These essays tell the story of inductive probability, from its inception in the work of Thomas Bayes to some surprising current developments. Hume and Bayes initiated a dialogue between inductive skepticism and probability theory that persists in various forms throughout the history of the subject. The skeptic insists that we start in a state of ignorance. How does one quantify ignorance? If knowledge gives rise to asymmetric probabilities, perhaps ignorance is properly characterized by symmetry. And non-trivial prior symmetries generate non-trivial inductive inference. Then perhaps symmetries are not quite such innocent representations of ignorance as one might have thought. That is a sketch of the theme that is developed in the title essay, “Symmetry and its Discontents”, and that runs throughout the book.

In the second section of this book, we meet Sir Alexander Cuming, who instigated important investigations by De Moivre and Stirling, before being sent to prison for fraud. We view Ramsey's famous essay “Truth and Probability” against the Cambridge background of Robert Leslie Ellis, John Venn and John Maynard Keynes. Fisher's discussion of inverse probabilities is set in the context of Boole, Venn, Edgeworth and Pearson and his various versions of the fiducial argument are examined. We learn of Alan Turing's undergraduate rediscovery of Lindeberg's central limit theorem, and of his later use of Bayesian methods in breaking the German naval code in World War II.

The last section deals with developments in inductive probability, which are still not generally well-known, and that some philosophers have thought impossible.