Plato's Meno: 86E-87A: The Geometricul Illustration of The Argument by Hypothesis'

Abstract

The formal structure of Plato's conception and application of geometrical illustration to question of virtue's teachability is clear. The objective is to state an hypothesis which will determine whether or not given property is ascribable to given object; that is, whether property, inscribable triangularly, is ascribable to joint object, given area and given circle, or whether property, teachable, is ascribable to object, virtue. Yet hypothesis adopted to provide determinative criterion in case of geometrical illustration is stated so succinctly that it has been subject to diverse interpretations. We use W. H. S. Rouse's translation of 87 A 3-6 to serve as point of beginning for our interpretation. If space is such that when you apply it to given of circle, it is deficient by space of same size as that which has been applied, one thing appears to follow, and if this be impossible, another. 2 Further, R. S. Bluck13 has given selective review of literature on this question which we take as representative and from which linguistic issues are drawn as follows: Does auroiU in given (87 A 3) refer to xcpLov (space) or to xixXoc (circle), as Rouse presumes and Butcher argues despite necessity to twist Greek bit at this point? Is Cook Wilson correct in holding that the given line has to be of circle; for if not, then would not bring it [the space] into relation with circle? 5 Or can the given be considered as a or side of figure into which, as its equivalent area, it has been transformed, as A. S. L. Farquharson argues?6 Does -orou'vp ... olov with addition of octu'ro in clause specifying deficient area (87 A 5), state that area is similar to (Butcher)