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Author: Gottlob Frege Publisher: John Wiley & Sons ISBN: 0631126945 Category : Mathematics Languages : en Pages : 146
Book Description
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: Gottlob Frege Publisher: John Wiley & Sons ISBN: 0631126945 Category : Mathematics Languages : en Pages : 146
Book Description
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: 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.
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.
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.
Author: A. Heyting Publisher: Elsevier ISBN: 1483278158 Category : Mathematics Languages : de Pages : 644
Book Description
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: 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.
Author: Yves Nievergelt Publisher: Springer Science & Business Media ISBN: 146120125X Category : Mathematics Languages : en Pages : 425
Book Description
This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Author: Kenneth Kunen Publisher: ISBN: 9781904987147 Category : Mathematics Languages : en Pages : 251
Book Description
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Author: Gottlob Frege
Author: Gottlob Frege
Author: Donald Gillies
Author: Gottlob Frege
Author: Alexandru Buium
Author: Gottlob Frege
Author: A. Heyting
Author: L.A. Harrington
Author: Yves Nievergelt
Author: Kenneth Kunen
Author: Ludwig Wittgenstein