Russell wrote a sentence in 1901 that destroyed the life's work of a man he had never met, and then spent a decade trying to repair the damage to his own.

The sentence is the paradox. Consider the set of all sets that are not members of themselves. Is it a member of itself? If it is, it is not; if it is not, it is. Frege had just finished the second volume of the work grounding arithmetic in logic, and Russell sent it to him. Frege's reply said the ground on which he had meant to build arithmetic had been rocked, and he added an appendix admitting it.

That is the shape of Russell's career: technical work of the first order, and consequences he did not always control.

The theory of descriptions

His single greatest technical contribution, published in Mind in 1905, and the reason people call this the beginning of analytic philosophy.

The puzzle: the present King of France is bald. There is no King of France. So is the sentence false? Then its negation — the present King of France is not bald — should be true, and that seems wrong too. Worse, the sentence appears to be about something that does not exist, which suggests non-existent things must in some sense be there to be talked about. Meinong had concluded exactly that.

Russell's move is to deny that the phrase names anything at all. The present King of France is bald is not subject-and-predicate; it is three claims at once: there is at least one King of France, there is at most one, and whatever is King of France is bald. The first is false, so the whole is false, and nothing non-existent has to exist for the sentence to mean something.

What made it famous is the method rather than the result. The grammatical form of a sentence can disguise its logical form, and philosophy's job is to find the real structure underneath. That program runs from here through the Tractatus, through the Vienna Circle, and into most of the twentieth century.

Principia, and what it cost

Principia Mathematica, with Whitehead, in three volumes between 1910 and 1913: an attempt to derive the whole of mathematics from logic alone. Ten years of work. It reaches the proof that 1 + 1 = 2 partway through the second volume.

The paradox had to be blocked, and Russell's device was the theory of types — a hierarchy in which a set cannot refer to itself. It works and it is ugly, and it required an axiom of reducibility that Russell himself never believed.

Then in 1931 Gödel proved that any system strong enough for arithmetic contains truths it cannot prove, and the logicist project as Russell conceived it was finished. He said afterwards that his intellect never fully recovered from the strain of writing it.

The by-products outlived the program. Modern logical notation, the regimentation of mathematical argument, and the conviction that formal technique can settle philosophical questions all come out of it.

The public life

He was imprisoned in 1918 for six months over an article about American troops in Britain, and again in 1961, aged eighty-nine, for a week, over nuclear disarmament. He lost his Cambridge lectureship for the first. A court in New York vacated his appointment in 1940 on the grounds that his views on sex made him unfit to teach.

He won the Nobel Prize in Literature in 1950 — not Peace, Literature — for writing, in the citation's words, in defense of humanitarian ideals and freedom of thought. He wrote A History of Western Philosophy to pay for things, it is unreliable in places and is still the most readable survey there is, and it made him rich.

The objection

The mismatch between the public moralist and the private man is the standard charge and it is largely fair.

He wrote extensively on marriage, honesty and the ethics of how people should treat one another, while conducting his own relationships with a carelessness his children documented. His son's and granddaughter's accounts are not flattering. The Beacon Hill school he ran with Dora Russell was progressive in principle and chaotic in practice.

The narrower philosophical objection is that logical atomism — the view that the world is made of simple facts corresponding to simple propositions — did not survive. Wittgenstein, who had supplied much of it, abandoned it first. Russell kept adjusting his position for sixty years, which his admirers call intellectual honesty and his critics call a failure to have one.

His introduction to the Tractatus was written to get the book published, and Wittgenstein thought he had misunderstood it throughout. Both things are true.