Five years ago, BBC journalists David Edmonds and John Eidinow scored a surprising commercial hit with their best seller “Wittgenstein’s Poker.” Their clever conceit was to write about a complex philosophical debate using the techniques of biography. Instead of simply exploring the intellectual differences between Ludwig Wittgenstein, the great dissolver of philosophical problems, and Karl Popper, the defender of the open society, Messrs. Edmonds and Eidinow built their book around a notorious altercation in 1946, when Wittgenstein allegedly menaced Popper with a fireplace poker. By making this scandal, as juicy as it gets in academic philosophy, the focus of their book, they were able to infuse an otherwise abstract debate with the gossipy glamour of a Vanity Fair profile.The success of “Wittgenstein’s Poker” spawned a new mini-genre – the most recent entry is Matthew Stewart’s “The Courtier and the Heretic,” about Spinoza and Leibniz – and gave a new lease on life to the ever-popular title formula, coined by Julian Barnes in “Flaubert’s Parrot.”

Now, in “Rousseau’s Dog” (Ecco, 340 pages, $25.95), Messrs. Edmonds and Eidinow have produced another charming essay in pop intellectual history.The recipe is that of “Wittgenstein’s Poker,” right down to the odd title; but where the poker was real and central to the story of the last book, the dog in the new one is mostly metaphorical. Jean-Jacques Rousseau did have a dog, Sultan, to which he was fiercely devoted; in 1766, when he fled persecution in Switzerland to seek asylum in England, Sultan was his closest companion. But Messrs. Edmonds and Eidinow have another kind of companion in mind, the one referred to by the journalist Friedrich Grimm, when he observed that Rousseau “takes with him a companion who will not suffer him to rest in peace.” This quality of soul might well be compared to a dog, since it hounded Rousseau to the end of his days. It was, as Messrs. Edmonds and Eidinow explain, “the writer’s deeply rooted belief that the world was hostile and treacherous, ready at any moment to betray him.”

If Rousseau’s dog is not quite as concrete as a poker, neither is the quarrel at the heart of the book as dramatically physical as Wittgenstein’s near-brawl with Popper. Instead, Rousseau’s poisonous feud with David Hume, the Scottish philosopher who was his rival in talent and reputation, was fought with letters and gossip. But while the two men never came to blows, their mutual hatred was intense enough to transfix the intelligentsia of England and France. All during the summer of 1766, the boldface names of the Enlightenment – D’Alembert, Diderot, Horace Walpole, even Frederick the Great and George III – were abuzz over the accusations that Hume and Rousseau hurled at one another. The achievement of “Rousseau’s Dog” is to make the 21st-century reader feel some of the excitement of this 18thcentury scandal, and some of its importance.

The fight between Hume and Rousseau was bitter as only a falling out between former friends can be. In fact, at the beginning of 1766, Hume was one of the only friends Rousseau had left. As Messrs. Edmonds and Eidinow show in their brief summary of Rousseau’s complicated life – a life so dramatic that it inspired the first modern autobiography, the “Confessions” – the Swiss writer was as trying to know as he was delightful to read. Rousseau was, in fact, the first example of that Romantic species, the Genius, conceived as a monstre sacree whose gifts give him the right, if not the obligation, to treat the people around him like dirt.

Rousseau’s ability to love mankind with a passionate, theatrical love while abusing the actual men and women with whom he came into contact set the precedent for abhorrent 19th-century “idealists” like Shelley and Wagner. The most glaring of his sins, which his enemies loved to use against him, was his abandonment of no fewer than five of his children to a foundling hospital, where they were very likely to die, simply because he refused to live the bourgeois life of a husband and father.

Like other impossible geniuses, Rousseau had no trouble attracting patrons. Leading figures of the ancien regime were eager to be associated with the man who blasted the aristocracy, the church, and society in general in works such as “La Nouvelle Heloise” and “Emile.” But few remained his benefactor for long, since he was as proud as any Spanish grandee, quick to repay kindness with suspicion. By 1766, Rousseau’s radicalism had made both France and Switzerland unlivable for him – his house in a Swiss village was stoned by angry neighbors – and he determined to try his luck in England.

Fortunately, as it seemed at first, Rousseau had a perfect cicerone in Hume, who was just about to return home after a stint as a British diplomat in Paris. Hume arranged to accompany Rousseau (and Sultan) on the Calais-Dover crossing,then helped to find lodgings for his guest; he even intervened with the king to get Rousseau a royal pension. In performing all these services, Hume was living up to his Parisian reputation as “le bon David,” the amiable, benevolent philosopher who had cut a wide swathe through French high society (especially its female contingent). He brushed aside the warning of the Baron D’Holbach, a leading philosophe and a confirmed enemy of Rousseau, who told Hume: “You don’t know your man. I will tell you plainly, you’re warming a viper in your bosom.”

It took about six months for Hume to come around to D’Holbach’s point of view. Exactly how Hume and Rousseau fell out is the substance of “Rousseau’s Dog,” a nearly gothic tale that the authors tell with relish. The “King of Prussia” letter, the three slaps, the 12 lies – these Sherlock Holmesian details keep the reader absorbed to the end. And while the drama is building, Messrs. Edmonds and Eidinow manage to sketch, in a few very broad strokes, the philosophical differences that make the Hume-Rousseau quarrel more than trivial.

For their differences were about more than personality; they represented contrary worldviews and philosophical temperaments.As the authors write: “Hume was an optimist, Rousseau a pessimist; Hume gregarious, Rousseau a loner. Hume was disposed to compromise, Rousseau to confrontation.” This does not tell you much about either man’s ideas, and it is possible to read “Rousseau’s Dog” without ever learning just why these ex-friends were such important and fascinating thinkers. But “Rousseau’s Dog” is not meant to be a textbook; it is an elegant entertainment, and it does not disappoint.

akirsch@nysun.com