The nature of mathematics : a critical survey

The Formal Character of Pure Mathematics This section describes the ideal arrangement of a branch of pure mathematics as a system of deductions from initial axioms. It is a consequence of the generality of pure mathematics that the subject-matter of such a system is indefinite : the axioms treat of any set of objects whose names will fit into the axioms. First published in 2000. This is Volume I of eight in the Philosophy of Logic and Mathematics series. Written in 1933, in The Nature of Mathematics offers a critical survey the author seeks to present a considered critical exposition of Principia Mathematica and to give supplementary accounts of the formalist and intuitionist doctrines in sufficient detail to lighten the paths of all who may be provoked to read the original papers.