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Author : Sergi Oms,Elia Zardini
Publisher : Cambridge University Press
Page : 345 pages
File Size : 41,7 Mb
Release : 2019-10-10
Category : Philosophy
ISBN : 9781107163997
Offers a systematic introduction and discussion of all the main solutions to the sorites paradox and its areas of influence.
Author : Inga Bones
Publisher : Brill Mentis
Page : 192 pages
File Size : 46,6 Mb
Release : 2020-10-23
Category : Sorites paradox
ISBN : 3957431972
This book reassesses philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox. The paradox consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or neither one is. Claim (3) is rendered plausible by an initial conviction that vague predicates like 'heap' tolerate small changes. The repeated application of a tolerance principle to claim (2), however, yields the further proposition that one grain of sand does make a heap - which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates. Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case.
Author : L. Burns
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401134941
This work is in two parts. It began as a general investigation of vagueness in natural languages. The Sorites Paradox came to dominate the work however, and the second part of the book consists in an discussion ofthat puzzle and related problems. The first part contains a general discussion ofthe nature ofvagueness and its sources. I discuss various conceptions of vagueness in chapter 1 and outline some of the problems to do with the conception of vagueness as a linguistic phenomenon. The most interesting of these is the Sorites paradox, which occurs where natural languages exhibit a particular variety of borderline case vagueness. I discuss some sources of vagueness of the borderline case variety, and views of the relation between linguistic behaviour and languages which are vague in this sense. I argue in chapter 2 that these problems are not to be easily avoided by statistical averaging techniques or attempts to provide a mathematical model of consensus in linguistic usage. I also consider in chapter 3 various approaches to the problem of providing an adequate logic and semantics for vague natural languages, and argue against two currently popular approaches to vagueness. These are supervaluation accounts which attempt to provide precise semantic models for vague languages based on the notion of specification spaces, and attempts to replace the laws ofclassical logic with systems offuzzy logic.
Author : Michael Huemer
Publisher : Springer
Page : 260 pages
File Size : 47,9 Mb
Release : 2018-06-28
Category : Philosophy
ISBN : 9783319904900
Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week . . . but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles.
Author : Doris Olin
Publisher : Routledge
Page : 233 pages
File Size : 45,6 Mb
Release : 2014-12-18
Category : Philosophy
ISBN : 9781317489238
Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.
Author : R. M. Sainsbury
Publisher : Cambridge University Press
Page : 191 pages
File Size : 43,7 Mb
Release : 2009-02-19
Category : Philosophy
ISBN : 9780521896320
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.
Author : Mr Dominic Hyde
Publisher : Ashgate Publishing, Ltd.
Page : 250 pages
File Size : 42,5 Mb
Release : 2012-10-01
Category : Philosophy
ISBN : 9781409485735
Resorting to natural law is one way of conveying the philosophical conviction that moral norms are not merely conventional rules. Accordingly, the notion of natural law has a clear metaphysical dimension, since it involves the recognition that human beings do not conceive themselves as sheer products of society and history. And yet, if natural law is to be considered the fundamental law of practical reason, it must show also some intrinsic relationship to history and positive law. The essays in this book examine this tension between the metaphysical and the practical and how the philosophical elaboration of natural law presents this notion as a "limiting-concept", between metaphysics and ethics, between the mutable and the immutable; between is and ought, and, in connection with the latter, even the tension between politics and eschatology as a double horizon of ethics. This book, contributed to by scholars from Europe and America, is a major contribution to the renewed interest in natural law. It provides the reader with a comprehensive overview of natural law, both from a historical and a systematic point of view. It ranges from the mediaeval synthesis of Aquinas through the early modern elaborations of natural law, up to current discussions on the very possibility and practical relevance of natural law theory for the contemporary mind.
Author : Diana Raffman
Publisher : Oxford University Press
Page : 241 pages
File Size : 46,6 Mb
Release : 2014-02
Category : Language Arts & Disciplines
ISBN : 9780199915101
In Unruly Words, Diana Raffman advances a new theory of vagueness which, unlike previous accounts, is genuinely semantic while preserving bivalence. According to this new approach, called the multiple range theory, vagueness consists essentially in a term's being applicable in multiple arbitrarily different, but equally competent, ways, even when contextual factors are fixed.
Author : John L. Bell
Publisher : Broadview Press
Page : 218 pages
File Size : 53,7 Mb
Release : 2016-04-18
Category : Philosophy
ISBN : 9781554813025
Since antiquity, opposed concepts such as the One and the Many, the Finite and the Infinite, and the Absolute and the Relative, have been a driving force in philosophical, scientific, and mathematical thought. Yet they have also given rise to perplexing problems and conceptual paradoxes which continue to haunt scientists and philosophers. In Oppositions and Paradoxes, John L. Bell explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, Bell not only motivates abstract conceptual thinking about the paradoxes at issue, but he also offers a compelling introduction to central ideas in such otherwise-difficult topics as non-Euclidean geometry, relativity, and quantum physics. These paradoxes are often as fun as they are flabbergasting. Consider, for example, the famous Tristram Shandy paradox: an immortal man composing an autobiography so slowly as to require a year of writing to describe each day of his life — he would, if he had infinite time, presumably never complete the work, although no individual part of it would remain unwritten. Or think of an office mailbox labelled “mail for those with no mailbox”—if this is a person’s mailbox, how can they possibly have “no mailbox”? These and many other paradoxes straddle the boundary between physics and metaphysics, and demonstrate the hidden difficulty in many of our most basic concepts.
Author : Giuseppina Ronzitti
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 41,7 Mb
Release : 2011-03-03
Category : Philosophy
ISBN : 9789400703759
This volume explores how vagueness matters as a specific problem in the context of theories that are primarily about something else. After an introductory chapter on the Sorites paradox, which exposes the various forms the paradox can take and some of the responses that have been pursued, the book proceeds with a chapter on vagueness and metaphysics, which covers important questions concerning vagueness that arise in connection with the deployment of certain key metaphysical notions. Subsequent chapters address the following: vagueness and logic, which discusses the sort of model theory that is suggested by the main, rival accounts of vagueness; vagueness and meaning, which focuses on contextualist, epistemicist, and indeterminist theories; vagueness and observationality; vagueness within linguistics, which focuses on approaches that take comparison classes into account; and the idea that vagueness in law is typically extravagant and that extravagant vagueness is a necessary feature of legal systems.
Author : Terence Horgan,Terry Horgan
Publisher : Oxford University Press
Page : 337 pages
File Size : 48,8 Mb
Release : 2017
Category : Mathematics
ISBN : 9780199858422
This volume brings together many of Terence Horgan's essays on paradoxes: Newcomb's problem, the Monty Hall problem, the two-envelope paradox, the sorites paradox, and the Sleeping Beauty problem. Newcomb's problem arises because the ordinary concept of practical rationality constitutively includes normative standards that can sometimes come into direct conflict with one another. The Monty Hall problem reveals that sometimes the higher-order fact of one's having reliably received pertinent new first-order information constitutes stronger pertinent new information than does the new first-order information itself. The two-envelope paradox reveals that epistemic-probability contexts are weakly hyper-intensional; that therefore, non-zero epistemic probabilities sometimes accrue to epistemic possibilities that are not metaphysical possibilities; that therefore, the available acts in a given decision problem sometimes can simultaneously possess several different kinds of non-standard expected utility that rank the acts incompatibly. The sorites paradox reveals that a certain kind of logical incoherence is inherent to vagueness, and that therefore, ontological vagueness is impossible. The Sleeping Beauty problem reveals that some questions of probability are properly answered using a generalized variant of standard conditionalization that is applicable to essentially indexical self-locational possibilities, and deploys preliminary probabilities of such possibilities that are not prior probabilities. The volume also includes three new essays: one on Newcomb's problem, one on the Sleeping Beauty problem, and an essay on epistemic probability that articulates and motivates a number of novel claims about epistemic probability that Horgan has come to espouse in the course of his writings on paradoxes. A common theme unifying these essays is that philosophically interesting paradoxes typically resist either easy solutions or solutions that are formally/mathematically highly technical. Another unifying theme is that such paradoxes often have deep-sometimes disturbing-philosophical morals.
Author : Kees van Deemter
Publisher : Oxford University Press
Page : 358 pages
File Size : 40,7 Mb
Release : 2012-05-24
Category : Computers
ISBN : 9780199645732
Our lives are full of inexactitude. We say a person is tall or an action is just without the precision of measurement on a dial. In this engaging account, Kees van Deemter explores vagueness, cutting across areas such as language, mathematical logic, and computing. He considers why vagueness is inherent, and why it is important in how we function.
Author : Roy T. Cook
Publisher : John Wiley & Sons
Page : 181 pages
File Size : 49,5 Mb
Release : 2013-04-03
Category : Philosophy
ISBN : 9780745665511
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 : Timothy Williamson
Publisher : Routledge
Page : 344 pages
File Size : 47,8 Mb
Release : 2002-01-04
Category : Philosophy
ISBN : 9781134770182
If you keep removing single grains of sand from a heap, when is it no longer a heap? From discussions of the heap paradox in classical Greece, to modern formal approaches like fuzzy logic, Timothy Williamson traces the history of the problem of vagueness. He argues that standard logic and formal semantics apply even to vague languages and defends the controversial, realist view that vagueness is a form of ignorance - there really is a grain of sand whose removal turns a heap into a non-heap, but we can never know exactly which one it is.
Author : Kit Fine
Publisher : Oxford University Press
Page : 192 pages
File Size : 46,9 Mb
Release : 2020-04-01
Category : Philosophy
ISBN : 9780197514979
Vagueness is a subject of long-standing interest in the philosophy of language, metaphysics, and philosophical logic. Numerous accounts of vagueness have been proposed in the literature but there has been no general consensus on which, if any, should be be accepted. Kit Fine here presents a new theory of vagueness based on the radical hypothesis that vagueness is a "global" rather than a "local" phenomenon. In other words, according to Fine, the vagueness of an object or expression cannot properly be considered except in its relation to other objects or other expressions. He then applies the theory to a variety of topics in logic, metaphysics and epistemology, including the sorites paradox, the problem of personal identity, and the transparency of mental phenomenon. This is the inaugural volume in the Rutgers Lectures in Philosophy series, presenting lectures from the most important contemporary thinkers in the discipline.