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Thesis Front Matter UNIVERSITY OF CALGARY FIGURE AND GROUND: CONSIDERATIONS ON THE METAPHYSICS AND LOGICS OF TIME by JAMES ROY SCOTT A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS DEPARTMENT OF PHILOSOPHY CALGARY, ALBERTA AUGUST, 2010 © JAMES ROY SCOTT 2010 Library and Archives Bibliothèque et Canada Archives Canada Published Heritage Direction du Branch Patrimoine de l’édition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre référence ISBN: 978-0-494-69610-1 Our file Notre référence ISBN: 978-0-494-69610-1 NOTICE: AVIS: The author has granted a non- L’auteur a accordé une licence non exclusive exclusive license allowing Library and permettant à la Bibliothèque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par télécommunication ou par l’Internet, prêter, telecommunication or on the Internet, distribuer et vendre des thèses partout dans le loan, distribute and sell theses monde, à des fins commerciales ou autres, sur worldwide, for commercial or non- support microforme, papier, électronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L’auteur conserve la propriété du droit d’auteur ownership and moral rights in this et des droits moraux qui protège cette thèse. Ni thesis. Neither the thesis nor la thèse ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent être imprimés ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author’s permission. In compliance with the Canadian Conformément à la loi canadienne sur la Privacy Act some supporting forms protection de la vie privée, quelques may have been removed from this formulaires secondaires ont été enlevés de thesis. cette thèse. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n’y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. UNIVERSITY OF CALGARY FACULTY OF GRADUATE STUDIES The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies for acceptance, a thesis entitled "FIGURE AND GROUND: CONSIDERATIONS ON THE METAPHYSICS AND LOGICS OF TIME" submitted by JAMES ROY SCOTT in partial fulfilment of the requirements of the degree of MASTER OF ARTS. Supervisor, Dr. Nicole Wyatt, Department of Philosophy Dr. J. J. MacIntosh, Department of Philosophy External Examiner, Dr. Bernard Linsky, Department of Philosophy, University of Alberta Date ii Abstract The thesis provides a survey and analysis of three-dimensional and four- dimensional theories of time. These theories are considered both from the perspective of experienced time and of physical time. It is argued that experienced time is tensed and finite. It is further argued that physical time can be modeled by various theories, and that the choice of temporal theory is largely determined by the basic tenets of a particular theory of the external world. Arthur Prior‟s tense logic and U-calculus are presented, and it is shown that tense logic models tensed time, while the U-calculus models tenseless time. Further, it is seen that the U-calculus can be reduced to tense logic. Following the development of a general hybrid modal logic, a temporal hybrid modal logic is presented which is shown to modal both tensed and tenseless time. iii Acknowledgements I would like to begin by acknowledging the contribution to my work of the University of Calgary Department of Philosophy faculty and staff. My work in philosophy occurred in two separate periods; one in the early 1990s and the second from 2007 until the present. During both these periods I benefited greatly from the willingness of members of the faculty to share so generously their expertise, passion for philosophy, and time. In particular, I would like to acknowledge the contributions of the following to my work: Brian Chellas, Brian Grant, Ish Haji, Ali Kazmi, Jack MacIntosh, Nicole Wyatt, and Richard Zach. I am especially grateful to Brian Chellas for his willingness nearly twenty years ago to serve as my advisor and to Nicole Wyatt who so cheerfully and ably provided me with the structure and guidance that I needed to complete this project. I always left her office with fresh ideas and reduced confusion. I would, additionally, like to express my appreciation to Bernard Linsky from the University of Alberta, Jack MacIntosh, and Nicole Wyatt for providing me with such helpful feedback in their role as examiners. I have enjoyed the practical and personal support of my family through both stages of my study of philosophy. My parents, Laura and Jim Scott, have supported me unconditionally through this, as in all my adventures. My wife, Sandra Scott, has been enormously supportive while I have worked on this project. She has endured being a “philosophy widow” with grace and good humour. I am very fortunate to have the support of my family in all I do. iv Finally, I would like to acknowledge the support of the Calgary Board of Education through the Professional Improvement Fellowship they provided during my Education Leave during the 2009 – 2010 school year. Without this generous support I would have been unable to complete this work. v Dedication This thesis is dedicated to Sandra and the Hobo for their unconditional support and companionship through this entire project. vi Table of Contents Approval Page ..................................................................................................................... ii Abstract .............................................................................................................................. iii Acknowledgements ............................................................................................................ iv Dedication .......................................................................................................................... vi Table of Contents .............................................................................................................. vii List of Figures and Illustrations ...........................................................................................x CHAPTER ONE: INTRODUCTION ..................................................................................1 CHAPTER TWO: THREE-DIMENSIONAL THEORIES OF TIME ................................6 2.1 McTaggart‟s Basic Metaphysics of Time ..................................................................7 2.1.1 Ontology and the C-Series .................................................................................7 2.1.2 The Temporal Relations ....................................................................................8 2.1.3 The Series ........................................................................................................10 2.2 The Unreality of Time .............................................................................................15 2.2.1 McTaggart‟s Argument ...................................................................................15 2.2.1.1 Premiss One: Change If and Only If the A-Series .................................16 2.2.1.2 Premiss Two: The A-Series Leads to a Contradiction ...........................18 2.2.2 Response to McTaggart‟s Argument ...............................................................20 2.2.2.1 The A-Theorists: Addressing Premiss Two ...........................................20 2.2.2.2 The B-Theorists: Addressing Premiss One ............................................29 2.2.3 The Unreality of Time: Summary of Responses to McTaggart‟s Argument ..48 2.3 Concluding Comments on Three-Dimensionalism ..................................................50 CHAPTER THREE: FOUR DIMENSIONALISM ...........................................................52 3.1 The Four-Dimensional View Overview ..................................................................52 3.2 Mereology ................................................................................................................54 3.2.1 Temporal Parts .................................................................................................54 3.2.2 Instantaneous Temporal Parts ..........................................................................56 3.2.3 Ersatz Temporal Parts ......................................................................................57 3.3 Special Relativity and Geometric Representations of Four-Dimensional Space- Time .......................................................................................................................58 3.3.1 Galilean Relativity ...........................................................................................58 3.3.2 Special Relativity .............................................................................................59 3.3.3 Temporal Parts and Special Relativity ............................................................67 3.4 Temporal Parts in Action .........................................................................................70 3.4.1 The Ship of Theseus ........................................................................................70 3.4.2 Temporary Coincidence ..................................................................................71
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