Principia Mathematica

Abstract

THIS work contains some thousands of propositions, each, with its proof, expressed in a shorthand so concise that if they were all expanded into ordinary language, the room taken up would be ten times as large at least; space, time, and mass are not considered at all, and arithmetic is merely foreshadowed by the introduction of the symbols o, 1, 2, and 2, How then, it may be asked, can the authors pretend to be writing about mathematics? The answer amounts to saying that for every branch of the tree of knowledge there is a corresponding root, and every advance in climbing seems to compel a similar advance in delving. Just as the discovery of non-Euclidean geometries led to the reconsideration of geometrical axioms, so Cantor's invention of transfinite numbers has reacted upon the theory of elementary arithmetic, and hence upon the whole of analysis and all its applications.

Principia Mathematica.

By Dr. A. N. Whitehead B. Russell. Vol. i. Pp. xv + 666. (Cambridge: University Press, 1910.) Price 25s. net.