Written about 380BC, Plato's Republic is still our blueprint for thinking about the relationship between justice and the state. But who exactly is the "philosopher king" that Plato envisages? Did he really advocate infanticide? And who will "guard the guardians"?

In the latest episode of The Big Ideas, Benjamen Walker talks Plato with philosophers Mark Kingwell, Mark Vernon, Julian Baggini and Guardian writer Charlotte Higgins.

The Critical Thinking A-level aims to teach pupils how to consider arguments, such as those of Greek philosopher Plato, from different ethical standpoints Photograph: Alamy