Circularity Truth And The Liar Paradox
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The Liar
Author | : Jon Barwise |
Publisher | : Oxford University Press |
Total Pages | : 207 |
Release | : 1987 |
Genre | : Language Arts & Disciplines |
ISBN | : 0195059441 |
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.
The Yablo Paradox
Author | : Roy T Cook |
Publisher | : OUP Oxford |
Total Pages | : 205 |
Release | : 2014-05-29 |
Genre | : Philosophy |
ISBN | : 0191648388 |
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.
The Liar:An Essay on Truth and Circularity
Author | : Jon Barwise |
Publisher | : Oxford University Press |
Total Pages | : 208 |
Release | : 1987-06-25 |
Genre | : Language Arts & Disciplines |
ISBN | : 0195363094 |
This monograph purports to provide a solution to semantical paradoxes like the Liar. The authors base this solution on J. L. Austin's idea of truth, which is fundamental to situation semantics. They compare two models of language, propositions and truth, one based on Russell and the other on Austin, as they bear on the Liar Paradox. In Russell's view, a sentence expresses a proposition, which is true or not. According to Austin, however, there is always a contextual parameter - the situation the sentence is about - that comes between the sentence and proposition. The Austinian perspective proves to have fruitful applications to the analysis of semantic paradox. The authors show that, on this account, the liar is a genuine diagonal argument. This argument can be shown to have profound consequences for our understanding of some of the most basic semantical mechanisms at work in our language. Jon Barwise is, with John Perry, a co-founder of the Centre for the Study of Language and Information at Stanford.
Saving Truth From Paradox
Author | : Hartry Field |
Publisher | : OUP Oxford |
Total Pages | : 432 |
Release | : 2008-03-06 |
Genre | : Philosophy |
ISBN | : 0191528161 |
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.
Circularity: A Common Secret To Paradoxes, Scientific Revolutions And Humor
Author | : Ron Aharoni |
Publisher | : World Scientific |
Total Pages | : 180 |
Release | : 2016-04-21 |
Genre | : Mathematics |
ISBN | : 9814723703 |
'Circularity' is the story of a Janus-faced conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question 'What is humor'. The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct.See Press Release: Vicious circles -- confusing, instructive, amusing?
Circularity, Definition, and Truth
Author | : André Leon Jo Chapuis |
Publisher | : |
Total Pages | : 420 |
Release | : 2000 |
Genre | : Definition (Philosophy) |
ISBN | : |
Reflections on the Liar
Author | : Bradley Armour-Garb |
Publisher | : Oxford University Press |
Total Pages | : 401 |
Release | : 2017-06-23 |
Genre | : Philosophy |
ISBN | : 0199896054 |
In recent years there have been a number of books-both anthologies and monographs-that have focused on the Liar Paradox and, more generally, on the semantic paradoxes, either offering proposed treatments to those paradoxes or critically evaluating ones that occupy logical space. At the same time, there are a number of people who do great work in philosophy, who have various semantic, logical, metaphysical and/or epistemological commitments that suggest that they should say something about the Liar Paradox, yet who have said very little, if anything, about that paradox or about the extant projects involving it. The purpose of this volume is to afford those philosophers the opportunity to address what might be described as reflections on the Liar.
The Liar Paradox and the Towers of Hanoi
Author | : Marcel Danesi |
Publisher | : Turner Publishing Company |
Total Pages | : 255 |
Release | : 2011-01-06 |
Genre | : Mathematics |
ISBN | : 1118045815 |
A walk through history's most mind-boggling puzzles Ever since the Sphinx asked his legendary riddle of Oedipus, riddles, conundrums, and puzzles of all sizes have kept humankind perplexed and amused. The Liar Paradox and the Towers of Hanoi takes die-hard puzzle mavens on a tour of the world's most enduringly intriguing braintwisters, from K?nigsberg's Bridges and the Hanoi Towers to Fibonacci's Rabbits, the Four Color Problem, and the Magic Square. Each chapter introduces the basic puzzle, discusses the mathematics behind it, and includes exercises and answers plus additional puzzles similar to the one under discussion. Here is a veritable kaleidoscope of puzzling labyrinths, maps, bridges, and optical illusions that will keep aficionados entertained for hours. Marcel Danesi (Etobicoke, ON, Canada) is the author of Increase Your Puzzle IQ
Semantic Singularities
Author | : Keith Simmons |
Publisher | : Oxford University Press |
Total Pages | : 260 |
Release | : 2018 |
Genre | : Language Arts & Disciplines |
ISBN | : 0198791542 |
This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism.