Yet these two very contrasting thinkers did have some common ground. While both were products of the "Age of Reason", neither believed that reason, as such, had any motive power: sentiment and sympathy were the generating forces of human behaviour. Both, too, had suffered from the disapproval of the ecclesiastical authorities (Calvinism being the doctrinal bedrock of Edinburgh as well as Geneva). On religious issues, indeed, Hume was the more radical of the two. While Rousseau preached his own portentous brand of "natural religion", Hume demolished all theological arguments, including "natural" ones.

With such very different temperaments, and largely different beliefs, it is a miracle that the warm friendship between them lasted as long as it did - which is to say, six months on Hume's side and about three on Rousseau's. While Hume exerted himself to honour and help his friend (commissioning his portrait; finding him a country retreat; even engineering the offer of a royal pension), Rousseau was spinning a web of dark suspicions, in which every offer of help was a malignant trick or a downright humiliation.

To Hume's astonishment, Rousseau sent him, from his rural retreat in Staffordshire, a long, denunciatory letter, in which every detail of the Scotsman's behaviour - even his blank stare - was solemnly held up as evidence. The text was clearly designed for publication. So Hume reluctantly decided to get his retaliation in first, by publishing the letter, his comments and a mass of other evidence proving his innocence and good faith. Yet such was the cult of Rousseau that most people in France, and many in England, took Rousseau's side. Hume, bruised and battered, and vindicated only among his friends, retired from the fray.