Charles S. Peirce on the Logic of Number

Download or read book Charles S. Peirce on the Logic of Number written by Paul Shields and published by . This book was released on 2012-10-24 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1881 the American philosopher Charles S. Peirce published a remarkable paper in The American Journal of Mathematics called "On the Logic of Number." Peirce's paper marked a watershed in nineteenth century mathematics, providing the first successful axiom system for the natural numbers. Awareness that Peirce's axiom system exists has been gradually increasing but the conventional wisdom among mathematicians is still that the first satisfactory axiom systems were those of Dedekind and Peano. The book analyzes Peirce's paper in depth, placing it in the context of contemporary work, and provides a proof of the equivalence of the Peirce and Dedekind axioms for the natural numbers.