Why did Plato put mathematics at the heart of education for the rulers of his ideal city? Why has mathematics played such a central role in Western philosophy? And just how do we acquire knowledge of necessary truths? Three philosophers of international repute tackle these questions. M. F. Burnyeat brings out Plato's distinctive vision of the world as it objectively is: the structures of mathematics are also the structures that express the nature of the human soul and the soul that governs the world. Ian Hacking highlights the phenomena associated with the actual experience of proof, which so impressed philosopher-mathematicians like Descartes and Leibniz and onlookers like Plato and Wittgenstein. Jonathan Bennett explores modal discovery in Locke and Leibniz, and the infallibility of reason in Descartes and Spinoza. The answers offered by these distinguished scholars make a significant contribution to our understanding of some of the great thinkers of the past.