Quine New Foundations And The Philosophy Of Set Theory
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Quine New Foundations And The Philosophy Of Set Theory
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Author : Sean Morris
language : en
Publisher: Cambridge University Press
Release Date : 2018-12-13
Quine New Foundations And The Philosophy Of Set Theory written by Sean Morris 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 2018-12-13 with History categories.
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Quine New Foundations And The Philosophy Of Set Theory
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Author : Sean Morris
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-21
Quine New Foundations And The Philosophy Of Set Theory written by Sean Morris 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 2021-01-21 with Philosophy categories.
Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.
Conceptions Of Set And The Foundations Of Mathematics
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Author : Luca Incurvati
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Conceptions Of Set And The Foundations Of Mathematics written by Luca Incurvati 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 2020-01-23 with History categories.
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Set Theory And Its Logic Revised Edition
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Author : Willard Van O QUINE
language : en
Publisher: Harvard University Press
Release Date : 2009-06-30
Set Theory And Its Logic Revised Edition written by Willard Van O QUINE and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-30 with Philosophy categories.
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Trading Ontology For Ideology
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Author : L. Decock
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-30
Trading Ontology For Ideology written by L. Decock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-30 with Philosophy categories.
Willard Van Orman Quine (1908-2000) was probably the most influential American philosopher of the twentieth century. In Trading Ontology for Ideology Lieven Decock offers an insightful analysis of the development of Quine's ontological views from his first texts in the early thirties onwards. The importance of Quine's work in logic and set theory for his ontology is highlighted. Decock argues that the tenet of extensionalism is at least as important as naturalism, and assesses the relation between the two. The other focus of the work is the relation between ontology, i.e. what there is, and ideology, i.e. what can be expressed by means of words. Decock shows that the interplay between ontology and ideology is far more complicated and interesting than has generally been assumed.
Universality In Set Theories
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Author : Manuel Bremer
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-02
Universality In Set Theories written by Manuel Bremer and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-02 with Philosophy categories.
The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?
Quine Conceptual Pragmatism And The Analytic Synthetic Distinction
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Author : Robert Sinclair
language : en
Publisher: Bloomsbury Publishing PLC
Release Date : 2022-08-01
Quine Conceptual Pragmatism And The Analytic Synthetic Distinction written by Robert Sinclair 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 2022-08-01 with Philosophy categories.
W. V. Quine’s occasional references to his ‘pragmatism’ have often been interpreted as suggesting a possible link to the American Pragmatism of Peirce, James, and Dewey. Quine, Conceptual Pragmatism, and the Analytic-Synthetic Distinction argues that the influence of pragmatism on Quine’s philosophy is more accurately traced to his teacher C.I. Lewis and his conceptual pragmatism from Mind and the World Order, and his later An Analysis of Knowledge and Valuation. Quine’s epistemological views share many affinities with Lewis’s conceptual pragmatism, where knowledge is conceived as a conceptual framework pragmatically revised in light of what future experience reveals. Robert Sinclair further defends and elaborates on this claim by showing how Lewis’s influence can be seen in several key episodes in Quine’s philosophical development. This not only highlights a forgotten element of the epistemological backdrop to Quine’s mid-century criticism of the analytic-synthetic distinction, but Sinclair further argues that it provides the central epistemological framework for the form and content of Quine’s later naturalized conception of epistemology.
New Directions In The Philosophy Of Mathematics
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Author : Thomas Tymoczko
language : en
Publisher: Princeton University Press
Release Date : 1998-02
New Directions In The Philosophy Of Mathematics written by Thomas Tymoczko 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 1998-02 with Mathematics categories.
The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
Set Theory With A Universal Set
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Author : T. E. Forster
language : en
Publisher: Oxford University Press on Demand
Release Date : 1995
Set Theory With A Universal Set written by T. E. Forster and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by othersets, specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets - the universal set - is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed inthese non-standard set theories has been boosted by their relevance to computer science.The second edition still concentrates largely on Quine's New Foundations, reflecting the author's belief that this provides the richest and most mysterious of the various systems dealing with set theories with a universal set. Also included is an expanded and completely revised account of the settheories of Church-Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power sets. Dr Foster here presents the reader with a useful and readable introduction for those interested in this topic, and a reference work for those already involved in this area.
Quine S Philosophy
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Author : Gary Kemp
language : en
Publisher: Bloomsbury Publishing
Release Date : 2023-08-24
Quine S Philosophy written by Gary Kemp and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-24 with Philosophy categories.
W.V. Quine is one of the leading figures of 20th century analytic philosophy, and still among the most influential. But his work can be challenging and complex, and indeed often misunderstood. In this updated introduction to Quine's thought, Gary Kemp examines his seemingly disparate views as a unified whole and offers a valuable guide for anyone approaching Quine for the first time. Informed by current debates and updated throughout, this edition now includes: · Thoroughly revised and expanded text · More references to commentaries, secondary literature and works by Quine · Suggestions for further reading · Newly introduced material on Empirical Content, Explication, Nominalism, The Purported Third Dogma, Theoreticity, Natural Selection and Linguistics. · Historical notes on Quine's relation to his predecessors and contemporaries Paying close attention to Quine's seminal works including Word and Object and Philosophy of Logic, Kemp explains how his philosophy relates to thinkers including Rudolf Carnap and Wittgenstein, as well as to more recent figures such as Donald Davidson and Noam Chomsky. Kemp clearly and accurately emphasizes the systematic nature of Quine's thought as one of naturalism. He advances our understanding of Quine and attests to his ongoing influence in philosophy of science, logic, language, ontology and epistemology. This unique introduction to Quine's philosophy is recommended for any student interested in Quine and the history of analytic philosophy.