DOCSLIB.ORG

1 Abstract. Rationality's Demands on Belief Alexander Liam Worsnip

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1 Abstract. Rationality's Demands on Belief Alexander Liam Worsnip Abstract. Rationality’s Demands on Belief Alexander Liam Worsnip 2015 It is common in the literature on practical rationality to distinguish between “structural” or “coherence” requirements of rationality on one hand, and substantive reasons on the other. When it comes to epistemology, however, this distinction is often overlooked, and its significance has not yet been fully appreciated. My dissertation is the first systematic attempt to remedy this. I show that coherence requirements have a distinctive and important role to play in epistemology, one that is not reducible to responding to evidence (reasons), and that must be theorized in its own right. Most radically, I argue that there is a core notion of rational belief, worth caring about and theorizing, that involves only conformity to coherence requirements, and on which – contrary to what most epistemologists either explicitly or implicitly assume – rationality does not require responding to one’s evidence. Though this can strike observers as a merely terminological stance, I show that this reaction is too quick, by arguing that there are cases of conflict between coherence requirements and responding to reasons – that is, where one cannot both satisfy the coherence requirements and respond to all of one’s reasons. As such, there is no single “umbrella” notion of rationality that covers both conformity to coherence requirements and responding to reasons. As well as trying to illuminate the nature and form of coherence requirements, I show that coherence requirements are of real epistemological significance, helping us to make progress in extant debates about higher-order evidence, doxastic voluntarism, deductive constraints, and (more briefly) conditionalization and peer disagreement. I argue that understanding the relevant norms in these areas as coherence requirements, rather than as claims about reasons, can help to resolve a number of problematic confusions and impasses in these debates. 1 Rationality’s Demands on Belief A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Alexander Liam Worsnip Dissertation Directors: Keith DeRose and Tamar Gendler May 2015 2 © 2015 by Alexander Liam Worsnip All rights reserved. 3 Summary Table of Contents Detailed Table of Contents (including Tables & Figures) 5 Acknowledgments 7 Introduction 11 Chapter 1 Rational Belief without Evidence-Responsiveness 51 Chapter 2 Rationality as Coherence Defended 101 Chapter 3 Narrow-Scoping for Wide-Scopers 163 Chapter 4 Believing at Will as a Failure of Coherence 225 Chapter 5 Coherence and Deductive Constraints on Belief 266 Conclusion 304 References 317 4 Detailed Table of Contents Acknowledgments 7 Introduction 11 0.1 A chasm 11 0.2 Disambiguation? 14 0.3 Substantive reasons versus coherence requirements – a more 20 detailed first pass at the distinction 0.4 What the coherentist view is not 26 0.5 Domains of rationality and domains of philosophy 32 0.6 Evidence, reasons, and ‘ought’ 34 0.7 The epistemological context of this dissertation 38 0.8 The plan for the dissertation 44 1 Rational Belief without Evidence-Responsiveness 51 1.1 A puzzle 51 1.2 A bit more on evidential support 56 1.3 (ILC) explicated and defended 57 1.4 (PIF) defended 71 1.5 Does (ILC) still have force in cases of iterative failure? 88 1.6 What kind of conflict? 91 1.7 The disambiguating response revisited 96 2 Rationality as Coherence Defended 101 2.1 The interest and importance of coherence requirements 101 2.2 The normativity of coherence requirements 111 2.3 The centrality of coherence to the ordinary concept of rationality 117 2.4 Attempts to vindicate the asymmetry 127 2.5 An error-theory for the asymmetry 138 2.6 Modified reasons-responsiveness views? 143 3 Narrow-Scoping for Wide-Scopers 163 3.1 Introduction 163 3.2 Wide-scoping vs. narrow-scoping about the fundamental 168 requirements of rationality 3.3 Wide-scope semantics 175 3.4 An alternative: contextualism 179 3.5 Contextualism vs. wide-scope semantics 185 3.6 Extending contextualism to (talk about) rationality 195 3.7 Further puzzles resolved 205 5 3.8 Detachment rules 217 4 Believing at Will as a Failure of Coherence 225 4.1 Introduction 225 4.2 What is it that’s difficult? 228 4.3 Is believing at will impossible? Some possible counterexamples 233 4.4 An explanation in terms of substantive norms? 237 4.5 An explanation in terms of coherence requirements? 243 4.6 Explaining the cases 252 4.7 The difficulty of transparent incoherence 259 5 Coherence and Deductive Constraints on Belief 266 5.1 Introduction 266 5.2 Deductive closure and the preface paradox challenge 267 5.3 Ways of formulating the challenge to closure 270 5.4 A new way of formulating the challenge 274 5.5 Defending weak fallibilism 278 5.6 Defending belief-credence coherence 288 5.7 Living without closure in the theory of belief 293 5.8 Consistency without closure? 298 5.9 Other deductive constraints 301 Conclusion 304 References 317 Tables & Figures Table 1: our puzzle 52 Figure 1: safety and KK failure 78 6 Acknowledgments This dissertation was written with the help of many people. First and foremost, I must thank my dissertation committee: my co-advisors, Keith DeRose and Tamar Gendler, and my other committee members, Steve Darwall, Bruno Whittle, and (as an external committee member) Ralph Wedgwood. I was lucky to, perhaps unusually, have a committee where every single member, in different ways, was generous with their time, and ultimately made a big contribution to the project and to my intellectual development more broadly. The final dissertation reflects the philosophical diversity of this group, which collectively spans a wide range of philosophical subfields and methodological approaches, and is, I think, all the better for that. Moreover, every member of the committee supported me in other important ways, offering crucial advice, encouragement and big-picture guidance as I shaped the project and, more recently, braved the academic job market. I also learnt a huge amount about teaching both from Keith (as his TA for Epistemology in Spring 2012) and from Steve (as his co-instructor for Rationality in Fall 2013). Both teaching experiences were accompanied by highly stimulating weekly discussions of the material we were covering, and much else besides. And both experiences had a profound effect on this dissertation, helping me to focus the project and to master crucial literature in a deep way by learning how to communicate it to undergraduates. One of the best things about pursuing my PhD at Yale was the opportunity to get wonderful feedback on my work from many other faculty members who were not formally on my committee. I must single out Dan Greco, Josh Knobe, and Zoltán Szabó in particular for going well beyond the call of duty in providing invaluable help with my work during the time I was at Yale. I also learnt a great deal from classes, discussions and exchanges with a number of other current or former Yale faculty members, including Facundo Alonso, George 7 Bealer, Michael Della Rocca, Paul Franks, Verity Harte, Shelly Kagan, Raul Saucedo, Sun-Joo Shin, Sam Shpall, Matt Smith, and Ken Winkler. Just as important was the opportunity to share and discuss ideas with my fellow Yale graduate students, past and present. For friendship, support and philosophical discussion, I’m especially grateful to Julia Borcherding, Julianne Chung, Eric Guindon, Jessica Keiser, Justin Khoo, Mark Maxwell, Jessie Munton, Aaron Norby, Jonathan Phillips, John Pittard, Daniel Putnam, Alex Silverman, Kelley Schiffman, Evan Rodriguez, Jonathan Vertanen, and Yuan Yuan. I must single out Julianne and John for their influence on this dissertation specifically. As fellow epistemologists and wonderful friends, they both helped to shape my thinking and philosophical development profoundly. Before coming to Yale I was both an undergraduate and a BPhil student at Oxford. I was lucky enough to have some wonderful philosophy teachers there, many of whose influence will be evident: in particular, Louise Braddock, John Broome, Roger Crisp, Terry Irwin, Ralph Walker, Ralph Wedgwood, and Dawn Wilson. Ralph Wedgwood deserves special thanks. As mentioned above, he ultimately served as an external member of my dissertation committee. He has been involved with my work and career for a greater sustained period of time than anyone else, having taught me in my very first term as a BPhil student, as I tried – often ineffectively – to get a feel for contemporary epistemology for the first time. I hope his patience with me then paid off, and feel privileged to now count him as a colleague and friend. Several other people read and provided very helpful feedback on versions of one or more chapters of the dissertation. For this, profound thanks to Daniel Fogal, Maria Lasonen- Aarnio, Ram Neta, and Daniel Whiting. An article that overlaps parts of chapter 2, especially sections 2.3-2.5, is forthcoming in Philosophical Quarterly, and a shortened version of chapter 3 8 is forthcoming in Synthese. Thanks to the anonymous referees for both articles for helpful written comments. Some of this material was presented at conferences or colloquia, where I received valuable comments and criticisms. An earlier version of chapter 1 was presented at the London School of Economics and at the St Louis Annual Conference on Reasons and Rationality. Chapter 4 was recently presented at the University of California, San Diego, the University of Pittsburgh, and the University of North Carolina, Chapel Hill. An earlier version of parts of chapter 5 were presented at a meeting of the Joint Session of the Aristotelian Society and the Mind Association at the University of Cambridge. I’m grateful to the audiences at all of these places, especially to my future colleagues at UNC.
Load more

Recommended publications
  • Logic, Reasoning, and Revision
    Logic, Reasoning, and Revision Abstract The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this paper I first place Harman’s challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms for belief can be captured. introduction The canons of classical deductive logic provide, at least according to a widespread but presumably naive view, general as well as infallible norms for reasoning. Obviously, few instances of actual reasoning have such prop- erties, and it is therefore not surprising that the naive view has been chal- lenged in many ways. Four kinds of challenges are relevant to the question of where the naive view goes wrong, but each of these challenges is also in- teresting because it allows us to focus on a particular aspect of the relation between deductive logic, reasoning, and logical revision. Challenges to the naive view that classical deductive logic directly yields norms for reason- ing come in two sorts. Two of them are straightforwardly revisionist; they claim that the consequence relation of classical logic is the culprit. The remaining two directly question the naive view about the normative role of logic for reasoning; they do not think that the philosophical notion of en- tailment (however conceived) is as relevant to reasoning as has traditionally been assumed.
    [Show full text]
  • Mathematical Logic
    Proof Theory. Mathematical Logic. From the XIXth century to the 1960s, logic was essentially mathematical. Development of first-order logic (1879-1928): Frege, Hilbert, Bernays, Ackermann. Development of the fundamental axiom systems for mathematics (1880s-1920s): Cantor, Peano, Zermelo, Fraenkel, Skolem, von Neumann. Giuseppe Peano (1858-1932) Core Logic – 2005/06-1ab – p. 2/43 Mathematical Logic. From the XIXth century to the 1960s, logic was essentially mathematical. Development of first-order logic (1879-1928): Frege, Hilbert, Bernays, Ackermann. Development of the fundamental axiom systems for mathematics (1880s-1920s): Cantor, Peano, Zermelo, Fraenkel, Skolem, von Neumann. Traditional four areas of mathematical logic: Proof Theory. Recursion Theory. Model Theory. Set Theory. Core Logic – 2005/06-1ab – p. 2/43 Gödel (1). Kurt Gödel (1906-1978) Studied at the University of Vienna; PhD supervisor Hans Hahn (1879-1934). Thesis (1929): Gödel Completeness Theorem. 1931: “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”. Gödel’s First Incompleteness Theorem and a proof sketch of the Second Incompleteness Theorem. Core Logic – 2005/06-1ab – p. 3/43 Gödel (2). 1935-1940: Gödel proves the consistency of the Axiom of Choice and the Generalized Continuum Hypothesis with the axioms of set theory (solving one half of Hilbert’s 1st Problem). 1940: Emigration to the USA: Princeton. Close friendship to Einstein, Morgenstern and von Neumann. Suffered from severe hypochondria and paranoia. Strong views on the philosophy of mathematics. Core Logic – 2005/06-1ab – p. 4/43 Gödel’s Incompleteness Theorem (1). 1928: At the ICM in Bologna, Hilbert claims that the work of Ackermann and von Neumann constitutes a proof of the consistency of arithmetic.
    [Show full text]
  • In Defence of Constructive Empiricism: Metaphysics Versus Science
    To appear in Journal for General Philosophy of Science (2004) In Defence of Constructive Empiricism: Metaphysics versus Science F.A. Muller Institute for the History and Philosophy of Science and Mathematics Utrecht University, P.O. Box 80.000 3508 TA Utrecht, The Netherlands E-mail: [email protected] August 2003 Summary Over the past years, in books and journals (this journal included), N. Maxwell launched a ferocious attack on B.C. van Fraassen's view of science called Con- structive Empiricism (CE). This attack has been totally ignored. Must we con- clude from this silence that no defence is possible against the attack and that a fortiori Maxwell has buried CE once and for all, or is the attack too obviously flawed as not to merit exposure? We believe that neither is the case and hope that a careful dissection of Maxwell's reasoning will make this clear. This dis- section includes an analysis of Maxwell's `aberrance-argument' (omnipresent in his many writings) for the contentious claim that science implicitly and per- manently accepts a substantial, metaphysical thesis about the universe. This claim generally has been ignored too, for more than a quarter of a century. Our con- clusions will be that, first, Maxwell's attacks on CE can be beaten off; secondly, his `aberrance-arguments' do not establish what Maxwell believes they estab- lish; but, thirdly, we can draw a number of valuable lessons from these attacks about the nature of science and of the libertarian nature of CE. Table of Contents on other side −! Contents 1 Exordium: What is Maxwell's Argument? 1 2 Does Science Implicitly Accept Metaphysics? 3 2.1 Aberrant Theories .
    [Show full text]
  • Interactive Models of Closure and Introspection
    Interactive Models of Closure and Introspection 1 introduction Logical models of knowledge can, even when confined to the single-agent perspective, differ in many ways. One way to look at this diversity suggests that there doesn’t have to be a single epistemic logic. We can simply choose a logic relative to its intended context of application (see e.g. Halpern [1996: 485]). From a philosophical perspective, however, there are at least two features of the logic of “knows” that are a genuine topic of disagreement, rather than a source of mere diversity or pluralism: closure and introspec- tion. By closure, I mean here the fact that knowledge is closed under known implication, knowing that p puts one in a position to come to know what one knows to be implied by p. By introspection, I shall (primarily) refer to the principle of positive introspection which stipulates that knowing puts one in a position to know that one knows.1 The seemingly innocuous princi- ple of closure was most famously challenged by Dretske [1970] and Nozick [1981], who believed that giving up closure—and therefore the intuitively plausible suggestion that knowledge can safely be extended by deduction— was the best way to defeat the sceptic. Positive introspection, by contrast, was initially defended in Hintikka’s Knowledge and Belief [1962], widely scrutinized in the years following its publication (Danto [1967], Hilpinen [1970], and Lemmon [1967]), and systematically challenged (if not conclu- sively rejected) by Williamson [2000: IV–V]. A feature of these two principles that is not always sufficiently acknowl- edged, is that that there isn’t a unique cognitive capability that corresponds to each of these principles.
    [Show full text]
  • Inconsistency and Uncertainty Handling in Lightweight Description Logics
    Inconsistency and uncertainty handling in lightweight description logics THÈSE présentée et soutenue publiquement le 5 juin 2015 en vue de l’obtention du Doctorat de l’Université d’Artois (Spécialité Informatique) par : Zied Bouraoui devant le jury composé de Anthony HUNTER Professor - University College London, United Kingdom (Rapporteur) Henri PRADE Directeur de recherche CNRS - IRIT Toulouse (Rapporteur) Salem BENFERHAT Professeur des universités - Université d’Artois (Directeur de Thèse) Sylvain LAGRUE Maître de conférences (HDR) - Université d’Artois (Examinateur) Marie-Laure MUGNIER Professeur des universités- Université de Montpellier II (Examinatrice) Odile PAPINI Professeur des universités - Université d’Aix Marseille (Examinatrice) Ramón PINO PÉREZ Professor - University of the Andes, Venezuela (Examinateur) Karim TABIA Maître de conférences - Université d’Artois (Examinateur) CENTRE DE RECHERCHE EN INFORMATIQUE DE LENS – CNRS UMR-8188 UNIVERSITÉ D’ARTOIS, RUE JEAN SOUVRAZ, S.P. 18 F-62307, LENS CEDEX FRANCE SECRÉTARIAT :TÉL.: +33(0)321791723–FAX : +33(0)321791770 http://www.cril.univ-artois.fr ABSTRACT Abstract This thesis investigates the dynamics of beliefs and uncertainty management in DL-Lite, one of the most important lightweight description logics. The first part of the thesis concerns the problem of han- dling uncertainty in DL-Lite. First, we propose an extension of the main fragments of DL-Lite to deal with the uncertainty associated with axioms using a possibility theory framework without additional ex- tra computational costs. We then study the revision of possibilistic DL-Lite bases when a new piece of information is available. Lastly, we propose a min-based assertional merging operator when assertions of ABox are provided by several sources of information having different levels of priority.
    [Show full text]
  • A Relevant Alternatives Analysis of Knowledge
    A RELEVANT ALTERNATIVES ANALYSIS OF KNOWLEDGE DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Joshua A. Smith, B. A., M. A. ***** The Ohio State University 2006 Dissertation Committee: Approved by Professor George Pappas, Adviser Professor Louise Antony Adviser Professor William Taschek Graduate Program in Philosophy ABSTRACT This project shows that a relevant alternatives account of knowledge is correct. Such accounts maintain that knowing that something is the case requires eliminating all of the relevant alternatives to what is believed. Despite generating a great deal of interest after Dretske and Goldman introduced them, relevant alternatives accounts have been abandoned by many due to the inability of those who defend such analyses to provide general accounts of what it is for an alternative to be relevant, and what it is for an alternative to be eliminated. To make sense of the notion of relevance, a number of relevant alternatives theorists have adopted contextualism, the view that the truth conditions for knowledge attributions shift from one conversational context to the next. The thought that the only way to make sense of relevance is to adopt a controversial thesis about how knowledge attributions work has led others to despair over the prospects for such accounts. I rescue the relevant alternatives approach to knowledge by providing the missing details, and doing so in purely evidentialist terms, thereby avoiding a commitment to contextualism. The account of relevance I develop articulates what it is for a state of affairs (possible world) to be relevant in terms of whether the person is in a good epistemic position in that state of affairs with respect to what the person actually believes.
    [Show full text]
  • Deductive Systems in Traditional and Modern Logic
    Deductive Systems in Traditional and Modern Logic • Urszula Wybraniec-Skardowska and Alex Citkin Deductive Systems in Traditional and Modern Logic Edited by Urszula Wybraniec-Skardowska and Alex Citkin Printed Edition of the Special Issue Published in Axioms www.mdpi.com/journal/axioms Deductive Systems in Traditional and Modern Logic Deductive Systems in Traditional and Modern Logic Editors Alex Citkin Urszula Wybraniec-Skardowska MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Editors Alex Citkin Urszula Wybraniec-Skardowska Metropolitan Telecommunications Cardinal Stefan Wyszynski´ USA University in Warsaw, Department of Philosophy Poland Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Axioms (ISSN 2075-1680) (available at: http://www.mdpi.com/journal/axioms/special issues/deductive systems). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03943-358-2 (Pbk) ISBN 978-3-03943-359-9 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.
    [Show full text]
  • The Weak Base Method for Constraint Satisfaction
    The Weak Base Method for Constraint Satisfaction Von der Fakult¨atf¨urElektrotechnik und Informatik der Gottfried Wilhelm Leibniz Universit¨atHannover zur Erlangung des Grades einer DOKTORIN DER NATURWISSENSCHAFTEN Dr. rer. nat. genehmigte Dissertation von Dipl.-Math. Ilka Schnoor geboren am 11. September 1979, in Eckernf¨orde 2008 Schlagw¨orter:Berechnungskomplexit¨at,Constraint Satisfaction Probleme, Uni- verselle Agebra Keywords: Computational complexity, Constraint satisfaction problems, Uni- versal algebra Referent: Heribert Vollmer, Gottfried Wilhelm Leibniz Universit¨atHannover Korreferent: Martin Mundhenk, Friedrich-Schiller-Universitt Jena Tag der Promotion: 21.11.2007 iii Danksagung Vor kurzem, so scheint es, begann ich erst mein Studium und nun habe ich diese Arbeit fertiggestellt. In dieser Zeit haben mich viele Menschen auf diesem Weg begleitet und unterst¨utzt.Zuerst sind da meine Betreuer zu nennen: Heribert Vollmer, der mich angeleitet und ermutigt hat und mich auf einer Stelle getra- gen hat, die es eigentlich gar nicht gab, und Nadia Creignou, die unerm¨udlich Verbesserungsvorschl¨agef¨urdiese Arbeit geliefert und viele Formulare f¨urmich ausgef¨ullthat. Dann meine Kollegen Michael Bauland und Anca Vais, die durch ihre lebhafte Art immer wieder Schwung ins Institut bringt und mit der ich gerne ein B¨urogeteilt habe. Und alle meine Coautoren. Ganz besonders Erw¨ahnenm¨ochte ich meine Eltern Frauke und J¨urgenJo- hannsen, die mir die wissenschaftliche Ausbildung erm¨oglicht und mich dabei immer unterst¨utzthaben. Und nat¨urlich Henning, der so vieles f¨urmich ist: Freund, Kollege und mein Mann, und der alle H¨ohenund Tiefen in der Entste- hung dieser Arbeit mit mir durchlebt hat. Euch allen vielen Dank! Acknowledgement Not long ago, it seems, I started to study Mathematics and now I have com- pleted this thesis.
    [Show full text]
  • A Computational Learning Semantics for Inductive Empirical Knowledge
    A COMPUTATIONAL LEARNING SEMANTICS FOR INDUCTIVE EMPIRICAL KNOWLEDGE KEVIN T. KELLY Abstract. This paper presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent's belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within the semantics, such as inductive skepticism, the logic of discov- ery, Duhem's problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch's paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know in- ductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge|as opposed to mere, true belief|through a community of gullible pupils. Keywords: learning, inductive skepticism, deductive closure, knowability, epistemic logic, serendipity, inference, truth conduciveness, bounded rationality, common knowl- edge. 1. Introduction Science formulates general theories. Can such theories count as knowledge, or are they doomed to the status of mere theories, as the anti-scientific fringe perennially urges? The ancient argument for inductive skepticism urges the latter view: no finite sequence of observations can rule out the possibility of future surprises, so universal laws and theories are unknowable. A familiar strategy for responding to skeptical arguments is to rule out skeptical possi- bilities as \irrelevant" (Dretske 1981).
    [Show full text]
  • Another Problem with Deductive Closure
    Paul D. Thorn HHU Düsseldorf, DCLPS, DFG SPP 1516 High rational personal probability (0.5 < r < 1) is a necessary condition for rational belief. Degree of probability is not generally preserved when one aggregates propositions. 2 Leitgeb (2013, 2014) demonstrated the ‘formal possibility’ of relating rational personal probability to rational belief, in such a way that: (LT) having a rational personal probability of at least r (0.5 < r < 1) is a necessary condition for rational belief, and (DC) rational belief sets are closed under deductive consequences. In light of Leitgeb’s result, I here endeavor to illustrate another problem with deductive closure. 3 Discounting inappropriate applications of (LT) and some other extreme views, the combination of (LT) and (DC) leads to violations of a highly plausible principle concerning rational belief, which I’ll call the “relevant factors principle”. Since (LT) is obviously correct, we have good reason to think that rational belief sets are not closed under deductive consequences. Note that Leitgeb’s theory is not the primary or exclusive target of the argument. 4 The following factors are sufficient to determine whether a respective agent’s belief in a given proposition, , is rational: (I) the agent’s relevant evidence bearing on , (II) the process that generated the agent’s belief that , (III) the agent’s degree of doxastic cautiousness, as represented by a probability threshold, s, (IV) the features of the agent’s practical situation to which belief in are relevant, and (V) the evidential standards applicable to the agent’s belief that , deriving the social context in which the agent entertains .
    [Show full text]
  • A Logic-Based Artificial Intelligence Approach
    ON THE FORMAL MODELING OF GAMES OF LANGUAGE AND ADVERSARIAL ARGUMENTATION Dissertation presented at Uppsala University to be publicly examined in Hö 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, Friday, February 27, 2009 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Abstract Eriksson Lundström, J. S. Z. 2009. On the Formal Modeling of Games of Language and Adversarial Argumentation. A Logic-Based Artificial Intelligence Approach. 244 pp. Uppsala. ISBN 978-91-506-2055-9. Argumentation is a highly dynamical and dialectical process drawing on human cognition. Success- ful argumentation is ubiquitous to human interaction. Comprehensive formal modeling and analysis of argumentation presupposes a dynamical approach to the following phenomena: the deductive logic notion, the dialectical notion and the cognitive notion of justified belief. For each step of an argumentation these phenomena form networks of rules which determine the propositions to be allowed to make sense as admissible, acceptable, and accepted. We present a metalogic framework for a computational account of formal modeling and system- atical analysis of the dynamical, exhaustive and dialectical aspects of adversarial argumentation and dispute. Our approach addresses the mechanisms of admissibility, acceptability and acceptance of arguments in adversarial argumentation by use of metalogic representation, reflection, and Artifi- cial Intelligence-techniques for dynamical problem solving by exhaustive search. We elaborate on a common conceptual framework of board games and argumentation games for pursuing the alternatives facing the adversaries in the argumentation process conceived as a game. The analogy to chess is beneficial as it incorporates strategic and tactical operations just as argu- mentation.
    [Show full text]
  • Page 439 DEDUCTIVE CLOSURE and EPISTEMIC CONTEXT YVES
    “02bouchard” i i 2011/12/6 page 439 i i Logique & Analyse 216 (2011), 439–451 DEDUCTIVE CLOSURE AND EPISTEMIC CONTEXT YVES BOUCHARD Abstract I argue in favor of the principle of deductive closure. I provide a characterization of the notion of epistemic context in terms of pre- suppositions in order to show how one can preserve deductive clo- sure by limiting its applicability to a given epistemic context. This analysis provides also a redefinition of relevant alternatives from an epistemological point of view, that avoids any appeal to a counter- factual interpretation of relevance. In that perspective, relevance is conceived as a presuppositional quality. In regard to the debate with the skeptic, it is shown that her argument relies upon a context shift that compromises deductive closure because it alters the presuppo- sitions at play. Finally, deductive closure is not only vindicated but is acknowledged as a contextual marker in the sense that a failure of deductive closure indicates a context shift. Epistemic closure The general principle of epistemic closure stipulates that epistemic prop- erties are transmissible through logical means. The principle of deductive closure (DC) or epistemic closure under known entailment, a particular in- stance of epistemic closure, has received a good deal of attention since the last thirty years or so. DC states that: if one knows that p, and she knows that p entails q, then she knows that q. It is generally accepted that DC con- stitutes an important piece of the skeptical argument, but the acceptance of an unqualified version of DC is still a matter of debate.
    [Show full text]