Frege And The Philosophy Of Mathematics

Author : Michael Dummett
Publisher : Harvard University Press
Page : 364 pages
File Size : 43,7 Mb
Release : 1991
Category : Mathematics
ISBN : 0674319354

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Frege by Michael Dummett Pdf

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 : William Demopoulos
Publisher : Harvard University Press
Page : 492 pages
File Size : 52,5 Mb
Release : 1995
Category : Mathematics
ISBN : 0674319427

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Frege's Philosophy of Mathematics by William Demopoulos Pdf

Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.

Author : L. Haaparanta
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 48,7 Mb
Release : 2013-03-09
Category : Philosophy
ISBN : 9789401583343

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Mind, Meaning and Mathematics by L. Haaparanta Pdf

At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Føllesdal's early classic on Husserl and Frege of 1958. The book brings together a number of new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy.

Author : Michael D. Resnik
Publisher : Unknown
Page : 258 pages
File Size : 43,9 Mb
Release : 1980
Category : Mathematics
ISBN : UCAL:B4246993

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Frege and the Philosophy of Mathematics by Michael D. Resnik Pdf

Author : Michele Friend
Publisher : Routledge
Page : 240 pages
File Size : 52,8 Mb
Release : 2014-12-05
Category : Philosophy
ISBN : 9781317493785

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Introducing Philosophy of Mathematics by Michele Friend Pdf

What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Author : Michael Beaney,Erich H. Reck
Publisher : Taylor & Francis
Page : 424 pages
File Size : 52,8 Mb
Release : 2005
Category : Philosophy
ISBN : 0415306043

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Gottlob Frege: Frege's philosophy of mathematics by Michael Beaney,Erich H. Reck Pdf

This collection brings together recent scholarship on Frege, including new translations of German material which is made available to Anglophone scholars for the first time.

Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 41,8 Mb
Release : 2020-03-24
Category : Mathematics
ISBN : 9780691202297

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Philosophy of Mathematics by Øystein Linnebo Pdf

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.

Author : Gottlob Frege
Publisher : John Wiley & Sons
Page : 146 pages
File Size : 47,5 Mb
Release : 1980
Category : Mathematics
ISBN : 9780631126942

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The Foundations of Arithmetic by Gottlob Frege Pdf

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 : Michael Dummett
Publisher : Harvard University Press
Page : 756 pages
File Size : 55,7 Mb
Release : 1981
Category : Mathematics
ISBN : 0674319311

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Frege by Michael Dummett Pdf

No one has figured more prominently in the study of German philosopher Gottlob Frege than Michael Dummett. This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of analytic philosophy. Frege: Philosophy of Language remains indispensable for an understanding of contemporary philosophy. Harvard University Press is pleased to reissue this classic book in paperback.

Author : Joan Weiner
Publisher : Open Court
Page : 176 pages
File Size : 54,6 Mb
Release : 2011-04-15
Category : Philosophy
ISBN : 9780812697520

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Frege Explained by Joan Weiner Pdf

What is the number one? How can we be sure that 2+2=4? These apparently ssimple questions have perplexed philosophers for thousands of years, but discussion of them was transformed by the German philosopher Gottlob Frege (1848-1925). Frege (pronounced Fray-guh)believed that arithmetic and all mathematics are derived from logic, and to prove this he developed a completely new approach to logic and numbers. Joan Weiner presents a very clear outline of Frege's life and ideas, showing how his thinking evolved through successive books and articles.

Author : Edmund Husserl
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401000604

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Philosophy of Arithmetic by Edmund Husserl Pdf

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.

Author : John P. Burgess
Publisher : Princeton University Press
Page : 270 pages
File Size : 54,9 Mb
Release : 2018-06-05
Category : Philosophy
ISBN : 9780691187068

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Fixing Frege by John P. Burgess Pdf

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.

Author : Tom Ricketts,Michael Potter
Publisher : Cambridge University Press
Page : 128 pages
File Size : 55,9 Mb
Release : 2010-09-02
Category : Philosophy
ISBN : 9781139825788

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The Cambridge Companion to Frege by Tom Ricketts,Michael Potter Pdf

Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.

Author : Gottlob Frege
Publisher : Unknown
Page : 683 pages
File Size : 43,8 Mb
Release : 2013-10
Category : Mathematics
ISBN : 9780199281749

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Gottlob Frege: Basic Laws of Arithmetic by Gottlob Frege Pdf

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.

Author : Donald Gillies
Publisher : Routledge
Page : 115 pages
File Size : 45,9 Mb
Release : 2013-01-11
Category : Mathematics
ISBN : 9781136721076

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Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals) by Donald Gillies Pdf

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.