Charles S Peirce On The Logic Of Number

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.

Charles Peirce’s Illustrations of the Logic of Science is an early work in the philosophy of science and the official birthplace of pragmatism. It contains Peirce’s two most influential papers: “The Fixation of Belief” and “How to Make Our Ideas Clear,” as well as discussions on the theory of probability, the ground of induction, the relation between science and religion, and the logic of abduction. Unsatisfied with the result and driven by a constant, almost feverish urge to improve his work, Peirce spent considerable time and effort revising these papers. After the turn of the century these efforts gained significant momentum when Peirce sought to establish his role in the development of pragmatism while distancing himself from the more popular versions that had become current. The present edition brings together the original series as it appeared in Popular Science Monthly and a selection of Peirce’s later revisions, many of which remained hidden in the mass of messy manuscripts that were left behind after his death in 1914.

Charles S. Peirce is generally regarded today as one of the most out-standing philosophers in American history, and especially as the inventor of pragmatism. Nevertheless, he also discovered several of the most important concepts of twentieth-century mathematical logic, including thequantifiers, the interpretation of first-order logic by means of relations, and the concept of logical consequence. There is very little general knowledge of Peirce's influence on the development of mathematical logic andalmost total ignorance of the details of that influence. The main technical results of this book establish that Peirce laid down the main elements of a framework for the model-theoretic line of development in mathematical logic.

Charles Sanders Peirce (1839-1914) was an American philosopher, physicist, mathematician and founder of pragmatism. This book provides readers with philosopher's only known, complete account of his own work. It comprises a series of lectures given in Cambridge, Massachusetts in 1898.

"These papers, the work of my students, have been so instructive to me, that I have asked and obtained permission to publish them in one volume. Two of them present new developments of the logical algebra of Boole. The volume contains two other papers relating to deductive logic and two papers upon inductive logic"--Preface. (PsycINFO Database Record (c) 2010 APA, all rights reserved)

Volume 8 of this landmark edition follows Peirce from May 1890 through July 1892 -- a period of turmoil as his career unraveled at the U.S. Coast and Geodetic Survey. The loss of his principal source of income meant the beginning of permanent penury and a lifelong struggle to find gainful employment. His key achievement during these years is his celebrated Monist metaphysical project, which consists of five classic articles on evolutionary cosmology. Also included are reviews and essays from The Nation inches.

This volume represents an important contribution to Peirce's work in mathematics and formal logic. An internationally recognized group of scholars explores and extends understandings of Peirce's most advanced work. The stimulating depth and originality of Peirce's thought and the continuing relevance of his ideas are brought out by this major book.

The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.

In this book, scholars examine the nature and significance of Peirce’s work on perception, iconicity, and diagrammatic thinking. Abjuring any strict dichotomy between presentational and representational mental activity, Peirce’s theories transform the Aristotelian, Humean, and Kantian paradigms that continue to hold sway today and forge a new path for understanding the centrality of visual thinking in science, education, art, and communication. This book is a key resource for scholars interested in Perice’s philosophy and its relation to contemporary issues in mathematics, philosophy of mind, philosophy of perception, semiotics, logic, visual thinking, and cognitive science.