The Meno and the Mysteries of Mathematics

  • G. E. R. Lloyd
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 240)


The principal object of the method of hypothesis introduced at Meno 86e ff is problem reduction. Vlastos,1 p. 123, put it: ‘the logical structure of the recommended method is entirely clear: when you are faced with a problematic proposition p, to “investigate it from a hypothesis,” you hit on another proposition h (the “hypothesis”), such that p is true if and only if h is true, and then shift your search from p to h, and investigate the truth of h, undertaking to determine what would follow (quite apart from p) if h were true and, alternatively, if it were false.’ That much is clear.2 But almost everything else is obscure, thanks very largely to the obscurities in the mathematical example. This has generated an enormous secondary literature, and no interpretation can be said to be completely free from difficulty. The object of this paper is to attempt a new approach to that problem. I shall argue that the very obscurity of Plato’s mathematical example is one of its points.


Equilateral Triangle Problem Reduction Mathematical Competence Rectangular Hyperbola Solid Figure 
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© Springer Science+Business Media Dordrecht 2004

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  • G. E. R. Lloyd

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