Cambridge: At the University Press, 1903. First edition of one of the key books in the history of mathematics. No subsequent volumes were published, as Russell abandoned this project to work on Principia Mathematica with Alfred North Whitehead. Top corners, head and foot of spine lightly worn. Endpapers lightly foxed, as usual. former owner's ink signature on front free endpaper. An unusually fine copy, bright and tight. Navy cloth with gilt spine. Large octavo. xxix, 534 pp. Item #15746
During his days at Trinity College, Cambridge, Russell began an intense study of the foundations of mathematics, in which he discovered "Russell's paradox," challenging the foundations of set theory. In 1903 he finished work the first volume of The Principles of Mathematics, intending to complete the project in a second volume where he planned to cover "a symbolic account of the assimilation of mathematics to logic. "After finding out that his mentor, Alfred North Whitehead, planned to publish a work with practically the same subject matter, he decided to collaborate with him instead (thus the second volume was never published). In seven parts: Part I: The Indefinables of Mathematics. Part II: Number. Part III. Quantity. Part IV. Order. Part V. Infinity and Continuity. Part V: Space. Part VII: Matter and Motion. He states in the preface: "The present work has two main objects. One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles…The other object of this work, which occupies Part I., is the explanation of the fundamental concepts which mathematics accepts as indefinable…"