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Belief Dynamics ILLC Dissertation Series 2001-08 Belief Dynamics ILLC Dissertation Series 2001-08 For further information about ILLC-publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam phone: +31-20-525 6051 fax: +31-20-525 5206 e-mail: [email protected] homepage: http://www.illc.uva.nl/ Belief Dynamics (Epistemo)logical Investigations Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magni¯cus prof. dr. J.J.M. Franse ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op dinsdag 13 november 2001, te 10.00 uur door Allard Martijn Tamminga geboren te Nijmegen Promotor: Prof. dr. F.J.M.M. Veltman Co-promotor: Prof. dr. H. Rott Afdeling Wijsbegeerte Faculteit der Geesteswetenschappen Universiteit van Amsterdam Nieuwe Doelenstraat 15 1012 CP Amsterdam Copyright °c 2001 by Allard Tamminga Cover design by [lowresmedia.com] Cover photos by Roesmann/Essamba Arts Printed and bound by Febodruk, Enschede ISBN: 90{5776{075{4 Notre t^ete est ronde pour permettre `a la pens¶ee de changer de direction. Francis Picabia v Contents Acknowledgments ix 1 Introduction 1 1.1 General Overview . 1 1.2 Summary . 2 2 Truth as Limit of Inquiry? 7 2.1 Introduction . 7 2.2 C.S. Peirce's Theory of Scienti¯c Inquiry . 10 2.2.1 Analytic and Synthetic Reasoning . 13 2.2.2 Deduction, Induction, and Abduction . 15 2.3 Truth in Terms of Inquiry . 19 2.3.1 The T{I Conditional versus Bivalence . 21 2.3.2 The I{T Conditional is Wide of the Mark . 24 2.4 Conclusion . 28 3 Isaac Levi's Epistemology: A Critique 29 3.1 Isaac Levi's Epistemology . 29 3.1.1 Non-Deductive Logic and the Belief-Doubt-Belief Model . 29 3.1.2 Epistemic States and Their Representations . 33 3.1.3 Revision of Corpora . 38 3.1.4 Two Applications . 47 3.2 A Critique . 50 3.2.1 Corpora? . 50 3.2.2 Contextual Parameters? . 51 3.3 Conclusion . 58 vii 4 Finite State Belief Dynamics 61 4.1 Paraconsistent Belief Revision? . 62 4.1.1 A Novel Approach . 63 4.2 Preliminaries . 64 4.2.1 An Algorithm for Finding Á's Minimal Valuations . 67 4.2.2 Finite States and Their Determiners . 69 4.2.3 Finite States: Information Span . 72 4.3 Operations of Information Change . 74 4.3.1 Expansion . 74 4.3.2 Contraction . 77 4.3.3 Revision . 80 4.4 Extractors: Operations of Belief Retrieval . 81 4.4.1 Making K? Consistent . 82 4.4.2 Selecting K?'s Most Consistent Valuations . 86 4.5 Future Work . 88 4.5.1 Finite State Belief Revision . 88 4.5.2 Relative Trustworthiness of the Sources . 89 4.5.3 Inconsistency-Adaptive Logics . 90 5 Conclusion 91 5.1 Summary of the Results . 91 5.2 Future Work . 92 A A Natural Deduction System for First Degree Entailment 95 A.1 Introduction . 95 A.1.1 First Degree Entailment . 95 A.1.2 Combined Systems . 96 A.2 Language and Semantics . 98 A.3 A Natural Deduction System . 99 A.4 Soundness . 101 A.5 Completeness . 102 A.6 Rejection Eliminated? . 107 Bibliography 111 Samenvatting 119 viii Acknowledgments First and foremost, thanks are due to my promotor, Frank Veltman, and to my co-promotor, Hans Rott. I thank them for the freedom of research they granted me, for their continuing encouragement, and for their constructive criticisms. Second, I wish to thank Johan van Benthem, Wiebe van der Hoek, Erik Krabbe, Michiel van Lambalgen, and Martin Stokhof, for their willingness to participate in the reading committee. Third, I thank Koji Tanaka for being the co-author of the Appendix. More- over, I thank Walter van der Star for translating the second and third chapters of my dissertation into English. Lastly, the following people discussed parts of the thesis with me and thus helped me to improve on the ¯nal text: Paul Dekker, Eduardo Ferm¶e, Jelle Gerbrandy, Carin Gotlieb, Paul Harrenstein, Wolfram Hinzen, Else de Jonge, Theo Kuipers, Karen Kwast, Rosja Mastop, Breannd¶an O¶ Nuall¶ain, Jeanne Pei- jnenburg, Graham Priest, Harry Stein, Anne Troelstra, and Sjoerd Zwart. The conversations with them has made the writing of this thesis an enjoyment. Parts of my thesis have been published as articles in journals. I would like to thank the journals for their kind permission to include these articles in the present thesis. Chapter 2 appeared in Dutch as `Waarheid als limiet van on- derzoek: de ontoereikendheid van Charles Sanders Peirce' waarheidsopvatting' in the Algemeen Nederlands Tijdschrift voor Wijsbegeerte 93, 2001, pages 73{92. The Appendix, the result of joint work with Koji Tanaka, appeared in 2001 as `A Natural Deduction System for First Degree Entailment' in the Notre Dame Journal of Formal Logic 40, 1999, pages 258{272. Amsterdam amt September, 2001. ix Chapter 1 Introduction 1.1 General Overview This thesis deals with the dynamics of belief. In three interconnected, though independent studies, a viable alternative to foundational approaches in episte- mology is explored. Rather than accept the research agenda dictated by tradi- tional epistemology, with its stress on the pursuit of conditions under which our beliefs are justi¯ed or even true, the present work follows the lead of American pragmatism, and focusses on the articulation and defense of criteria according to which a change of mind may be judged legitimate. The second and third chapters discuss the attempts of two pragmatist philoso- phers, Charles Sanders Peirce and Isaac Levi, to formulate and to formalize the belief-doubt-belief model, a model that sets out to set forth systematically the optimal strategies according to which to change our minds. In the course of this undertaking, more and more logical considerations come to the fore, culminating in a discussion and an evaluation of formal systems for belief change. It is argued that belief change systems, despite the naturalistic setting in which they were ¯rst conceived, have outgrown their pragmatist origin and have metamorphosed into a branch of philosophical logic, where empirical considerations have become obsolete. To restore the connection between logical theory and epistemological practice, a case is made for reformulations of belief change systems that are cleared from elements that obstruct practical applications and empirical tests. In the fourth chapter, a belief change system is presented that (1) uses ¯nite representations of epistemic states, (2) can deal with inconsistencies adequately, (3) has ¯nite operations of change, (4) can do without, but does not rule out, extra-logical elements, and (5) only licenses consistent beliefs. An Appendix, where the underlying logic of the belief change system of the fourth chapter is studied proof-theoretically, concludes the thesis. 1 2 Chapter 1. Introduction 1.2 Summary In order to pave the way for more fruitful logical and epistemological investiga- tions within the pragmatist tradition in philosophy, the second chapter clears the ground from metaphysical entanglements that result from the wish to construct theories of truth and reality, a wish that has, by and large, dominated the in- terests of pragmatist philosophers (and not only them) until the present day. A focus on the necessary and su±cient conditions for a statement to be true or on a conception of reality which is adequate to a preferred reading of the truth predicate still obfuscate research in contemporary epistemology, as they tend to restrict philosophical research to questions which have resisted plausible answers for ages. Hence, the second chapter purports to show that Peirce's metaphysical aspi- rations for de¯nitions of truth and reality in terms of a theory of inquiry cannot coherently be met by a pragmatist theory of knowledge. In order to come to grips with Peirce's de¯nition of truth as the ideal limit of inquiry, a succinct exposition of Peirce's theory of inquiry and his philosophical logic is given. Attention is paid to deductive, inductive, and abductive reasoning and their interrelations, so as to be in a position to sketch Peirce's early ideas concerning the pragmatist belief- doubt-belief model, a model that will be the guiding line of this thesis. With his investigations into that model, Peirce aimed to articulate the `method of science', a method that enables us to adapt our present pattern of expectations for the better in case of surprising or even contrary experience. Peirce maintained that if we would consciously follow the method of science, we would ultimately reach a pattern of expectations that would never be thwarted by any future experience. Since such a pattern of expectations would lead to the very same practical con- sequences as a true `theory of the world', to borrow a phrase of Quine's, Peirce's pragmatist stand on meaning forbids him to withhold the predicate `true' from that pattern of expectations. Thus Peirce accounts for the notion of truth. In the remainder of the second chapter, the arguments of the foremost rep- resentative of a group of contemporary apologists of Peirce's account of truth, Cheryl Misak, are subjected to scrutiny and found to be insu±cient: the princi- ple of bivalence is defended improperly and her main argumentation for a Peircean account of truth turns out to be incompatible with a pragmatist epistemology. Hence, Peircean accounts of truth are found to be inadequate. Rather than accept the problem setting of traditional philosophy, with its focus on truth and reality, and plead, in the face of the failure of Peircean accounts of truth, for some alter- native view on truth, the chapter ends with a plea for a more modest approach.
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