This is the story which two American professors, Robert Zaretsky and John Scott, set out to tell. They recount it with elegance and sympathy (and some dry humour), and manage to get much of the lives of these two thinkers, plus major walk-on parts for Boswell and Voltaire, into a fairly short book.

At first, one assumes that the account of Hume's run-in with Rousseau will become a springboard for the study of their contrasting philosophies - as the subtitle suggests. But gradually one realises that the personal story is the real subject of the work; this is a book about a biographical episode, in which it just so happens that the psychological questions arising from it shade off delicately into philosophical issues about passion, reason and belief.

For the most part, this task is so well performed that one can confidently recommend this book as a user-friendly entrée into the world of 18th-century intellectual life. But there is one very strange error. The authors declare that Hume is "unnamed" in Rousseau's Confessions; whereas book 12 of that work not only contains a discussion of Hume, but also describes how Rousseau was urged to put himself in Hume's hands by one of the Parisian literary ladies, and implies that that lady, on a visit to Môtiers, secretly incited the stoning of his house. So those stones were really thrown at him not by the local peasants, but by a distant, malign and Scottish invisible hand.

Let us not beat about the bush here. Rousseau had become a paranoiac. Psychology and philosophy can wander hand-in-hand in all kinds of fascinating ways; but there must come a point, on the descent into mental illness, where philosophy has to stop and wave goodbye.