Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

This article presents for the first time in english lesniewski's analysis of russell's antinomy as the analysis is given in lesniewski's 1914 paper "czy klasa klas, nie podporzadkowanych sobie, jest podporzadkowana sobie?" is the class of classes which are not subordinate to themselves subordinate to itself? it is shown how the concepts appearing in this paper, written in colloquial polish, were later incorporated and expressed as fundamental axioms and theorems of his theory of collective classes, mereology. in the 1914 paper (...) he asserted: i call any object p an object subordinate to a class k if in some sense of the expression "a" the following two conditions hold: 1) k is a class (of objects) "a", 2) p is an "a". using this explication of "p is subordinate to a class k," he showed that both of the following statements are false: a) the class of classes which are not subordinate to themselves is subordinate to itself, b) the class of classes which are not subordinate to themselves is not subordinate to itself; thus showing that russell's antinomy cannot be generated since its initial assumptions are false. (shrink)