ABSTRACT
When writing on Plato in The Open Society (Chapter 6: 'Totalitarian Justice'), I came to comment on the Platonic theory of justice and Plato's distinction between 'arithmetical' equality and 'proportionate' (or 'geometrical') equality; and I appended to my note 9 of that chapter the results of a study of Plato and geometry, here reprinted in Section 1. I later added an addendum with the title 'Plato and Geometry', here reprinted as Section 2. After this follows Section 3, which contains Addendum II from O.S., vol. I, entitled 'The Dating of the Theaetetus', written in 1961. The following Sections 4 and 5 contain reprints of texts that were first published in this version in Studies in Philosophy, ed. J. N. Findlay, Oxford, 1966, as sections VII and VIII of my paper 'On the Sources of Knowledge and of Ignorance', which also appeared as the Introduction to C. & R., but with fewer notes than here. Section 6, entitled 'The Cosmological Origins of Euclidean Geometry', is a discussion note on a paper by Professor Árpád Szabó, first published in Problems in the Philosophy of Mathematics, ed. I. Lakatos, vol. I, Amsterdam, 1967, pp. 18-20, and the final Section 7 is a reprint of'Plato, Timaeus 54e—55a', first published in The Classical Review, N.S. 20, 1970, pp. 4—5.
