Paradoxes Between Truth And Proof
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Paradoxes Between Truth And Proof
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Author : Mattia Petrolo
language : en
Publisher: Springer Nature
Release Date : 2024-12-04
Paradoxes Between Truth And Proof written by Mattia Petrolo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-04 with Mathematics categories.
This book is a collection of essays that offer original logical and philosophical investigations into the century-long endeavor to understand paradoxes. It bridges the gap between the two most prominent traditions in the analysis of paradoxes: the truth-theoretic and proof-theoretic approaches. The truth-theoretic tradition stems from Alfred Tarski's solution to the semantic paradoxes, while the proof-theoretic tradition dates back to Dag Prawitz's analysis of set-theoretic paradoxes in terms of structural proof theory. Rather than viewing these traditions as competing perspectives, this volume advocates for the idea that a deeper understanding of paradoxes requires insights from both truth-theoretic and proof-theoretic conceptions of language and meaning. Although the collection does not aim to be exhaustive, it seeks to highlight the vast scope of the subject and its deep connections to various fields of inquiry. The essays are organized into four sections: the first focuses on methodology, the second and third examine paradoxes through the conventional lenses of logical investigation—semantics and syntax—, and the fourth presents a selection of paradoxes that extend beyond the interplay between syntax and semantics, exploring other dimensions of human rationality.
Saving Truth From Paradox
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Author : Hartry Field
language : en
Publisher: OUP Oxford
Release Date : 2008-03-06
Saving Truth From Paradox written by Hartry Field and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-06 with Philosophy categories.
Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the Gödel incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches. Part One examines Tarski's, Kripke’s, and Lukasiewicz’s theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the paradoxes: approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists’ claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.
Paradoxes
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Author : R. M. Sainsbury
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-19
Paradoxes written by R. M. Sainsbury 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 2009-02-19 with Philosophy categories.
A paradox can be defined as an unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Many paradoxes raise serious philosophical problems, and they are associated with crises of thought and revolutionary advances. The expanded and revised third edition of this intriguing book considers a range of knotty paradoxes including Zeno's paradoxical claim that the runner can never overtake the tortoise, a new chapter on paradoxes about morals, paradoxes about belief, and hardest of all, paradoxes about truth. The discussion uses a minimum of technicality but also grapples with complicated and difficult considerations, and is accompanied by helpful questions designed to engage the reader with the arguments. The result is not only an explanation of paradoxes but also an excellent introduction to philosophical thinking.
Truth And Paradox
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Author : Tim Maudlin
language : en
Publisher: Oxford University Press
Release Date : 2006
Truth And Paradox written by Tim Maudlin 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 2006 with Philosophy categories.
Truth and Paradox offers a comprehensive account of truth values and the norms governing claims about truth, based on a new approach to logic and semantics. Since the seminal work of Tarski in the mid-twentieth century, the Liar paradox and other related paradoxes have stood in the way of a precise philosophical account of truth. Tim Maudlin draws on analogies from mathematical physics to explicate the origin of classical truth-value gaps, and to provide an account of truth that avoids any hierarchy of languages or of truth predicates. He also closely investigates our reasoning about truth, including apparently unobjectionable reasoning about the paradoxical sentences. The fallacies in that reasoning are located not in any inferences concerning truth, but in the foundations of standard logic. Blocking the paradoxical arguments requires emendation of classical logic, and the requisite emendations call into question the existence of any a priori logical truths. Maudlin also includes a discussion of facts and factuality, most particularly the question of whether there are any facts about truth. All philosophers interested in logic and language will find this a stimulating read.
The Yablo Paradox
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Author : Roy T. Cook
language : en
Publisher:
Release Date : 2014
The Yablo Paradox written by Roy T. Cook and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Philosophy categories.
Roy T. Cook examines the Yablo paradox--a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others later than it in the sequence--with special attention paid to the idea that this paradox provides us with a semantic paradox that involves no circularity. The three main chapters of the book focus, respectively, on three questions that can be (and have been) asked about the Yablo construction. First we have the Characterization Problem, which asks what patterns of sentential reference (circular or not) generate semantic paradoxes. Addressing this problem requires an interesting and fruitful detour through the theory of directed graphs, allowing us to draw interesting connections between philosophical problems and purely mathematical ones. Next is the Circularity Question, which addresses whether or not the Yablo paradox is genuinely non-circular. Answering this question is complicated: although the original formulation of the Yablo paradox is circular, it turns out that it is not circular in any sense that can bear the blame for the paradox. Further, formulations of the paradox using infinitary conjunction provide genuinely non-circular constructions. Finally, Cook turns his attention to the Generalizability Question: can the Yabloesque pattern be used to generate genuinely non-circular variants of other paradoxes, such as epistemic and set-theoretic paradoxes? Cook argues that although there are general constructions-unwindings--that transform circular constructions into Yablo-like sequences, it turns out that these sorts of constructions are not 'well-behaved' when transferred from semantic puzzles to puzzles of other sorts. He concludes with a short discussion of the connections between the Yablo paradox and the Curry paradox.
Revenge Of The Liar
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Author : J. C. Beall
language : en
Publisher:
Release Date : 2023
Revenge Of The Liar written by J. C. Beall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Liar paradox categories.
J.C. Beall presents 14 new essays and an extensive introduction, which examine the nature of the liar paradox and its resistance to any attempt to solve it.
Paradoxes From A To Z
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Author : Michael Clark
language : en
Publisher: Routledge
Release Date : 2012
Paradoxes From A To Z written by Michael Clark and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Philosophy categories.
Paradoxes from A to Z, Third edition is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus' Ship, and the Prisoner's Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills.
Formal Theories Of Truth
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Author : J. C. Beall
language : en
Publisher: Oxford University Press
Release Date : 2018
Formal Theories Of Truth written by J. C. Beall 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 2018 with Language Arts & Disciplines categories.
Truth is one of the oldest and most central topics in philosophy. Formal theories explore the connections between truth and logic, and they address truth-theoretic paradoxes such as the Liar. Three leading philosopher-logicians now present a concise overview of the main issues and ideas in formal theories of truth. Beall, Glanzberg, and Ripley explain key logical techniques on which such formal theories rely, providing the formal and logical background needed to develop formal theories of truth. They examine the most important truth-theoretic paradoxes, including the Liar paradoxes. They explore approaches that keep principles of truth simple while relying on nonclassical logic; approaches that preserve classical logic but do so by complicating the principles of truth; and approaches based on substructural logics that change the shape of the target consequence relation itself. Finally, inconsistency and revision theories are reviewed, and contrasted with the approaches previously discussed. For any reader who has a basic grounding in logic, this book offers an ideal guide to formal theories of truth.
The Liar
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Author : Jon Barwise
language : en
Publisher: Oxford University Press
Release Date : 1987
The Liar written by Jon Barwise 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 1987 with Language Arts & Disciplines categories.
Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Barwise and Etchemendy model and compare Russellian and Austinian conceptions of propositions, and develop a range of model-theoretic techniques--based on Aczel's work--that open up new avenues in logical and formal semantics.
Paradoxes From A To Z
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Author : Head of German Dictionaries Michael Clark
language : en
Publisher: Routledge
Release Date : 2002-09-11
Paradoxes From A To Z written by Head of German Dictionaries Michael Clark and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-11 with Philosophy categories.
First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.