An Essay on the Foundations of Geometry by Bertrand Russell (PDF)

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About the bookMy thanks are due to Mr G. F. Stout and Mr A. N. Whitehead for kindly reading my proofs; and helping me by many useful criticisms. To Mr Whitehead I owe; also; the inestimable assistance of constant criticism and suggestion throughout the course of construction; especially as regards the philosophical importance of projective Geometry.—from this book

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⭐Geometry has been at the heart of western intellectual thinking since the Ancient Greeks. Euclid’s style became the model for thinking, logic and proof. We have suffered from this ever since. This book was Bertrand Russell’s first philosophical book: it could have been his last. Few have read it because it is almost unreadable; it is turgid, dense, excessively academic and deservedly ignored.This book began life as Russell’s undergraduate dissertation at Cambridge, polished on the US lecture circuit and published in 1897 by The Cambridge University Press. For a perspective on Russell’s life, see my review of “Bertrand Russell – A Life” by Caroline Moorehead. His private education at home involved studying history and mathematics. He was admitted to Trinity College, Cambridge in 1890, where he studied mathematics. This was quite appropriate because this was the subject that Trinity was world-famous for. He graduated seventh in his class but then got his First Class degree in the Moral Sciences – a subject he was later to become infamous for as a prolific author. He was encouraged to write a dissertation as this was the only way for post-graduate study and if successful might result in a paid Trinity Fellowship. One of his teachers (James Ward, a Kantian) suggested writing on the new, controversial subject of Non-Euclidean Geometry (then called ‘metageometry’). He produced his first draft (134 pages) in three months: a testimony to his prolific writing talent. The only manuscript was examined in 1895 by two of his teachers, Ward and Alfred North Whitehead. The book was quite well received in France, where the foundations of mathematics were a hot topic but were largely ignored elsewhere, as too specialized. In fact, even Russell eventually did not view it too highly for in his intellectual biography (“My Philosophical Development”– 1959) he himself considered it “severely negatively”, regarding it as: “somewhat foolish”. In retrospect, he admits that he was first inspired by Kant’s question, ‘how is geometry possible?’, later acknowledging that it had been obsoleted by Einstein’s Theory of General Relativity (1916) and in summary: “I do not think there is anything valid therein.” This later judgment reflected Russell’s eventual position that he was using the ‘scientific method’ that discarded work later shown to deficient in evidence or logic. Philosophically, this was reinforced by Russell’s abandonment of Idealism and his eventual return to his adolescent commitment to the tradition of British Empiricism.

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