Logicism and its Philosophical Legacy

Author: William Demopoulos

Publisher: Cambridge University Press

ISBN: 1139620290

Category: Mathematics

Page: N.A

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The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas by the principal figures in the history of the subject - Frege, Russell, Ramsey and Carnap - and in doing so illuminate current concerns about the nature of mathematical and theoretical knowledge. Issues addressed include the nature of arithmetical knowledge in the light of Frege's theorem; the status of realism about the theoretical entities of physics; and the proper interpretation of empirical theories that postulate abstract structural constraints.

Logicism and the Philosophy of Language

Selections from Frege and Russell

Author: Arthur Sullivan

Publisher: Broadview Press

ISBN: 1770483292

Category: Philosophy

Page: 298

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Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology gathers together these foundational writings, and frames them with an extensive historical introduction. This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts.

Philosophy of Logic

Author: N.A

Publisher: Elsevier

ISBN: 9780080466637

Category: Mathematics

Page: 1218

View: 1946

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The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert’s program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights. - Written by leading logicians and philosophers - Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic - Clear, in-depth expositions of technical detail - Progressive organization from general considerations to informal to symbolic logic to nonclassical logics - Presents current work in symbolic logic within a unified framework - Accessible to students, engaging for experts and professionals - Insightful philosophical discussions of all aspects of logic - Useful bibliographies in every chapter

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Author: Paolo Mancosu

Publisher: Oxford University Press on Demand

ISBN: 0195132440

Category: Drama

Page: 275

View: 6524

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The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

Frege

A Philosophical Biography

Author: Dale Jacquette

Publisher: Cambridge University Press

ISBN: 9780521863278

Category: Philosophy

Page: 702

View: 5449

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Gottlob Frege (1848-1925) is one of the founding figures of analytic philosophy, whose contributions to logic, philosophical semantics, philosophy of language, and philosophy of mathematics set the agenda for future generations of theorists in these and related areas. Dale Jacquette's lively and incisive biography charts Frege's life from its beginnings in small-town north Germany, through his student days in Jena, to his development as an enduringly influential thinker. Along the way Jacquette considers Frege's ground-breaking Begriffschrift (1879), in which he formulated his 'ideal logical language', his magisterial Grundgesetze der Arithmetik (1893 and 1903), and his complex relation to thinkers including Husserl and especially Russell, whose Paradox had such drastic implications for Frege's logicism. Jacquette concludes with a thoughtful assessment of Frege's legacy. His rich and informative biography will appeal to all who are interested in Frege's philosophy.

Rudolf Carnap and the Legacy of Logical Empiricism

Author: R CREATH

Publisher: Springer Science & Business Media

ISBN: 940073929X

Category: Science

Page: 204

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This Institute's Yearbook for the most part, documents its recent activities and provides a forum for the discussion of exact philosophy, logical and empirical investigations, and analysis of language. This volume holds a collection of papers on various aspects of the work of Rudolf Carnap by an international group of distinguished scholars.​

F. P. Ramsey: Philosophical Papers

Author: F. P. Ramsey,D. H. Mellor

Publisher: Cambridge University Press

ISBN: 9780521376211

Category: Philosophy

Page: 257

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Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The latter gives the definitive form and defence of the reduction of mathematics to logic undertaken in Russell and Whitehead's Principia Mathematica; the former includes the most profound and original studies of universals, truth, meaning, probability, knowledge, law and causation, all of which are still constantly referred to, and still essential reading for all serious students of these subjects.

Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939

Author: Ludwig Wittgenstein

Publisher: University of Chicago Press

ISBN: 022630860X

Category: Philosophy

Page: 300

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For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

The Historical Turn in Analytic Philosophy

Author: E. Reck

Publisher: Springer

ISBN: 1137304871

Category: Philosophy

Page: 372

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During the last 25 years, a large number of publications on the history of analytic philosophy have appeared, significantly more than in the preceding period. As most of these works are by analytically trained authors, it is tempting to speak of a 'historical turn' in analytic philosophy. The present volume constitutes both a contribution to this body of work and a reflection on what is, or might be, achieved in it. The twelve new essays, by an international group of contributors, range from case studies on individual philosophers (Russell, Carnap, Quine, and Ryle) through discussions of broader themes in the history of analytic philosophy (in logic and philosophy of language, philosophy of mathematics, epistemology, philosophy of mind and psychology) to related methodological reflections (on the relationship between doing analytic philosophy and studying the history of philosophy, on various forms of philosophical history, and on their respective benefits).

Logicism, Intuitionism, and Formalism

What Has Become of Them?

Author: Sten Lindstr©œm,Erik Palmgren,Krister Segerberg,Viggo Stoltenberg-Hansen

Publisher: Springer Verlag

ISBN: 9781402089251

Category: Mathematics

Page: 512

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This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Russell's Unknown Logicism

A Study in the History and Philosophy of Mathematics

Author: S. Gandon

Publisher: Springer

ISBN: 1137024658

Category: Mathematics

Page: 263

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In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

The Foundations of Arithmetic

A Logico-Mathematical Enquiry Into the Concept of Number

Author: Gottlob Frege,J. L. Austin

Publisher: Northwestern University Press

ISBN: 0810106051

Category: Mathematics

Page: 119

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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.

Reflexive Epistemology

The Philosophical Legacy of Otto Neurath

Author: D. Zolo

Publisher: Springer Science & Business Media

ISBN: 9400924151

Category: Science

Page: 206

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Professor Danilo Zolo has written an account of Otto Neurath's epistemology which deserves careful reading by all who have studied the development of 20th century philosophy of science. Here we see the philosophical Neurath in his mature states of mind, the vigorous critic, the scientific Utopian, the pragmatic realist, the sociologist of physics and of language, the unifier and encyclopedist, always the empiricist and always the conscience of the Vienna Circle. Zolo has caught the message of Neurath's ship-at-sea in the reflexivity of language, and he has sensibly explicated the persisting threat posed by consistent conventionalism. And then Zolo beautifully articulates of the 'epistemological priority of sociology'. the provocative theme Was Neurath correct? Did he have his finger on the pulse of empiricism in the time of a genuine unity of the sciences? His friends and colleagues were unable to follow all the way with him, but Danilo Zolo has done so in this stimulating investigation of what he tellingly calls Otto Neurath's 'philosophical legacy' . R.S.COHEN ix ABBREVIATIONS 'Pseudo' = [Otto Neurath], 'Pseudorationalismus der Falsifikation', Erkenntnis,5 (1935), pp. 353--65. Foundations = [Otto Neurath], Foundations of the Social Sciences, in International Encyclopedia of Unified Science, vol. 2, no. 1, pp. 1-51, Chicago: The University of Chicago Press, 1944. ES = Otto Neurath, Empiricism and Sociology, ed. by M. Neurath and R.S. Cohen, Dordrecht and Boston: D. Reidel, 1973.

Philosophers and Religious Leaders

Author: Christian D. Von Dehsen,Scott L. Harris

Publisher: Greenwood Publishing Group

ISBN: 9781573561525

Category: Biography & Autobiography

Page: 246

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Two hundred alphabetically arranged illustrated profiles include a discussion of the person's work, a summary of the impact of his or her work on those who followed, and a timeline listing important dates.

The Logic of Concept Expansion

Author: Meir Buzaglo

Publisher: Cambridge University Press

ISBN: 9780521807623

Category: Mathematics

Page: 182

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This innovative study offers stimulating discussions of the relation of conceptual expansion to truth, meaning, reference, ontology and paradox.

Relevant Logic

A Philosophical Interpretation

Author: Edwin D. Mares

Publisher: Cambridge University Press

ISBN: 9780521829236

Category: Philosophy

Page: 229

View: 7169

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This book introduces the reader to relevant logic and provides it with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used ('relevant') in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The book ends by examining various applications of relevant logic and presenting some interesting open problems.

The Physicist and the Philosopher

Einstein, Bergson, and the Debate That Changed Our Understanding of Time

Author: Jimena Canales

Publisher: Princeton University Press

ISBN: 1400865778

Category: Science

Page: 488

View: 4488

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On April 6, 1922, in Paris, Albert Einstein and Henri Bergson publicly debated the nature of time. Einstein considered Bergson's theory of time to be a soft, psychological notion, irreconcilable with the quantitative realities of physics. Bergson, who gained fame as a philosopher by arguing that time should not be understood exclusively through the lens of science, criticized Einstein's theory of time for being a metaphysics grafted on to science, one that ignored the intuitive aspects of time. The Physicist and the Philosopher tells the remarkable story of how this explosive debate transformed our understanding of time and drove a rift between science and the humanities that persists today. Jimena Canales introduces readers to the revolutionary ideas of Einstein and Bergson, describes how they dramatically collided in Paris, and traces how this clash of worldviews reverberated across the twentieth century. She shows how it provoked responses from figures such as Bertrand Russell and Martin Heidegger, and carried repercussions for American pragmatism, logical positivism, phenomenology, and quantum mechanics. Canales explains how the new technologies of the period—such as wristwatches, radio, and film—helped to shape people’s conceptions of time and further polarized the public debate. She also discusses how Bergson and Einstein, toward the end of their lives, each reflected on his rival’s legacy—Bergson during the Nazi occupation of Paris and Einstein in the context of the first hydrogen bomb explosion. The Physicist and the Philosopher is a magisterial and revealing account that shows how scientific truth was placed on trial in a divided century marked by a new sense of time.

Theory of the Subject

Author: Alain Badiou

Publisher: A&C Black

ISBN: 0826496733

Category: Psychology

Page: 367

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Badiou is widely considered to be France's most important and exciting contemporary thinker. Much of Badiou's earlier work (including Being and Event) can only be fully understood with a clear grasp of Theory of the Subject, one of his most important works.