On 25 October 1946, Popper (then at the London School of Economics), was invited to present a paper entitled "Are There Philosophical Problems?" at a meeting of the Cambridge University Moral Sciences Club, which was chaired by Wittgenstein. The two started arguing vehemently over whether there existed substantial problems in philosophy, or merely linguistic puzzles—the position taken by Wittgenstein. In Popper's, and the popular account, Wittgenstein used a fireplace poker to emphasize his points, gesturing with it as the argument grew more heated. When challenged by Wittgenstein to state an example of a moral rule, Popper (later) claimed to have replied "Not to threaten visiting lecturers with pokers", upon which (according to Popper) Wittgenstein threw down the poker and stormed out. Wittgenstein's Poker collects and characterizes the accounts of the argument, as well as establishing the context of the careers of Popper, Wittgenstein and Bertrand Russell, also present at the meeting.
The book follows three narrative threads, each pivoting off the 1946 confrontation at Cambridge; the first is a documentary investigation into what precisely took place and the controversy over the differing accounts from observers; the second, a comparative personal history of the philosophers, contrasting their origins in Vienna and their differing ascents to philosophical prominence; and thirdly an exploration of the philosophical significance of the disagreement between the two and its relevance for the great debates in the early 20th century concerning the philosophy of language.