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The World Is Not Enough: an Enquiry Into Realism About Modality

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The World Is Not Enough: an Enquiry Into Realism About Modality THE WORLD IS NOT ENOUGH: AN ENQUIRY INTO REALISM ABOUT MODALITY A thesis submitted to Kent State University in partial fulfillment of the requirements for the degree of Master of Arts By Ryan J. Comeau August, 2013 Thesis written by Ryan J. Comeau B.A., Grand Valley State University, 2011 M.A., Kent State University, 2013 Approved by Deborah C. Smith _________________________________, Advisor David Odell-Scott _________________________________, Chair, Department of Philosophy James L. Blank ___________________________________, Dean, College of Arts and Sciences ii TABLE OF CONTENTS ACKNOWLEDGMENTS ...............................................................................................................v CHAPTER 1. INTRODUCTION .......................................................................................................................1 1.1 Modality .........................................................................................................................1 1.2 Kripkean semantics and the accessibility relation .........................................................4 1.3 The de re/de dicto distinction ........................................................................................6 1.4 The distinction between actualist and possibilist quantification ....................................7 1.5 Scope of the thesis .........................................................................................................8 2. LEWIS’ MODAL REALISM ....................................................................................................11 2.1 Introduction ..................................................................................................................11 2.2 What are possible worlds? ...........................................................................................11 2.3 Motivation for Lewis’ view .........................................................................................18 2.4 Ersatzism ......................................................................................................................23 2.5 Extreme Realism ..........................................................................................................26 2.6 Conclusion ...................................................................................................................27 3. STALNAKER’S MODAL REALISM ......................................................................................28 3.1 Introduction ..................................................................................................................28 3.2 Stalnaker’s account of possible worlds ........................................................................28 3.3 Merely possible objects ................................................................................................32 3.4 Stalnaker’s semantic model .........................................................................................38 iii 3.5 Moderate Realism ........................................................................................................40 3.6 Summary ......................................................................................................................43 4. A PROPOSAL CONCERNING REALISM ABOUT MODALITY ........................................44 4.1 Introduction ..................................................................................................................44 4.2 Need possible worlds be concrete? ..............................................................................45 4.3 Mind-independence ......................................................................................................50 4.4 Possible worlds as representations ...............................................................................53 4.5 Is Stalnaker a realist? ...................................................................................................54 4.6 Conclusions ..................................................................................................................58 BIBLIOGRAPHY ..........................................................................................................................60 iv ACKNOWLEDGEMENTS First and foremost, I would like to thank my advisor, Dr. Deborah Smith. The time she has spent commenting on drafts and discussing material with me had to amount to about as much time as I spent writing this thesis. Without her patience and help, I would not have finished this project. Secondly, I would like to thank my readers, Dr. Gina Zavota, Dr. Thomas Norton-Smith, and Dr. Donald White for agreeing to read and try to figure out what it might be that I am actually trying to say. I would also like to thank the philosophy department, specifically Dr. Michael Byron and Dr. David Odell- Scott at Kent State University for all of the opportunities and experiences that they have given me. Finally, I would not be where I am today if it was not for my parents. They have always supported me in whatever path I choose to follow, and for that I cannot thank them enough. v CHAPTER 1 INTRODUCTION This thesis involves the topic of modal metaphysics, and so deals with theories of possible worlds. There are many questions that one could ask about the nature of possible worlds and the possible objects they contain. However, the focus in my thesis will be on the question of what constitutes realism about modality. Generally speaking, modal realism entails the idea that possible worlds are real entities. It is common for an area of metaphysics to develop independently and for a system of logic appropriate to that area of metaphysics to arise afterword in response to the metaphysics. However, modal metaphysics developed in the latter half of the 20th century in response to Kripke’s semantics for modal logic. It was the role of possible worlds in Kripkean semantics that led philosophers to inquire about the nature of possible worlds. I will begin this introductory chapter with a brief discussion of modalality and Kripke’s semantics for modal logic. 1.1 Modality To understand the theories presented later in this thesis, we must first distinguish modal statements from non-modal statements. Consider the following statements: (1) The sky is blue (2) Ryan Comeau was born on 04/10/1988 1 2 (3) 2+2=4 (4) Ryan Comeau was born on 04/11/1988. (5) The sky is purple. The above statements all have truth-values that are determined by the way things actually are. In this case (1), (2), and (3) are true while (4) and (5) are false. But consider the following sentences: (6) The sky could have been red (i.e. it is possible for the sky to have been red). (7) Ryan Comeau could have been born on 04/11/1988. (8) Necessarily, 2+2=4. (9) Necessarily, nothing can be a square and a circle at the same time. (6)-(9) are modal claims. These are statements about what is possible or necessarily so. Notice that we must provide truth conditions for such statements in a different manner than we do for non-modal statements. With non-modal statements the statement is true or false in virtue of the way the world actually is. However, in the case of non-modal statements, nothing occurring in the actual world is sufficient to determine their truth- values. The first account developed to analyze modal statements is usually attributed to Gottfried Leibniz. His account of modal statements allows us to treat modal terms (e.g. ‘possibly’, ‘necessarily’, etc.) as quantifiers that range over what he called possible worlds. What actually is the case is what goes on here, in this world. This is one way for a world to be. Other worlds are other possibilities. Every way that a world could possibly 3 be is a way that some world is. Consequently, whenever x might be the case, there is a world where x is the case. Thus, modality can be conceived as quantification over possible worlds. The following two truth conditions stem from this idea: (a) ‘Necessarily P’ is true iff ‘P’ is true in all possible worlds. (b) ‘Possibly P’ is true iff ‘P’ is true in some (at least one) possible world. Generally speaking, modal logic works with two modal operators: the possibility operator ‘◊’ and the necessity operator ‘□’. Both attach to sentences to make sentences, or attach to open formulas to make open formulas. For example, we might write ‘◊ for some x, x is a swan and x is blue’ to mean that possibly some swan is blue. Or we might write ‘□ for all x, if x is a swan then x is a bird’ to mean necessarily all swans are birds. Further, the operator ‘◊’ can be defined from ‘□’ by letting ◊P = ~□~P and the operator ‘□’ can be defined from ‘◊’ by letting □P = ~◊~P. Modal logic is the logic of modal operators. In modal logic, the notion of a truth-value differs from that of the notion of a truth-value in other logics. There are world relative assessments of the truth-value of a sentence on modal logic. The idea is that ‘the grass is green’ is no longer simply true or false. It is true at world w (a world in which grass is green) and false at w* (a world in which grass is red). Similarly, the set of things that exist will vary from world to world (we need world relative domains), and the set of things that are, e.g., blue will vary from world to world (the extensions of predicates will be world relative). Although Leibniz did not present a formal semantics, we can present the sort of formal semantics for 4 Leibnizian modal logic. 1 This formulization involves a set of worlds, world relative domains, world relative
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