure. For any de nition, it must be possible to frame it in the form: ‘Only As are always Bs’. How does Meno react to this? He dismisses Socrates’ proposal as

1 Sharples 1985, 131.