The Principles of Mathematics, Russell’s fourth book, was first published in 1903; it was reprinted unchanged in 1937 with a new introduction. The original edition was the first member in one of two series of books that Russell proposed to write during his lifetime.
In the first volume of his Autobiography (1967), covering the years 1872 to 1914, he recollected one of the most important days of his life: “I remember a cold bright day in early spring when I walked by myself in the Tiergarten, and made projects of future work. I thought that I would write one series of books on the philosophy of the sciences from pure mathematics to physiology, and another series of books on social questions. I hoped that the two series might ultimately meet in a synthesis at once scientific and practical.
My scheme was largely inspired by Hegelian ideas. Nevertheless, I have to some extent followed it in later years, as much at any rate as could have been expected. The moment was an important and formative one as regards my purposes.” The year was 1895, and the city was Berlin, where Russell and his first wife had gone to study German social democracy.
In other writings Russell added that the first series of books would begin at a very high level of abstraction and gradually grow more practical, whereas the second set would begin with practical matters and aim at becoming always more abstract; the final volume in each series would then be a similar blend of the practical and the abstract, and thus permit a grand synthesis of the two series in one magnum opus.
Russell was not yet 23 when this vision occurred to him, but as is clear from the above quotation, the initial planning of The Principles of Mathematics had already begun.
At other places in his writings, he states that his interest in the foundations of mathematics stemmed from an earlier interest in the foundations of physics, or “the problem of matter” as he usually referred to it, which was stymied when he realized the dependence of physics on a soundly based mathematics. His preliminary examination of the problem of matter must then have occurred at about the same time as the Tiergarten experience.
By 1895 he already had two books in the works: the first, German
Social Democracy (1896), reported the results of his Berlin studies; the second,
An Essay on the Foundations of Geometry (1897), was his dissertation for a Fellowship at Trinity College, Cambridge. On the strength of it he was elected a
Fellow on 10 October 1895. For book publication it had to be revised, which
accounts for the delay of two years. While he was revising it, he began work
on Principles.
