Fixing Frege
Fixing Frege

Author: John P. Burgess

Publisher: Princeton University Press

Published: 2018-06-05

Total Pages: 270

ISBN-13: 0691187061

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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
Fixing Frege

Author: John P. Burgess

Publisher: Princeton University Press

Published: 2005-07-25

Total Pages: 276

ISBN-13: 9780691122311

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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
Frege's Theorem

Author: Richard G. Heck

Publisher: OUP Oxford

Published: 2011-09-29

Total Pages: 336

ISBN-13: 0191619655

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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
Taking Frege at His Word

Author: Joan Weiner

Publisher: Oxford University Press, USA

Published: 2021-01-10

Total Pages: 346

ISBN-13: 0198865473

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This study offers a new interpretation of the writings of Gottlob Frege. It advances our understanding of the history of analytic philosophy, and shows that Frege's writings have important significance for the way we should approach contemporary problems concerning language, logic, and mathematics.

The Cambridge Companion to Frege
The Cambridge Companion to Frege

Author: Tom Ricketts

Publisher: Cambridge University Press

Published: 2010-09-02

Total Pages:

ISBN-13: 113982578X

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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.

Essays on Frege's Basic Laws of Arithmetic
Essays on Frege's Basic Laws of Arithmetic

Author: Philip A. Ebert

Publisher: Oxford University Press

Published: 2019-09-11

Total Pages: 672

ISBN-13: 0191020052

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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.

Frege Synthesized
Frege Synthesized

Author: L. Haaparanta

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 391

ISBN-13: 9400945523

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cake, even though it is typically given the pride of place in expositions in Frege's semantics. As a part of this attempted reversal of emphasis, Jaakko Hintikka has also called attention to the role Frege played in convincing almost everyone that verbs for being had to be treated as multiply ambiguous between the "is" of identity, the "is" of predication, the "is" of existence, and the "is" of class-inclusion - a view that had been embraced by few major figures (if any) before Frege, with the exception of John Stuart Mill and Augustus De Morgan. Hintikka has gone on to challenge this ambiguity thesis. At the same time, Frege's role in the genesis of another major twentieth-century philosophical movement, the phenomenological one, has become an important issue. Even the translation of Frege's key term "Bedeutung" as "reference" has become controversial. The interpretation of Frege is thus thrown largely back in the melting pot. In editing this volume, we have not tried to publish the last word on Frege. Even though we may harbor such ambitions ourselves, they are not what has led to the present editorial enterprise. What we have tried to do is to bring together some of the best ongoing work on Frege. Even though the ultimate judgment on our success lies with out readers, we want to register our satisfaction with all the contributions.

A Companion to Nineteenth-Century Philosophy
A Companion to Nineteenth-Century Philosophy

Author: John Shand

Publisher: John Wiley & Sons

Published: 2019-04-10

Total Pages: 528

ISBN-13: 1119210038

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Investigate the challenging and nuanced philosophy of the long nineteenth century from Kant to Bergson Philosophy in the nineteenth century was characterized by new ways of thinking, a desperate searching for new truths. As science, art, and religion were transformed by social pressures and changing worldviews, old certainties fell away, leaving many with a terrifying sense of loss and a realization that our view of things needed to be profoundly rethought. The Blackwell Companion to Nineteenth-Century Philosophy covers the developments, setbacks, upsets, and evolutions in the varied philosophy of the nineteenth century, beginning with an examination of Kant’s Transcendental Idealism, instrumental in the fundamental philosophical shifts that marked the beginning of this new and radical age in the history of philosophy. Guiding readers chronologically and thematically through the progression of nineteenth-century thinking, this guide emphasizes clear explanation and analysis of the core ideas of nineteenth-century philosophy in an historically transitional period. It covers the most important philosophers of the era, including Hegel, Fichte, Schopenhauer, Mill, Kierkegaard, Marx, Nietzsche, Bradley, and philosophers whose work manifests the transition from the nineteenth century into the modern era, such as Sidgwick, Peirce, Husserl, Frege and Bergson. The study of nineteenth-century philosophy offers us insight into the origin and creation of the modern era. In this volume, readers will have access to a thorough and clear understanding of philosophy that shaped our world.

Prospects for Meaning
Prospects for Meaning

Author: Richard Schantz

Publisher: Walter de Gruyter

Published: 2012-07-30

Total Pages: 676

ISBN-13: 3110216884

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Original papers by leading international authors address the most important problem in the philosophy of language, the question of how to assess the prospects of developing a tenable theory of meaning, given the influential sceptical attacks mounted against the concept of meaning by Willard Van Quine and Saul Kripke and their adherents in particular. Thus the texts attempt to answer the fundamental questions – of whether there are meanings, and, if there are, of what they are and of the form a serious philosophical theory of meaning should take.

Origins and Varieties of Logicism
Origins and Varieties of Logicism

Author: Francesca Boccuni

Publisher: Taylor & Francis

Published: 2021-11-29

Total Pages: 419

ISBN-13: 1000508110

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This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.