Abstract

This paper argues that Socrates’ second definition of figure in Plato’s Meno (76a5–7) is deliberately insufficient: It states only a necessary condition for something’s being a figure, not a condition that is necessary as well as sufficient. For although it is true that every figure (in plane geometry) is (or corresponds to) a limit of a solid, not every limit of solid is a figure, i.e. not if the solid has a curved surface. It is argued that this mistake is one Meno was meant to detect, since one of the three concepts he has been asked to agree to beforehand (75e1–76a3), namely the concept ‘plane’, has not been used in the definition. If this concept is put to work, we get a proper definition of figure, i. e. figure is the plane limit of a solid. Meno’s failure shows that he did not grasp the import of Socrates’ first definition of figure (at 75b9–1), and hence not what this example was meant to show him on a definition generally. Socrates’ first account of figure did indeed state a proper definition of figure, taking the definiens to be a necessary as well as a sufficient condition for the definiendum, as shown by the two words standing in for quantifiers, ‘only’ and ‘always’. Some general lessons about the importance of the dramatic elements in a Platonic dialogue are drawn from this interpretation.