The ‘noble lie’ is crucial within the political philosophy of the Republic, as the ideology of the charter myth needed to motivate the citizens of the Republic’s good city in general, and the rulers in particular, to care above all for its well-being. I look first at the way lying figured in the Greeks’ imaginary and their political discourse, particularly that of the Athenian democracy; then at ethical dimensions of Socrates’ notion of ‘useful lie’, and his distinction between deception by speech and deception in the soul. What makes the ‘noble lie’ useful is its ability (if believed) to instil in citizens love for their community (not merely calculation that promotion of its well-being is in their own self-interest), through representation of their human identity as membership of a single family, with their core affections and obligations directed to their mother country. It is that sense of basic identity and commensurate obligation, not dialectically based grasp of eternal truth, which will persuade philosophers to take their part in ruling the city. Finally, I tackle the issue – its difficulty highlighted by Socrates himself – of how belief in the narrative is to be secured.

This chapter concerns the measurement of the dependence between variates, by exploiting the additional information contained in joint (rather than just marginal) distribution and density functions. For this multivariate context, we also generalize the third description of randomness seen earlier, i.e., moments and their generating functions. Joint moments and their generating functions are introduced, along with covariances, variance matrices, the Cauchy–Schwarz inequality, and joint c.f.s and their inversion into joint densities. We show how the law of iterated expectations makes use of conditioning when taking expectations with respect to more than one variate. We measure dependence via conditional densities, distributions, moments, and cumulants.