On Common Solutions to the Liar and the Sorites
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Dialetheists' Lies About the Liar
PRINCIPIA 22(1): 59–85 (2018) doi: 10.5007/1808-1711.2018v22n1p59 Published by NEL — Epistemology and Logic Research Group, Federal University of Santa Catarina (UFSC), Brazil. DIALETHEISTS’LIES ABOUT THE LIAR JONAS R. BECKER ARENHART Departamento de Filosofia, Universidade Federal de Santa Catarina, BRAZIL [email protected] EDERSON SAFRA MELO Departamento de Filosofia, Universidade Federal do Maranhão, BRAZIL [email protected] Abstract. Liar-like paradoxes are typically arguments that, by using very intuitive resources of natural language, end up in contradiction. Consistent solutions to those paradoxes usually have difficulties either because they restrict the expressive power of the language, orelse because they fall prey to extended versions of the paradox. Dialetheists, like Graham Priest, propose that we should take the Liar at face value and accept the contradictory conclusion as true. A logical treatment of such contradictions is also put forward, with the Logic of Para- dox (LP), which should account for the manifestations of the Liar. In this paper we shall argue that such a formal approach, as advanced by Priest, is unsatisfactory. In order to make contradictions acceptable, Priest has to distinguish between two kinds of contradictions, in- ternal and external, corresponding, respectively, to the conclusions of the simple and of the extended Liar. Given that, we argue that while the natural interpretation of LP was intended to account for true and false sentences, dealing with internal contradictions, it lacks the re- sources to tame external contradictions. Also, the negation sign of LP is unable to represent internal contradictions adequately, precisely because of its allowance of sentences that may be true and false. -
Semantical Paradox* Tyler Burge
4 Semantical Paradox* Tyler Burge Frege remarked that the goal of all sciences is truth, but that it falls to logic to discern the laws of truth. Perceiving that the task of determining these laws went beyond Frege’s conception of it, Tarski enlarged the jurisdiction of logic, establishing semantics as truth’s lawyer.1 At the core of Tarski’s theory of truth and validity was a diagnosis of the Liar paradox according to which natural language was hopelessly infected with contradiction. Tarski construed himself as treating the disease by replacing ordinary discourse with a sanitized, artificial construction. But those interested in natural language have been dissatisfied with this medication. The best ground for dis satisfaction is that the notion of a natural language’s harboring contradictions is based on an illegitimate assimilation of natural language to a semantical system. According to that assimilation, part of the nature of a “language” is a set of postulates that purport to be true by virtue of their meaning or are at least partially constitutive of that “language”. Tarski thought that he had identified just such postulates in natural language as spawning inconsistency. But postulates are contained in theories that are promoted by people. Natural languages per se do not postulate or Tyler Burge, “Semantical Paradox", reprinted from The Journal of Philosophy 76 (1979), 169-98. Copyright © 1979 The Journal of Philosophy. Reprinted by permission of the Editor of The Journal of Philosophy and the author. * I am grateful to Robert L. Martin for several helpful discussions; to Herbert Enderton for proving the consistency (relative to that of arithmetic) of an extension of Construction C3; to Charles Parsons for stimulating exchanges back in 1973 and 1974; and to the John Simon Guggenheim Foundation for its support. -
The Liar Paradox As a Reductio Ad Absurdum Argument
University of Windsor Scholarship at UWindsor OSSA Conference Archive OSSA 3 May 15th, 9:00 AM - May 17th, 5:00 PM The Liar Paradox as a reductio ad absurdum argument Menashe Schwed Ashkelon Academic College Follow this and additional works at: https://scholar.uwindsor.ca/ossaarchive Part of the Philosophy Commons Schwed, Menashe, "The Liar Paradox as a reductio ad absurdum argument" (1999). OSSA Conference Archive. 48. https://scholar.uwindsor.ca/ossaarchive/OSSA3/papersandcommentaries/48 This Paper is brought to you for free and open access by the Conferences and Conference Proceedings at Scholarship at UWindsor. It has been accepted for inclusion in OSSA Conference Archive by an authorized conference organizer of Scholarship at UWindsor. For more information, please contact [email protected]. Title: The Liar Paradox as a Reductio ad Absurdum Author: Menashe Schwed Response to this paper by: Lawrence Powers (c)2000 Menashe Schwed 1. Introduction The paper discusses two seemingly separated topics: the origin and function of the Liar Paradox in ancient Greek philosophy and the Reduction ad absurdum mode of argumentation. Its goal is to show how the two topics fit together and why they are closely connected. The accepted tradition is that Eubulides of Miletos was the first to formulate the Liar Paradox correctly and that the paradox was part of the philosophical discussion of the Megarian School. Which version of the paradox was formulated by Eubulides is unknown, but according to some hints given by Aristotle and an incorrect version given by Cicero1, the version was probably as follows: The paradox is created from the Liar sentence ‘I am lying’. -
Philosophy 1
Philosophy 1 PHILOSOPHY VISITING FACULTY Doing philosophy means reasoning about questions that are of basic importance to the human experience—questions like, What is a good life? What is reality? Aileen Baek How are knowledge and understanding possible? What should we believe? BA, Yonsei University; MA, Yonsei University; PHD, Yonsei University What norms should govern our societies, our relationships, and our activities? Visiting Associate Professor of Philosophy; Visiting Scholar in Philosophy Philosophers critically analyze ideas and practices that often are assumed without reflection. Wesleyan’s philosophy faculty draws on multiple traditions of Alessandra Buccella inquiry, offering a wide variety of perspectives and methods for addressing these BA, Universitagrave; degli Studi di Milano; MA, Universitagrave; degli Studi di questions. Milano; MA, Universidad de Barcelona; PHD, University of Pittsburgh Visiting Assistant Professor of Philosophy William Paris BA, Susquehanna University; MA, New York University; PHD, Pennsylvania State FACULTY University Stephen Angle Frank B. Weeks Visiting Assistant Professor of Philosophy BA, Yale University; PHD, University of Michigan Mansfield Freeman Professor of East Asian Studies; Professor of Philosophy; Director, Center for Global Studies; Professor, East Asian Studies EMERITI Lori Gruen Brian C. Fay BA, University of Colorado Boulder; PHD, University of Colorado Boulder BA, Loyola Marymount University; DPHIL, Oxford University; MA, Oxford William Griffin Professor of Philosophy; Professor -
A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics
FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition) NL(A1 A2) = ( T1 ({1}T2) T2 ({1}T1) T1T2 ({1}T1) ({1}T2), I1 ({1}I2) I2 ({1}I1) I1 I2 ({1}I1) ({1} I2), F1 ({1}F2) F2 ({1} F1) F1 F2 ({1}F1) ({1}F2) ). NL(A1 A2) = ( {1}T1T1T2, {1}I1I1I2, {1}F1F1F2 ). NL(A1 A2) = ( ({1}T1T1T2) ({1}T2T1T2), ({1} I1 I1 I2) ({1}I2 I1 I2), ({1}F1F1 F2) ({1}F2F1 F2) ). ISBN 978-1-59973-080-6 American Research Press Rehoboth 1998, 2000, 2003, 2005 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS (fourth edition) NL(A1 A2) = ( T1 ({1}T2) T2 ({1}T1) T1T2 ({1}T1) ({1}T2), I1 ({1}I2) I2 ({1}I1) I1 I2 ({1}I1) ({1} I2), F1 ({1}F2) F2 ({1} F1) F1 F2 ({1}F1) ({1}F2) ). NL(A1 A2) = ( {1}T1T1T2, {1}I1I1I2, {1}F1F1F2 ). NL(A1 A2) = ( ({1}T1T1T2) ({1}T2T1T2), ({1} I1 I1 I2) ({1}I2 I1 I2), ({1}F1F1 F2) ({1}F2F1 F2) ). ISBN 978-1-59973-080-6 American Research Press Rehoboth 1998, 2000, 2003, 2005 1 Contents: Preface by C. Le: 3 0. Introduction: 9 1. Neutrosophy - a new branch of philosophy: 15 2. Neutrosophic Logic - a unifying field in logics: 90 3. Neutrosophic Set - a unifying field in sets: 125 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics: 129 5. Addenda: Definitions derived from Neutrosophics: 133 2 Preface to Neutrosophy and Neutrosophic Logic by C. -
Leibniz and the Sorites
Leibniz and the Sorites Samuel Levey, Dartmouth College Abstract The sorites paradox receives its most sophisticated early modem discussion in Leibniz's writings. In an important early document Lcibniz holds that vague terms have sharp boundaries of application, but soon thereafter he comes to adopt a form of nihilism about vagueness: and it later proves to be his settled view that vagueness results from semantical indeterminacy. The reason for this change of mind is unclear, and Leibniz does not ap pear to have any grounds for it. I suggest that his various treatments of the sorites do not spring from a single integrated view of vagueness, and that his early position reflects a mercenary interest in the sorites paradox-an interest to use the sorites to reach a conclu sion in metaphysics rather than to examine vagueness as a subject to be understood in its own right. The later nihilist stance rei1ects Leibniz's own (if undefended) attitude to wards vagueness. term that is vague in the philosopher's sense-such as 'rich', 'poor', A 'bald', 'heap' -characteristically admits of borderline cases, lacks a clearly defined extension, and is susceptible to the sorites paradox or "paradox of the heap.'" Take 'poor' for example. Someone with only a small amount of money may appear to be neither poor nor not poor, but on the borderline, even in the estimation of a competent language user fully informed about the amount of money the person has, the relative distributions of wealth in the community, and so on. The term 'poor' imposes no clear boundary between the poor and the not poor-it fails to single out a least number n such that anyone with at least 11 pennies is not poor while anyone with fewer than n pennies is poor-with cases seeming instead to fall into a spectrum across which poverty shades off gradually. -
Alethic Fictionalism, Alethic Nihilism, and the Liar Paradox
Philos Stud (2017) 174:3083–3096 DOI 10.1007/s11098-016-0847-4 Alethic fictionalism, alethic nihilism, and the Liar Paradox 1 2 Bradley Armour-Garb • James A. Woodbridge Published online: 23 December 2016 Ó Springer Science+Business Media Dordrecht 2016 Abstract Recently, several philosophers have proposed fictionalist accounts of truth- talk, as a means for resolving the semantic pathology that the Liar Paradox appears to present. These alethic fictionalists aim to vindicate truth-talk as a kind of as if dis- course, while rejecting that the talk attributes any real property of truth. Liggins (Analysis 74:566–574, 2014) has recently critically assessed one such proposal, Beall’s (The law of non-contradiction: new philosophical essays. Oxford University Press, New York, pp 197–216, 2004) constructive methodological deflationist (henceforth, ‘CMD’), offering objections to Beall’s proposed alethic fictionalism that potentially generalize to other alethic fictionalist accounts. Liggins further argues that CMD supports a classically consistent response to the Liar Paradox—one that can be extracted from CMD, while leaving its putatively problematic fictionalist elements behind in favor of alethic nihilism. In this paper, after establishing that Liggins’s criticisms of CMD are off base, we show that the classical resolution of the Liar Paradox that he proposes is unworkable. Since his resistance to alethic fictionalism turns out to be unmotivated, we conclude that this approach is still worth considering as a framework for a resolution of the Liar Paradox. Keywords Truth Á Liar Paradox Á Fictionalism Á Pretense & Bradley Armour-Garb [email protected] James A. Woodbridge [email protected] 1 Department of Philosophy, University at Albany—SUNY, Albany, NY, USA 2 Department of Philosophy, University of Nevada, Las Vegas, NV, USA 123 3084 B. -
The Sorites Paradox
The sorites paradox phil 20229 Jeff Speaks April 17, 2008 1 Some examples of sorites-style arguments . 1 2 What words can be used in sorites-style arguments? . 3 3 Ways of solving the paradox . 3 1 Some examples of sorites-style arguments The paradox we're discussing today and next time is not a single argument, but a family of arguments. Here are some examples of this sort of argument: 1. Someone who is 7 feet in height is tall. 2. If someone who is 7 feet in height is tall, then someone 6'11.9" in height is tall. 3. If someone who is 6'11.9" in height is tall, then someone 6'11.8" in height is tall. ...... C. Someone who is 3' in height is tall. The `. ' stands for a long list of premises that we are not writing down; but the pattern makes it pretty clear what they would be. We could also, rather than giving a long list of premises `sum them up' with the following sorites premise: For any height h, if someone's height is h and he is tall, then someone whose height is h − 0:100 is also tall. This is a universal claim about all heights. Each of the premises 2, 3, . is an instance of this universal claim. Since universal claims imply their instances, each of premises 2, 3, . follows from the sorites premise. This is a paradox, since it looks like each of the premises is true, but the con- clusion is clearly false. Nonetheless, the reasoning certainly appears to be valid. -
The Liar: an Essay in Truth and Circularity, by Jon Barwise and John Etchemendy, Oxford University Press, New York and Oxford, 1987, Xii + 185 Pp., $19.95
216 BOOK REVIEWS BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 20, Number 2, April 1989 ©1989 American Mathematical Society 0273-0979/89 $1.00 + $.25 per page The Liar: An essay in truth and circularity, by Jon Barwise and John Etchemendy, Oxford University Press, New York and Oxford, 1987, xii + 185 pp., $19.95. ISBN 0-19-505072-x Consider the classic Liar sentence: "This sentence is false." It claims that it is false. So if we assume that a sentence is true if and only if what it claims is the case, then the Liar is true if and only if it is false. People have thought about this paradox for centuries. Despite this, there is no single standard "solution." An attempted resolution of the paradox would tell us which of our intuitions are sound and which need further clarification. It would point out where and why our naive reasoning leads us to a contradiction. Modern logic applies mathematical methods to the modeling and study of truth, proof, computation, and infinity. The paradoxes of semantics and set theory were important in the development of the field. The reason for working on the paradoxes of any field is not only to secure a foundation. The deeper reason is that by introducing, discarding, and clarifying the concepts that lead to paradox we are lead to the central ideas and questions of the field. We see from The Liar that the paradoxes are still a source of inspiration in logic. The book is a new, exciting contribution to the study of truth. -
Kierkegaard and the Funny by Eric Linus Kaplan a Dissertation
Kierkegaard and the Funny By Eric Linus Kaplan A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Philosophy in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Alva Noë, co-chair Professor Hubert Dreyfus, co-chair Professor Sean D. Kelly Professor Deniz Göktürk Summer 2017 Abstract Kierkegaard and the Funny by Eric Linus Kaplan Doctor of Philosophy in Philosophy University of California, Berkeley Professor Alva Noë, co-chair Professor Hubert Dreyfus, co-chair This dissertation begins by addressing a puzzle that arises in academic analytic interpretations of Kierkegaard’s Concluding Unscientific Postscript. The puzzle arises when commentators try to paraphrase the book’s philosophical thesis “truth is subjectivity.” I resolve this puzzle by arguing that the motto “truth is subjectivity” is like a joke, and resists and invites paraphrase just as a joke does. The connection between joking and Kierkegaard’s philosophical practice is then deepened by giving a philosophical reconstruction of Kierkegaard's definition of joking as a way of responding to contradiction that is painless precisely because it sees the way out in mind. Kierkegaard’s account of joking and his account of his own philosophical project are used to mutually illuminate each other. The dissertation develops a phenomenology of retroactive temporality that explains how joking and subjective thinking work. I put forward an argument for why “existential humorism” is a valuable approach to life for Kierkegaard, but why it ultimately fails, and explain the relationship between comedy as a way of life and faith as a way of life, particularly as they both relate to risk. -
Vagueness and Precisifications
Vagueness and Precisifications Mats Grimsgaard Master’s Thesis in Philosophy Supervisor: Olav Asheim Department of Philosophy, Classics, History of Art and Ideas UNIVERSITY OF OSLO Spring 2014 Abstract The aim of this thesis is to explore the role of precisifications of vague predicates. Basically, the idea is that vague predicates can be, and are in fact, made more precise without altering their underlying concepts or truth-conditions. Vague terms and their precisifications are conceived as more or less precise instances of the same lexical entities. Precisifications are employed in several leading views on how we interpret and understand vague language, and how we utilize and reason with partial concepts and inexact knowledge—which covers most, if not all, human thinking and speaking. Although precisifications play important roles in the semantics of vagueness, they are not as straightforwardly understood as they might appear. There is more than one way to cash out the notion of precisifications, which have important im- plications for what extent various theories might be seen as a sufficient analysis of vagueness itself, as opposed to mere simulations of vagueness. Yet, many authors seem to have little concern for this issue. As a result, a term that is cen- tral to some of the most popular responses to vagueness might turn out to be ambiguous, if not vague. In chapter 1 I present and discuss the most vicious feature of vagueness: its tendency to generate paradoxes. This provides a general overview of the topic and introduces some important terms and concepts. Chapter 2 is a discussion of how to cash out the notion of precisifications, and not least ‘admissible precisi- fications’. -
The Liar Paradox: Tangles and Chains Author(S): Tyler Burge Source: Philosophical Studies: an International Journal for Philosophy in the Analytic Tradition, Vol
The Liar Paradox: Tangles and Chains Author(s): Tyler Burge Source: Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, Vol. 41, No. 3 (May, 1982), pp. 353-366 Published by: Springer Stable URL: http://www.jstor.org/stable/4319529 Accessed: 11-04-2017 02:26 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms Springer is collaborating with JSTOR to digitize, preserve and extend access to Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition This content downloaded from 128.97.244.236 on Tue, 11 Apr 2017 02:26:37 UTC All use subject to http://about.jstor.org/terms TYLER BURGE THE LIAR PARADOX: TANGLES AND CHAINS (Received 20 March, 1981) In this paper I want to use the theory that I applied in 'Semantical paradox' to the Liar and Grelling paradoxes to handle some subtler versions of the Liar.! These new applications will serve as tools for sharpening some of the pragmatic principles and part of the underlying motivation of the theory. They also illustrate the superiority of our theory to previous ones in the hier- archical tradition. The heart of the theory is that 'true' is an indexical-schematic predicate.