Introduction IT is generally agreed that Charles Sanders Peirce was one of America's greatest philosophers, yet even today there is little agreement as to ...

: In the Cambridge Conferences Lectures of 1898 Peirce defines a continuum as a "collection of so vast a multitude" that its elements "become welded into one another." He links the transinfinity (the "vast multitude") of a continuum to the confusion of its elements by a line of mathematical reasoning closely related to Cantor's Theorem. I trace the mathematical and philosophical roots of this conception of continuity, and examine its unresolved tensions, which arise mainly from difficulties in Peirce's theory of (...) collections. (shrink)

This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...) the first time. (shrink)

Essays offer a glimpse of the Vienna-born philosopher's personality, character, and life's work.

This article aims to demonstrate that a careful examination of Peirce's original manuscripts shows that there are five main periods in Peirce's evolution in his mathematical and philosophical conceptualizations of continuity. The aim of this article is also to establish the relevance of Peirce's reflections on continuity for philosophers and mathematicians.