The Foundations of Arithmetic

The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.

The Foundations of Arithmetic

The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics and in general ontology.

The Foundations of Arithmetic

Part of the Longman Library of Primary Sources in Philosophy,” this edition ofFrege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for ...

The Foundations of Arithmetic

Part of the Longman Library of Primary Sources in Philosophy,” this edition ofFrege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for readers. A General Introduction includes the work's historical context, a discussion of historical influences, and biographical information on Gottlob Frege. The conclusion discusses how the work has influenced other philosophers and why it is important today. Annotations and notes from the editor clarify difficult passages for greater understanding, and a bibliography gives the reader additional resources for further study.

Gottlob Frege Foundations of Arithmetic

Part of theLongman Library of Primary Sources in Philosophy, this edition of Frege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for ...

Gottlob Frege  Foundations of Arithmetic

Part of theLongman Library of Primary Sources in Philosophy, this edition of Frege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for undergraduates.

Frege Dedekind and Peano on the Foundations of Arithmetic Routledge Revivals

This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic.

Frege  Dedekind  and Peano on the Foundations of Arithmetic  Routledge Revivals

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.

David Hilbert s Lectures on the Foundations of Arithmetic and Logic 1917 1933

Constructive arithmetic, as presented here, is developed on a basis stricter than that which appears a little later as ... and Bernays recognized; consequently, this approach cannot secure the foundations of classical mathematics.

David Hilbert s Lectures on the Foundations of Arithmetic and Logic 1917 1933

The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.

Frege Dedekind and Peano on the Foundations of Arithmetic

This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic.

Frege  Dedekind  and Peano on the Foundations of Arithmetic

First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.

Frege

In this superb survey of his evolving ideas, Anthony Kenny explains and assesses the full range of Frege's work and reveals why it still forms an ideal introduction to modern analytic philosophy.

Frege

"Although almost unknown in his lifetime, it was Gottlob Frege (1848-1925) who set the agenda for much of twentieth-century philosophy." "His 'concept script' overthrew Aristotle's long-established system of logic and underlies all subsequent developments in the subject. His radically new approach to the foundations of arithmetic, based on fresh definitions of the terms 'zero', 'one' and 'successor', revolutionized our understanding of mathematics. And his important insights into the nature of language and meaning provided the framework for Russell, Wittgenstein and twentieth-century linguistic analysis. In this superb survey of his evolving ideas, Anthony Kenny explains and assesses the full range of Frege's work and reveals why it still forms an ideal introduction to modern analytic philosophy. Even after seventy years, he concludes, Frege remains an absolutely central figure, one of those rare thinkers who wrote 'prose which is accessible and attractive on first acquaintance and yet which repays rereading over a lifetime'."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Wittgenstein s Lectures on the Foundations of Mathematics Cambridge 1939

Here] he was led by something, not entirely by arithmetic; for if we express <p((j>) in ordinary words, ... Wittgenstein: What I want to talk about is: (1) In what sense can one say at all that logic is the foundation of arithmetic?

Wittgenstein s Lectures on the Foundations of Mathematics  Cambridge  1939

"From his return to Cambridge in 1929 to his death in 1951, Wittgenstein influenced philosophy almost exclusively through teaching and discussion. These lecture notes indicate what he considered to be salient features of his thinking in this period of his life."--Publisher's description.

The Foundations of Mathematics in the Theory of Sets

We all have intuitions about “ infinite processes ” in arithmetic as well . But Dedekind and Frege , when they came to investigate the logical foundations of arithmetic , took it as the very starting point of their investigations ...

The Foundations of Mathematics in the Theory of Sets

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Logicism and the Philosophy of Language

This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts.

Logicism and the Philosophy of Language

Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology gathers together these foundational writings, and frames them with an extensive historical introduction. This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts.