The Principles of Mathematics is a book written by Bertrand Russell in 1903. In it he presented his famous paradox and argued his thesis that mathematics and logic are identical.[1]
The book presents a view of the foundations of mathematics and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others. In 1937 Russell prepared a new introduction saying, "Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject." Further editions were printed in 1938, 1951, 1996, and 2009.
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Reviews were prepared by G. E. Moore and Charles Sanders Peirce, but Moore's was never published[2] and that of Peirce was, as one author described it, "so brief and cursory that I am convinced that he never read the book."[3] However, a long and generally favorable review was written by G. H. Hardy and appeared in Times Literary Supplement (Issue #88, 18 September 1903). Hardy titles his review "The Philosophy of Mathematics" and expects the book to appeal more to philosophers than mathematicians. But he says
In 1904 another review appeared in Bulletin of the American Mathematical Society (11(2):74–93) written by Edwin Bidwell Wilson.He says "The delicacy of the question is such that even the greatest mathematicians and philosophers of to-day have made what seem to be substantial slips of judgement and have shown on occasions an astounding ignorance of the essence of the problem which they were discussing. ... all too frequently it has been the result of a wholly unpardonable disregard of the work already accomplished by others." Wilson recounts the developments of Peano that Russell reports, and takes the occasion to correct Henri Poincaré who had ascribed them to David Hilbert. In praise of Russell, Wilson says "Surely the present work is a monument to patience, perseverance, and thoroughness."(page 88)
In 1959 Russell wrote My Philosophical Development in which he recalled the impetus to write the Principles:
Recalling the book after his later work, he provides this evaluation:
Such self-deprecation from the author after half a century of philosophical growth is understandable. On the other hand, Jules Vuillemin wrote in 1968
Russel's Principles of 1903 also looms large in Ivor Grattan-Guinness' study of the roots of modern logic.
The Principles of Mathematics consists of 59 chapters divided into seven parts: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. There is an anticipation of relativity physics in the final part as the last three chapters consider Newton's laws of motion, absolute and relative motion, and Hertz's dynamics. However, Russell rejects what he calls "the relational theory", and says on page 489
In his review, Hardy (1903) says "Mr. Russell is a firm believer in absolute position in space and time, a view as much out of fashion nowadays that Chapter [58: Absolute and Relative Motion] will be read with peculiar interest."