The book begins with a discussion of Benjamin Peirce’s linear associative algebra and then considers this and other early influences on the logic of is son, C. S. Peirce. A discussion of the early algebraic logicians such as Boole, Jevons and De Morgan follows, culminating in a detailed analysis of C. S. Peirce’s seminal paper “Description of a Notation for the Logic of Relatives.” His further developments of the 1880s, including quantificational logic are also traced. At the end of his life, Peirce looked to his graphical logic system - the existential graphs - to provide the logic of the future.

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.

This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis’s association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.

For scholars working on almost any aspect of American thought, The Bloomsbury Encyclopedia to Philosophers in America presents an indispensable reference work. Selecting over 700 figures from the Dictionary of Early American Philosophers and the Dictionary of Modern American Philosophers, this condensed edition includes key contributors to philosophical thought. From 1600 to the present day, entries cover psychology, pedagogy, sociology, anthropology, education, theology and political science, before these disciplines came to be considered distinct from philosophy. Clear and accessible, each entry contains a short biography of the writer, an exposition and analysis of his or her doctrines and ideas, a bibliography of writings and suggestions for further reading. Featuring a new preface by the editor and a comprehensive introduction, The Bloomsbury Encyclopedia to Philosophers in America includes 30 new entries on twenty-first century thinkers including Martha Nussbaum and Patricia Churchland. With in-depth overviews of Waldo Emerson, Margaret Fuller, Noah Porter, Frederick Rauch, Benjamin Franklin, Thomas Paine and Thomas Jefferson, this is an invaluable one-stop research volume to understanding leading figures in American thought and the development of American intellectual history.

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.

This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.

Benjamin Peirce was one of the principal contributors to nineteenth-century American science. He gained international prominence from his work on the perturbations of Neptune, and his Linear Associative Algebra was the first important mathematical research done by an American. He was a key figure in the professionalization of American science; and, as superintendent of the United States Coast Survey, he was an effective scientific administrator. Peirce also played an important role in the education of many American scientists, including Simon Newcomb, the most widely honored and recognized American scientist of the generation after Peirce, and Peirce's son. Charles Saunders. Peirce belonged to an impressive family of American intellectuals. The intellectual tradition in the family is apparent with Peirce's feminist mother, and his scholarly father, who wrote a history of Harvard College. The tradition finds its climax in Peirce's son, Charles, perhaps the most exceptional mind the United States has yet produced.

Joseph W. Dauben, a leading authority on the history of mathematics in Europe, China, and North America, has played a pivotal role in promoting international scholarship over the last forty years. This Festschrift volume, showcasing recent historical research by leading experts on three continents, offers a global perspective on important themes in this field.

Peirce's contemporaries had the advantage of some popular lectures on the graphs (the Lowell Lectures of 1903, principally), but his graphical publications were few and not easy to understand, as he admitted himself.