The Foundations Of Arithmetic

Author : Gottlob Frege
Publisher : John Wiley & Sons
ISBN 13 : 0631126945
Total Pages : 146 pages
Book Rating : 4.42/5 ( download)

DOWNLOAD NOW!

Download or read book The Foundations of Arithmetic written by Gottlob Frege and published by John Wiley & Sons. This book was released on 1980 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: A philosophical discussion of the concept of number In the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.

Author : Alexandru Buium
Publisher : American Mathematical Society
ISBN 13 : 1470475774
Total Pages : 357 pages
Book Rating : 4.72/5 ( download)

DOWNLOAD NOW!

Download or read book Foundations of Arithmetic Differential Geometry written by Alexandru Buium and published by American Mathematical Society. This book was released on 2023-11-20 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Donald Gillies
Publisher : Routledge
ISBN 13 : 113672107X
Total Pages : 115 pages
Book Rating : 4.76/5 ( download)

DOWNLOAD NOW!

Download or read book Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) written by Donald Gillies and published by Routledge. This book was released on 2013-01-11 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Gottlob Frege
Publisher : Univ of California Press
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4./5 ( download)

DOWNLOAD NOW!

Download or read book The Basic Laws of Arithmetic written by Gottlob Frege and published by Univ of California Press. This book was released on 1967 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Gottlob Frege
Publisher : Northwestern University Press
ISBN 13 : 0810106051
Total Pages : 144 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book The Foundations of Arithmetic written by Gottlob Frege and published by Northwestern University Press. This book was released on 1980-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : A. Heyting
Publisher : Elsevier
ISBN 13 : 1483278158
Total Pages : 644 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book Philosophy and Foundations of Mathematics written by A. Heyting and published by Elsevier. This book was released on 2014-05-12 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examines mathematics and experience and mathematics and logic. Topics include denumerably unfinished sets, continuum problem, logic of relations, consistency proofs for formal systems independent of their interpretation, infinite numbers, and problems of space and time. The text is a valuable reference for students, mathematicians, and researchers interested in the contributions of Brouwer in the studies on the philosophy and foundations of mathematics.

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.01/5 ( download)

DOWNLOAD NOW!

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michael Dummett
Publisher : Harvard University Press
ISBN 13 : 9780674319356
Total Pages : 364 pages
Book Rating : 4.54/5 ( download)

DOWNLOAD NOW!

Download or read book Frege written by Michael Dummett and published by Harvard University Press. This book was released on 1991 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

Author : Garret Sobczyk
Publisher : Springer Science & Business Media
ISBN 13 : 0817683852
Total Pages : 370 pages
Book Rating : 4.56/5 ( download)

DOWNLOAD NOW!

Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Author : Gottlob Frege
Publisher : Routledge
ISBN 13 : 1000154424
Total Pages : 129 pages
Book Rating : 4.29/5 ( download)

DOWNLOAD NOW!

Download or read book Gottlob Frege: Foundations of Arithmetic written by Gottlob Frege and published by Routledge. This book was released on 2020-07-24 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.