Download or read book The Yablo Paradox written by Roy T Cook and published by OUP Oxford. This book was released on 2014-05-29 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Yablo Paradox written by Roy T. Cook and published by Oxford University Press, USA. This book was released on 2014 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Roy T. Cook examines the Yablo paradox, a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others that follow it. He focuses on questions of characterization, circularity and generalizability, and pays special attention to the idea that it provides us with a semantic paradox that involves no circularity.
Download or read book Aboutness written by Stephen Yablo and published by Princeton University Press. This book was released on 2016-11-08 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Paradoxes from A to Z written by Michael Clark and published by Psychology Press. This book was released on 2002 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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?
Download or read book Semantic Singularities written by Keith Simmons and published by Oxford University Press. This book was released on 2018 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keith Simmons presents an original, unified solution to the semantic paradoxes which have dogged attempts to give a consistent account of the logic of natural language since antiquity: the Liar paradox and the paradoxes of reference and predication.
Download or read book Diagonalization in Formal Mathematics written by Paulo Guilherme Santos and published by Springer Nature. This book was released on 2020-01-04 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Material Beings written by Peter Van Inwagen and published by Cornell University Press. This book was released on 1990-12-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Paradoxes written by Roy T. Cook and published by John Wiley & Sons. This book was released on 2013-04-03 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Formal Theories of Truth written by Jc Beall and published by Oxford University Press. This book was released on 2018-03-08 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Limited Inc written by Jacques Derrida and published by Northwestern University Press. This book was released on 1988 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signature event context -- Summary of "Reiterating the differences"--Limited Inc a b c -- Afterword : toward an ethic of discussion.
Download or read book Diagonalization and Self reference written by Raymond M. Smullyan and published by Oxford Logic Guides. This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The firstchapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.
Download or read book Philosophy of Language written by Michael P. Wolf and published by Taylor & Francis. This book was released on 2023-02-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers readers a collection of 50 short chapter entries on topics in the philosophy of language. Each entry addresses a paradox, a longstanding puzzle, or a major theme that has emerged in the field from the last 150 years, tracing overlap with issues in philosophy of mind, cognitive science, ethics, political philosophy, and literature. Each of the 50 entries is written as a piece that can stand on its own, though useful connections to other entries are mentioned throughout the text. Readers can open the book and start with almost any of the entries, following themes of greatest interest to them. Each entry includes recommendations for further reading on the topic. Philosophy of Language: 50 Puzzles, Paradoxes, and Thought Experiments is useful as a standalone textbook, or can be supplemented by additional readings that instructors choose. The accessible style makes it suitable for introductory level through intermediate undergraduate courses, as well as for independent learners, or even as a reference for more advanced students and researchers. Key Features: Uses a problem-centered approach to philosophy of language (rather than author- or theory-centered) making the text more inviting to first-time students of the subject. Offers stand-alone chapters, allowing students to quickly understand an issue and giving instructors flexibility in assigning readings to match the themes of the course. Provides up-to-date recommended readings at the end of each chapter, or about 500 sources in total, amounting to an extensive review of the literature on each topic.
Download or read book Understanding the Infinite written by Shaughan Lavine and published by Harvard University Press. This book was released on 2009-06-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible history and philosophical commentary on our notion of infinity. 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. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
Download or read book The Three Paradoxes written by Paul Hornschemeier and published by Fantagraphics Books. This book was released on 2007-07-02 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Three Paradoxes is an intricate and complex autobiographical comic by one of the most talented and innovative young cartoonists today. The story begins with a story inside the story: the cartoon character Paul Hornschemeier is trying to finish a story called "Paul and the Magic Pencil." Paul has been granted a magical implement, a pencil, and is trying to figure out what exactly it can do. He isn't coming up with much, but then we zoom out of this story to the creator, Paul, whose father is about to go on a walk to turn off the lights in his law office in the center of the small town. Abandoning the comic strip temporarily, Paul leaves with his camera, in order to fulfill a promise to his girlfriend that he would take pictures of the places that affected him as a child. Each "chapter" of the story is drawn in a completely different style, with strikingly unique production and color themes, and yet, somehow, despite (or perhaps because of) this non-linear progression, it all comes together as one story: a story questioning change, progress, and worth within the author's life.
Download or read book Logic and Its Applications written by Kamal Lodaya and published by Springer. This book was released on 2012-12-22 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 5th Indian Conference on Logic and Its Applications, ICLA 2013, held in Chennai, India, in January 2013. The 15 revised full papers presented together with 7 invited talks were carefully reviewed and selected from numerous submissions. The papers cover the topics related to pure and applied logic, foundations and philosophy of mathematics and the sciences, set theory, model theory, proof theory, areas of theoretical computer science, artificial intelligence and other disciplines which are of direct interest to mathematical and philosophical logic.
Download or read book Self Reference written by S.J. Bartlett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-reference, although a topic studied by some philosophers and known to a number of other disciplines, has received comparatively little explicit attention. For the most part the focus of studies of self-reference has been on its logical and linguistic aspects, with perhaps disproportionate emphasis placed on the reflexive paradoxes. The eight-volume Macmillan Encyclopedia of Philosophy, for example, does not contain a single entry in its index under "self-reference", and in connection with "reflexivity" mentions only "relations", "classes", and "sets". Yet, in this volume, the introductory essay identifies some 75 varieties and occurrences of self-reference in a wide range of disciplines, and the bibliography contains more than 1,200 citations to English language works about reflexivity. The contributed papers investigate a number of forms and applications of self-reference, and examine some of the challenges posed by its difficult temperament. The editors hope that readers of this volume will gain a richer sense of the sti11largely unexplored frontiers of reflexivity, and of the indispensability of reflexive concepts and methods to foundational inquiries in philosophy, logic, language, and into the freedom, personality and intelligence of persons.
Download or read book On the Brink of Paradox written by Agustin Rayo and published by MIT Press. This book was released on 2019-04-02 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.
