This paper argues that the hypothesis proposed in the Meno is the proposition ‘virtue is good’ alone, and that its epistemic nature is essentially insecure. It has been an object of huge scholarly debate which other hypothesis Socrates posited with regard to the relationship between virtue and knowledge. This debate is, however, misleading in the sense of making us believe that the hypothesis that virtue is good is regarded as a truism in the light of the process of positing a (...) higher hypothesis described in the Phaedo and the Republic. I argue that the hypothesis in question is presented as a result of the earlier discussion of Meno's third definition of virtue, which implies the consequence that morally correct actions are beneficial whether or not accompanied by conventional goods such as wealth and honour. The underlying role of presenting it as a hypothesis is therefore to postpone demonstrating the truth of a controversial thesis which needs a substantial justification. In conclusion, I s... (shrink)

This paper re-constructs Plato's ‘philosophy of geometry’ by arguing that he uses a geometrical method of hypothesis in his account of the cosmos’ generation in the Timaeus. Commentators on Plato's philosophy of mathematics often start from Aristotle's report in the Metaphysics that Plato admitted the existence of mathematical objects in-between ( metaxu) Forms and sensible particulars ( Meta. 1.6, 987b14–18). I argue, however, that Plato's interest in mathematics was centred on its methodological usefulness for philosophical inquiry, rather than on questions (...) of mathematical ontology. My key passage of interest is Timaeus’ account of the generation of the primary bodies in the cosmos, i.e. fire, air, water and earth ( Tim. 48b–c, 53b–56c). Timaeus explains the primary bodies’ origin by hypothesising two right-angled triangles as their starting-point ( arkhê) and describing their individual geometrical constitution. This hypothetical operation recalls the hypothetical method which Socrates introduces in the Meno (86e–87b), as well as the use of hypotheses by mathematicians which is described in the Republic (510b–c). Throughout the passage, Timaeus is focussed on explicating the bodies in terms of their formal structure, without however considering the ontological status of the triangles in relation to the physical world. (shrink)