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Author: Roy T Cook Publisher: OUP Oxford ISBN: 0191648388 Category : Philosophy Languages : en Pages : 205
Book Description
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.
Author: Roy T Cook Publisher: OUP Oxford ISBN: 0191648388 Category : Philosophy Languages : en Pages : 205
Book Description
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.
Author: Roy T Cook Publisher: OUP Oxford ISBN: 0191043494 Category : Philosophy Languages : en Pages : 208
Book Description
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.
Author: Stephen Yablo Publisher: Princeton University Press ISBN: 140084598X Category : Philosophy Languages : en Pages : 237
Book Description
Aboutness has been studied from any number of angles. Brentano made it the defining feature of the mental. Phenomenologists try to pin down the aboutness-features of particular mental states. Materialists sometimes claim to have grounded aboutness in natural regularities. Attempts have even been made, in library science and information theory, to operationalize the notion. But it has played no real role in philosophical semantics. This is surprising; sentences have aboutness-properties if anything does. Aboutness is the first book to examine through a philosophical lens the role of subject matter in meaning. A long-standing tradition sees meaning as truth-conditions, to be specified by listing the scenarios in which a sentence is true. Nothing is said about the principle of selection--about what in a scenario gets it onto the list. Subject matter is the missing link here. A sentence is true because of how matters stand where its subject matter is concerned. Stephen Yablo maintains that this is not just a feature of subject matter, but its essence. One indicates what a sentence is about by mapping out logical space according to its changing ways of being true or false. The notion of content that results--directed content--is brought to bear on a range of philosophical topics, including ontology, verisimilitude, knowledge, loose talk, assertive content, and philosophical methodology. Written by one of today's leading philosophers, Aboutness represents a major advance in semantics and the philosophy of language.
Author: Keith Simmons Publisher: Oxford University Press ISBN: 0198791542 Category : Language Arts & Disciplines Languages : en Pages : 260
Book Description
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.
Author: Paulo Guilherme Santos Publisher: Springer Nature ISBN: 3658291117 Category : Mathematics Languages : en Pages : 94
Book Description
In this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential interpretation is given. From that, a general structure of diagonalization with paradoxes is presented. Finally, the author studies a general theory of diagonalization with the help of examples from mathematics.
Author: Michael Clark Publisher: Psychology Press ISBN: 9780415228084 Category : Paradox Languages : en Pages : 234
Book Description
'This sentence is false'. Is it? If a hotel with an infinite number of rooms is fully occupied, can it still accommodate a new guest? How can we have emotional responses to fiction, when we know that the objects of our emotions do not exist?
Author: Peter Van Inwagen Publisher: Cornell University Press ISBN: 1501713035 Category : Philosophy Languages : en Pages : 310
Book Description
According to Peter van Inwagen, visible inanimate objects do not, strictly speaking, exist. In defending this controversial thesis, he offers fresh insights on such topics as personal identity, commonsense belief, existence over time, the phenomenon of vagueness, and the relation between metaphysics and ordinary language.
Author: Roy T. Cook Publisher: John Wiley & Sons ISBN: 0745665519 Category : Philosophy Languages : en Pages : 181
Book Description
Paradoxes are arguments that lead from apparently true premises, via apparently uncontroversial reasoning, to a false or even contradictory conclusion. Paradoxes threaten our basic understanding of central concepts such as space, time, motion, infinity, truth, knowledge, and belief. In this volume Roy T Cook provides a sophisticated, yet accessible and entertaining, introduction to the study of paradoxes, one that includes a detailed examination of a wide variety of paradoxes. The book is organized around four important types of paradox: the semantic paradoxes involving truth, the set-theoretic paradoxes involving arbitrary collections of objects, the Soritical paradoxes involving vague concepts, and the epistemic paradoxes involving knowledge and belief. In each of these cases, Cook frames the discussion in terms of four different approaches one might take towards solving such paradoxes. Each chapter concludes with a number of exercises that illustrate the philosophical arguments and logical concepts involved in the paradoxes. Paradoxes is the ideal introduction to the topic and will be a valuable resource for scholars and students in a wide variety of disciplines who wish to understand the important role that paradoxes have played, and continue to play, in contemporary philosophy.
Author: J. C. Beall Publisher: Oxford University Press ISBN: 0198815670 Category : Language Arts & Disciplines Languages : en Pages : 151
Book Description
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.
Author: Shaughan Lavine Publisher: Harvard University Press ISBN: 0674039998 Category : Philosophy Languages : en Pages : 386
Book Description
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.
Author: Roy T Cook
Author: Roy T Cook
Author: Roy T Cook
Author: Stephen Yablo
Author: Keith Simmons
Author: Paulo Guilherme Santos
Author: Michael Clark
Author: Peter Van Inwagen
Author: Roy T. Cook
Author: J. C. Beall
Author: Shaughan Lavine