Fixing Frege

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Fixing Frege

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Author : John P. Burgess
language : en
Publisher: Princeton University Press
Release Date : 2018-06-05

Fixing Frege written by John P. Burgess and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Philosophy categories.

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.

Fixing Frege

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Author : John P. Burgess
language : en
Publisher: Princeton University Press
Release Date : 2005-07-25

Fixing Frege written by John P. Burgess and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-25 with Mathematics categories.

Gottlob Frege's attempt to found mathematics on a grand logical system came to grief when Bertrand Russell discovered a contradiction in it. This book surveys consistent restrictions in both the old and new versions of Frege's system, determining just how much of mathematics can be reconstructed in each.

Frege S Theorem

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Author : Richard G. Heck
language : en
Publisher: OUP Oxford
Release Date : 2011-09-29

Frege S Theorem written by Richard G. Heck and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Philosophy categories.

Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterly fundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that arithmetic follows, purely logically, from a near definition. As Crispin Wright was the first to make clear, that means that Frege's logicism, long thought dead, might yet be viable. Heck probes the philosophical significance of the Theorem, using it to launch and then guide a wide-ranging exploration of historical, philosophical, and technical issues in the philosophy of mathematics and logic, and of their connections with metaphysics, epistemology, the philosophy of language and mind, and even developmental psychology. The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues. There are also new postscripts to five of the essays, which discuss changes of mind, respond to published criticisms, and advance the discussion yet further.

Taking Frege At His Word

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Author : Joan Weiner
language : en
Publisher:
Release Date : 2020

Taking Frege At His Word written by Joan Weiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.

He is thought to have introduced-and made crucial contributions to-the project of giving an account of the workings of natural language. Yet, despite the great admiration most contemporary philosophers feel for Frege, it also is widely believed that he committed a large number of serious, and inexplicable, blunders. If Frege really meant to be constructing a theory of the working of natural language, then a significant number of his stated views-including views he portrayed as central to his philosophical picture-are straightforwardly wrong. But did Frege really mean to be giving an account of the workings of language? He never explicitly said so. And, as Joan Weiner shows in Taking Frege at his Word, if we take seriously Frege's own accounts of what he means to be doing, a very different and exciting philosophical project comes into view. The apparent blunders in his writings turn out not to be blunders at all. Moreover, far from turning Frege's writings into an object of purely antiquarian interest, the Frege Weiner uncovers has on offer new ways of addressing of important contemporary philosophical problems. Book jacket.

Essays On Frege S Basic Laws Of Arithmetic

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Author : Philip A. Ebert
language : en
Publisher: Oxford University Press
Release Date : 2019-09-11

Essays On Frege S Basic Laws Of Arithmetic written by Philip A. Ebert and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Philosophy categories.

The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege's masterpiece, not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.

The Cambridge Companion To Frege

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Author : Tom Ricketts
language : en
Publisher: Cambridge University Press
Release Date : 2010-09-02

The Cambridge Companion To Frege written by Tom Ricketts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Philosophy categories.

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.

Gottlob Frege Frege S Philosophy Of Mathematics

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Author : Michael Beaney
language : en
Publisher: Taylor & Francis
Release Date : 2005

Gottlob Frege Frege S Philosophy Of Mathematics written by Michael Beaney and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Philosophy categories.

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.

Frege

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Author : Dale Jacquette
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-04

Frege written by Dale Jacquette and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Biography & Autobiography categories.

A rich and informative biography of one of the most important and influential figures of analytic philosophy.

Frege On Thinking And Its Epistemic Significance

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Author : Pieranna Garavaso
language : en
Publisher: Bloomsbury Publishing PLC
Release Date : 2014-11-12

Frege On Thinking And Its Epistemic Significance written by Pieranna Garavaso and has been published by Bloomsbury Publishing PLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-12 with Philosophy categories.

Pieranna Garavaso and Nicla Vassallo investigate Gottlob Frege's notion of thinking (das Denken) to provide a new analysis of a largely unexplored area of the philosopher's work. Confronting Frege's deeply seated and widely emphasized anti-psychologism, Frege on Thinking and Its Epistemic Significance claims that the objective human science that Frege proposed can only be possible through a nuanced notion of thinking as neither merely psychological nor merely logical. Focusing on what Frege says about thinking in many passages from his works, Garavaso and Vassallo argue that Frege was engaged with issues that are still alive in contemporary debates, such as the definition of knowledge and the necessary role of language in conceptual thinking and in the expression of thoughts. Frege on Thinking and Its Epistemic Significance is essential not only for those interested in a new and original reading of Frege’s philosophy, but also for anyone engaged in epistemology, logic, psychology, philosophy of language, and the history of analytic philosophy.

Gottlob Frege Basic Laws Of Arithmetic

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Author : Gottlob Frege
language : en
Publisher:
Release Date : 2013-10

Gottlob Frege Basic Laws Of Arithmetic written by Gottlob Frege and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10 with Mathematics categories.

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.