Nelson Goodman's acceptance and critique of certain methods and tenets of positivism, his defence of nominalism and phenomenalism, his formulation of a new riddle of induction, his work on notational systems, and his analysis of the arts place him at the forefront of the history and development of American philosophy in the twentieth-century. However, outside of America, Goodman has been a rather neglected figure. In this first book-length introduction to his work Cohnitz and Rossberg assess Goodman's lasting contribution to philosophy and show that although some of his views may be now considered unfashionable or unorthodox, there is much in Goodman's work that is of significance today. The book begins with the "grue"-paradox, which exemplifies Goodman's way of dealing with philosophical problems. After this, the unifying features of Goodman's philosophy are presented - his constructivism, conventionalism and relativism - followed by an discussion of his central work, The Structure of Appearance and its significance in the analytic tradition. The following chapters present the technical apparatus that underlies his philosophy, his mereology and semiotics, which provides the background for discussion of Goodman's aesthetics. The final chapter examines in greater depth the presuppositions underlying his philosophy.

Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors' introduction to the topic of abstractionism, five contributions deal with the semantics and meta-ontology of Abstractionism, as well as the so-called Caesar Problem. Four papers then discuss abstractionist epistemology, focusing on the idea of implicit definitions and non-evidential warrants (entitlements) to account for a priori mathematical knowledge. This is followed by four chapters concerning the mathematics of Abstractionism, in particular the issue of impredicativity, the Bad Company objection, and the question of abstractionist set theory. Finally, the last section of the book contains three contributions that discuss Frege's application constraint within an abstractionist setting.

Nelson Goodman's distinctive contributions to such diverse areas of philosophy as epistemology, metaphysics, semiotics, logic, philosophy of language, science, and art, and his engagement with the work of Rudolf Carnap and other prominent figures in the analytic tradition, places him at the forefront of the history and development of Anglo-American philosophy in the twentieth century. Although recently the significance of Goodman's work has not been sufficiently appreciated, Daniel Cohnitz and Marcus Rossberg show that much of it is of relevance for contemporary philosophy. This book, the first comprehensive introduction to Goodman's philosophy, examines and assesses his contribution. The book begins with Goodman's New Riddle of Induction, the so-called "Grue"-paradox, which exemplifies his way of dealing with philosophical problems, and thus provides an introduction to Goodman's thought. It then covers his central work, The Structure of Appearance, as well as his philosophy of art, philosophy of language, his conventionalism, constructionalism and relativism. The technical apparatus that is required to understand Goodman's work, in particular his mereology and theory of symbols, is introduced in an accessible manner in the course of the book. The final chapter locates Goodman's position in contemporary debates and discusses recent criticisms.

The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege's masterpiece, not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (originally published in two volumes, 1893 and 1903), with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework within which his technical contributions were conceived and developed has been so deep that he has a strong case to be regarded as the inventor of much of the agenda of modern analytical philosophy itself. Two of Frege's three principal books - the Begriffsschrift (1879) and Grundlagen der Arithmetik (1884) - have been available in English translation for many years, as have all the most important of his other, article-length writings. Grundgesetze was to have been the summit of Frege's life's work - a rigorous demonstration of how the fundamental laws of the classical pure mathematics of the natural and real numbers could be derived from principles which, in his view, were purely logical. A letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that Axiom V of his system, governing identity for value-ranges, led to contradiction. But much of the main thrust of Frege's project can be salvaged. The continuing importance of the Grundgesetze lies not only in its bearing on issues in the foundations of mathematics but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work.

The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was to be the pinnacle of Freges lifes work. It represents the final stage of his logicist project the idea that arithmetic and analysis are reducible to logic and contains his mature philosophy of mathematics and logic. The aim of Basic Laws of Arithmetic is to demonstrate the logical nature of mathematical theorems by providing gapless proofs in Frege's formal system using only basic laws of logic, logical inference, and explicit definitions. The work contains a philosophical foreword, an introduction to Frege's logic, a derivation of arithmetic from this logic, a critique of contemporary approaches to the real numbers, and the beginnings of a logicist treatment of real analysis. As is well-known, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that his basic law V, governing the identity of value-ranges, leads into inconsistency. Frege discusses a revision to basic law V written in response to Russells letter in an afterword to volume II. The continuing importance of Basic Laws of Arithmetic lies not only in its bearing on issues in the foundations of mathematics and logic but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. Philip Ebert and Marcus Rossberg present the first full English translation of both volumes of Freges major work preserving the original formalism and pagination. The edition contains a foreword by Crispin Wright and an extensive appendix providing an introduction to Frege's formal system by Roy T. Cook.