The Foundations of Arithmetic

Author: Gottlob Frege
Publisher: Northwestern University Press
ISBN: 0810106051
Category : Mathematics
Languages : en
Pages : 144

Book Description
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 Basic Laws of Arithmetic

Author: Gottlob Frege
Publisher: Univ of California Press
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 208

Book Description

Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals)

Author: Donald Gillies
Publisher: Routledge
ISBN: 113672107X
Category : Mathematics
Languages : en
Pages : 115

Book Description
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.

Foundations of Arithmetic Differential Geometry

Author: Alexandru Buium
Publisher: American Mathematical Society
ISBN: 1470475774
Category : Mathematics
Languages : en
Pages : 357

Book Description
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

Harvey Friedman's Research on the Foundations of Mathematics

Author: L.A. Harrington
Publisher: Elsevier
ISBN: 9780080960401
Category : Mathematics
Languages : en
Pages : 407

Book Description
This volume discusses various aspects of Harvey Friedman's research in the foundations of mathematics over the past fifteen years. It should appeal to a wide audience of mathematicians, computer scientists, and mathematically oriented philosophers.

Logical Foundations of Mathematics and Computational Complexity

Author: Pavel Pudlák
Publisher: Springer Science & Business Media
ISBN: 3319001191
Category : Mathematics
Languages : en
Pages : 699

Book Description
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.

Handbook of Proof Theory

Author: S.R. Buss
Publisher: Elsevier
ISBN: 0080533183
Category : Mathematics
Languages : en
Pages : 823

Book Description
This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

The Foundations of Mathematics in the Theory of Sets

Author: John P. Mayberry
Publisher: Cambridge University Press
ISBN: 9780521770347
Category : Mathematics
Languages : en
Pages : 454

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

Gottlob Frege: Foundations of Arithmetic

Author: Gottlob Frege
Publisher: Routledge
ISBN: 1000154424
Category : Philosophy
Languages : en
Pages : 129

Book Description
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.

Principia Mathematica

Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688

Book Description