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Many readers who have been intrigued over the years by the titles of Matte Blanco's major works The Unconscious as Infinite Sets: An Essay in BiLogic (1975, London: Duckworth) and Thinking, Feeling and Being (1988, London and New York: Routledge) may have been put off by Matte Blanco's concern to write books that would be equally sophisticated and rigorous for the mathematician and logician as for the psychoanalyst. The problem was recognised in the preparation of the second book, in which Eric Rayner contributed to a helpful introduction to the main arguments of The Unconscious as Infinite Sets. New readers' need for a helping hand is part of the inspiration for this book, though by no means the sum of its ambitions. The key underlying aim is for readers to appreciate Rayner's thesis that Matte Blanco's formalising of the logical structures underlying the Freudian unconscious offers psychoanalytic theory the best chance of reintegrating itself with mainstream science, as well as of giving psychoanalysis some new and clinically useful hypotheses. However, Rayner identifies a paradox in his opening chapter—‘a few varied and more or less sane intellectuals, psychoanalysts and others find bi-logic illuminating and useful; but many more, even if they have heard of it, are baffled and probably bored’ (p. 2). This book aims to find a bridge between the two positions and to discuss the logical aspects as far as possible in ordinary language.