Contextual Effects on Vagueness and the Sorites Paradox: a Preliminary
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Vagueness Susanne Bobzien and Rosanna Keefe
Vagueness Susanne Bobzien and Rosanna Keefe I—SUSANNE BOBZIEN COLUMNAR HIGHER-ORDER VAGUENESS, OR VAGUENESS IS HIGHER-ORDER VAGUENESS Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn’t (Williamson’s) is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this. In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system qs4m+bf+fin. It corresponds to the class of transitive, reflexive and final frames. With borderlineness (unclarity, indeterminacy) defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague. Like Williamson’s, the theory proposed here has no clear borderline cas- es in Sorites sequences. I argue that objections that there must be clear bor- derline cases ensue from the confusion of two notions of borderlineness— one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness para- doxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. This paper proposes that vagueness is higher-order vagueness. At first blush this may seem a very peculiar suggestion. It is my hope that the following pages will dispel the peculiarity and that the advantages of the proposed theory will speak for themselves. -
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 -
• Today: Language, Ambiguity, Vagueness, Fallacies
6060--207207 • Today: language, ambiguity, vagueness, fallacies LookingLooking atat LanguageLanguage • argument: involves the attempt of rational persuasion of one claim based on the evidence of other claims. • ways in which our uses of language can enhance or degrade the quality of arguments: Part I: types and uses of definitions. Part II: how the improper use of language degrades the "weight" of premises. AmbiguityAmbiguity andand VaguenessVagueness • Ambiguity: a word, term, phrase is ambiguous if it has 2 or more well-defined meaning and it is not clear which of these meanings is to be used. • Vagueness: a word, term, phrase is vague if it has more than one possible and not well-defined meaning and it is not clear which of these meanings is to be used. • [newspaper headline] Defendant Attacked by Dead Man with Knife. • Let's have lunch some time. • [from an ENGLISH dept memo] The secretary is available for reproduction services. • [headline] Father of 10 Shot Dead -- Mistaken for Rabbit • [headline] Woman Hurt While Cooking Her Husband's Dinner in a Horrible Manner • advertisement] Jack's Laundry. Leave your clothes here, ladies, and spend the afternoon having a good time. • [1986 headline] Soviet Bloc Heads Gather for Summit. • He fed her dog biscuits. • ambiguous • vague • ambiguous • ambiguous • ambiguous • ambiguous • ambiguous • ambiguous AndAnd now,now, fallaciesfallacies • What are fallacies or what does it mean to reason fallaciously? • Think in terms of the definition of argument … • Fallacies Involving Irrelevance • or, Fallacies of Diversion • or, Sleight-of-Hand Fallacies • We desperately need a nationalized health care program. Those who oppose it think that the private sector will take care of the needs of the poor. -
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. -
Fuzziness-Vagueness-Generality-Ambiguity. Journal of Pragmatics (Elsevier Science B.V
Fuzziness-vagueness-generality-ambiguity. Journal of Pragmatics (Elsevier Science B.V. in New York & Amsterdam), 1998, 29 (1): pp 13-31. Fuzziness---Vagueness---Generality---Ambiguity1 Qiao Zhang Published by Journal of Pragmatics (Elsevier Science B.V. in New York & Amsterdam), 1998, 29(1): pp 13-31. Contact: Dr Grace Zhang Department of Languages and Intercultural Education Curtin University of Technology GPO Box 1987 Perth, Western Australia 6845 Australia Tel: +61 8 9266 3478 Fax: +61 8 9266 4133 Email: [email protected] Abstract In this paper, I attempt to distinguish four linguistic concepts: fuzziness, vagueness, generality and ambiguity. The distinction between the four concepts is a significant matter, both theoretically and practically. Several tests are discussed from the perspectives of semantics, syntax and pragmatics. It is my contention that fuzziness, vagueness, and generality are licensed by Grice's Co-operative Principle, i.e. they are just as important as precision in language. I conclude that generality, vagueness, and fuzziness are under-determined, and ambiguity is over-determined. Fuzziness differs from generality, vagueness, and ambiguity in that it is not simply a result of a one-to- many relationship between a general meaning and its specifications; nor a list of possible related interpretations derived from a vague expression; nor a list of unrelated meanings denoted by an ambiguous expression. Fuzziness is inherent in the sense that it has no clear-cut referential boundary, and is not resolvable with resort to context, as opposed to generality, vagueness, and ambiguity, which may be contextually eliminated. It is also concluded that fuzziness is closely involved with language users' judgments. -
Quantifying Aristotle's Fallacies
mathematics Article Quantifying Aristotle’s Fallacies Evangelos Athanassopoulos 1,* and Michael Gr. Voskoglou 2 1 Independent Researcher, Giannakopoulou 39, 27300 Gastouni, Greece 2 Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece; [email protected] or [email protected] * Correspondence: [email protected] Received: 20 July 2020; Accepted: 18 August 2020; Published: 21 August 2020 Abstract: Fallacies are logically false statements which are often considered to be true. In the “Sophistical Refutations”, the last of his six works on Logic, Aristotle identified the first thirteen of today’s many known fallacies and divided them into linguistic and non-linguistic ones. A serious problem with fallacies is that, due to their bivalent texture, they can under certain conditions disorient the nonexpert. It is, therefore, very useful to quantify each fallacy by determining the “gravity” of its consequences. This is the target of the present work, where for historical and practical reasons—the fallacies are too many to deal with all of them—our attention is restricted to Aristotle’s fallacies only. However, the tools (Probability, Statistics and Fuzzy Logic) and the methods that we use for quantifying Aristotle’s fallacies could be also used for quantifying any other fallacy, which gives the required generality to our study. Keywords: logical fallacies; Aristotle’s fallacies; probability; statistical literacy; critical thinking; fuzzy logic (FL) 1. Introduction Fallacies are logically false statements that are often considered to be true. The first fallacies appeared in the literature simultaneously with the generation of Aristotle’s bivalent Logic. In the “Sophistical Refutations” (Sophistici Elenchi), the last chapter of the collection of his six works on logic—which was named by his followers, the Peripatetics, as “Organon” (Instrument)—the great ancient Greek philosopher identified thirteen fallacies and divided them in two categories, the linguistic and non-linguistic fallacies [1]. -
On Common Solutions to the Liar and the Sorites
On Common Solutions to the Liar and the Sorites Sergi Oms Sardans Aquesta tesi doctoral està subjecta a la llicència Reconeixement 3.0. Espanya de Creative Commons. Esta tesis doctoral está sujeta a la licencia Reconocimiento 3.0. España de Creative Commons. This doctoral thesis is licensed under the Creative Commons Attribution 3.0. Spain License. On Common Solutions to the Liar and the Sorites Sergi Oms Sardans Phd in Cognitive Science and Language Supervisor: Jose´ Mart´ınez Fernandez´ Tutor: Manuel Garc´ıa-Carpintero Sanchez-Miguel´ Department of Philosophy Faculty of Philosophy University of Barcelona CONTENTS Abstract iv Resum v Acknowledgements vi 1 Introduction 1 1.1 Truth . 1 1.2 The Liar . 3 1.3 The Formal Liar . 6 1.4 The Sorites ............................ 10 1.5 Forms of the Sorites ....................... 12 1.6 Vagueness . 17 1.7 This Dissertation . 18 2 The notion of Paradox 20 2.1 A Minor Point . 20 2.2 The Traditional Definition . 22 2.3 Arguments and Premises . 25 2.4 The Logical Form . 28 2.5 A First Attempt . 29 2.6 The Notion of Paradox . 31 2.7 Two Consequences . 35 2.8 Two Objections . 36 3 Solving Paradoxes 39 3.1 Solving One Paradox . 39 3.2 Solving more than One Paradox . 45 3.3 Van McGee: Truth as a Vague Notion . 47 i CONTENTS ii 3.3.1 The Sorites in Partially Interpreted Languages . 47 3.3.2 The Liar and vagueness . 49 3.3.3 Solving the Paradoxes . 54 4 Why a Common Solution 56 4.1 Why a Common Solution? . -
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. -
Vagueness and Quantification
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Research Information System University of Turin Vagueness and Quantification (postprint version) Journal of Philosophical Logic first online, 2015 Andrea Iacona This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinc- tion which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it out- lines some implications of the account provided which bear on three debated issues concerning quantification. 1 Preliminary clarifications Let us start with some terminology. First of all, the term `quantifier expres- sion' will designate expressions such as `all', `some' or `more than half of', which occurs in noun phrases as determiners. For example, in `all philoso- phers', `all' occurs as a determiner of `philosophers', and the same position can be occupied by `some' or `more than half of'. This paper focuses on simple quantified sentences containing quantifier expressions so understood, such as the following: (1) All philosophers are rich (2) Some philosophers are rich (3) More than half of philosophers are rich Although this is a very restricted class of sentences, it is sufficiently repre- sentative to deserve consideration on its own. In the second place, the term `domain' will designate the totality of things over which a quantifier expression is taken to range. -
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’.