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Naturalness, Intrinsicality, and Duplication

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Naturalness, Intrinsicality, and Duplication Naturalness, Intrinsicality, and Duplication Theodore Sider Ph.D. thesis, University of Massachusetts. Committee: Phillip Bricker (chair), Fred Feldman, Edmund Gettier, Angelika Kratzer May 1993 Acknowledgments I would like to thank various people for their verbal and written comments on earlier stages of this dissertation. Of course, none of these people are re- sponsible for the views I express. I am indebted to Mark Aronszajn, Lynne Baker, David Braun, Earl Conee, David Cowles, Max Cresswell, David Den- by, Fred Feldman, Richard Feldman, Edmund Gettier, Larry Holm, Ned Markosian, Deborah Modrak, and R. Cranston Paull. I am especially indebted to my dissertation director, Phillip Bricker. He consistently gave me excellent comments and helped me to see more mistakes than I care to remember. For whatever there is of value in this dissertation, he deserves much of the credit. i Abstract This dissertation explores the concepts of naturalness, intrinsicality, and du- plication. An intrinsic property is had by an object purely in virtue of the way that object is considered in itself. Duplicate objects are exactly similar, considered as they are in themselves. The perfectly natural properties are the most fundamental properties of the world, upon which the nature of the world depends. In this dissertation I develop a theory of intrinsicality, naturalness, and duplication and explore their philosophical applications. Chapter 1 intro- duces the notions, gives a preliminary survey of some proposed conceptual connections between the notions, and sketches some of their proposed ap- plications. Chapter 2 gives my background assumptions and introduces no- tational conventions. In chapter 3 I present a theory of naturalness. Although I take ‘natural’ as a primitive, I clarify this notion by distinguishing and explicating various conceptions of naturalness. In chapter 4 I give a theory of various notions related to naturalness, es- pecially intrinsicality and duplication. I show that ‘intrinsic’ and ‘duplicate’ are interde nable, and then give analyses of these and other notions in terms of naturalness. If, as I think likely, naturalness cannot be analyzed, then what is the proper response? David Lewis suggests: accept naturalness as a primitive. I am sympathetic to this proposal, but not to the form Lewis gives it: chapter 5 contains an argument against Lewis’s theory of naturalness. In chapter 6 I reject the idea that naturalness is analyzable in terms of immanent universals. I focus on the work of D. M. Armstrong. I also criticize Armstrong’s arguments against transcendent universals. In chapter 7 I address criticisms of David Lewis’s de nition of ‘intrinsic’ offered by Mike Dunn. ii ABSTRACT iii In chapter 8 I discuss the possibility of analyzing our three notions. I discuss de ning ‘natural’ in terms of supervenience and other concepts, and then criticize attempts by Jaegwon Kim and Michael Slote to analyze intrin- sicality in terms of “quasi-logical” concepts. Finally, in chapter 9 I present a new application for the notion of natu- ralness: the statement of “metrical realism” in the philosophy of space and time. Contents Acknowledgments i Abstract ii 1 Introducing Three Notions 1 1.1 Intrinsicality and Duplication . 1 1.2 Naturalness . 8 1.3 The Structure of the Dissertation . 11 2 Preliminaries 14 2.1 Metaphysical Assumptions . 14 2.2 Language . 21 3 Conceptions of Naturalness 23 3.1 Introduction . 23 3.2 Conception 1 . 25 3.2.1 Supervenience, Microphysicality, and Property “Com- binations” . 25 3.2.2 A Complication . 38 3.2.3 Relative Naturalness According to Conception 1 . 40 3.3 Conception 2 . 49 3.3.1 Perfect Naturalness . 49 3.3.2 Relative Naturalness According to Conception 2 . 52 3.4 Choosing a Conception of Naturalness . 54 3.5 Conclusion . 59 4 Intrinsicality, Duplication, and other Notions 61 4.1 Intrinsicality and Duplication Are “Interde nable” . 61 iv CONTENTS v 4.2 Duplication and Beyond . 65 4.2.1 Duplication . 66 4.2.2 Other Concepts . 71 4.2.3 Consequences of the de nitions . 73 5 Naturalness and Arbitrariness 77 5.1 Primitive Class Naturalism . 77 5.2 Against Primitive Class Naturalism . 79 5.2.1 Pairs and Relations . 79 5.2.2 Benacceraf’s Argument . 80 5.2.3 An Argument against Primitive Class Naturalism . 82 5.2.4 Response 1: “The Argument Proves Too Much” . 92 5.2.5 Response 2: Primitive Ordered Pairs . 94 5.3 Naturalness and “Kripkenstein” . 96 6 Properties, Universals, and Naturalness 99 6.1 Sparseness vs. Abundance; Immanence vs. Transcendence . 99 6.2 Universals and Naturalness . 106 6.3 Armstrong’s Objections to Transcendent Universals . 110 6.3.1 Two Theories of Abundant Universals . 110 6.3.2 Armstrong’s Arguments against Transcendent Univer- sals . 112 6.4 Conclusion . 128 7 Dunn on Intrinsicality 129 7.1 Dunn’s Criticisms of Lewis . 129 7.1.1 Dunn’s Formulation of Lewis’s View . 129 7.1.2 Dunn’s First Objection . 133 7.1.3 Dunn’s Second Objection . 134 7.2 Dunn’s Theory of Intrinsicality . 138 7.3 Two Conceptions of Intrinsicality . 140 8 Analysis of the Notions 144 8.1 Can We De ne ‘Natural’? . 144 8.2 Can We De ne ‘Intrinsic? . 147 8.2.1 Preliminaries . 148 8.2.2 Kim’s De nition . 149 8.2.3 Slote’s Project . 150 CONTENTS vi 8.2.4 Slote’s Analysis of Alteration . 150 8.2.5 Slote’s Analysis of Alikeness . 156 9 Naturalness and Metrical Realism 168 9.1 Preliminaries . 168 9.2 Metrical Realism . 170 9.2.1 Introduction to Metrical Realism . 170 9.2.2 Physical Distance Functions . 171 9.2.3 The Proposal Generalized . 173 9.2.4 The Proposal Re ned . 175 9.3 The Problem of Extra Relations . 178 9.4 Contingency of the Metric . 180 9.4.1 An Argument . 180 9.4.2 Rejecting Premise (1)—Relation splitting . 181 9.4.3 Rejecting Premise (2) . 184 List of Figures 4.1 Endlessly conjunctive properties . 69 6.1 Particulars: TU vs. IU . 104 vii Chapter 1 Introducing Three Notions 1.1 Intrinsicality and Duplication Today my brother got a haircut. Yesterday Mike had the property having long hair; today he does not. By losing this property my brother changed. When my only brother got his much-needed haircut, I too lost a property: the property having a long-haired brother. But when the haircut occurred, I did not change. Mike’s haircut changed Mike, not me, despite the fact that we each thereby lost properties we formerly had (and gained new ones as well). This is because the property Mike lost, having long hair, is an intrinsic property, whereas the property I lost, having a long-haired brother, is not. Consider the property having long hair. When someone has this property, he has it in virtue of the way he is in himself. In contrast, when a person has the property having a long-haired brother, he does not have this purely in virtue of the way he is himself; he has this property partly in virtue of the way someone else is (namely, his brother) and partly in virtue of the relations he bears to that someone else (namely, the being the only brother of relation). When an object x has an intrinsic property, then, this is in virtue of the way x is, and not a matter of the ways other objects are, nor of the way x stands with respect to other objects. Intrinsic properties are “non-relational” and “purely qualitative”. If an object has an intrinsic property, then so must any “perfect duplicate” of that object. In contrast, extrinsic (non-intrinsic) properties may differ between perfect duplicates. Marble A may be a perfect duplicate of marble B despite the fact that A has, while B lacks, the property being ten feet from Ted. Shapes, sizes, masses—these are intrinsic properties. 1 CHAPTER 1. INTRODUCING THREE NOTIONS 2 Locations, speeds, ownerships (e.g. being owned by Ted)—these are extrinsic properties. I hope that the preceding paragraph has helped you grasp the notion of an intrinsic property, if you were not already familiar with that notion. But I suspect that you distrust the value of what I have said as an analysis of the notion, on grounds of circularity. You may ask me to explain the locutions I used in that paragraph: ‘duplicate’, and ‘had in virtue of the way an object is in itself’, for example. What is the “way an object is in itself”, if not the conjunction of its intrinsic properties? What is it for two objects to be “duplicates”, if not for them to have exactly the same intrinsic properties? Let us focus a little more closely on the notion of duplication, and its re- lation to intrinsicality. Objects that are perfect duplicates are exactly similar, down to the last detail of the smallest part. It is likely that there are no actual pairs of macroscopic duplicates. Even two marbles made by the best manu- facturing techniques are bound to differ slightly—a stray atom here or there. The differences may not be perceptible, but if they are there then the marbles cannot be duplicates, for duplicates may not have any (intrinsic) differences whatsoever. Of course, no pair of objects, even a pair of perfect duplicates, will share all properties. For consider any two objects a and b—only a will have the property being a. Although it is likely that there are no two actual macroscopic duplicates, it may be that there are pairs of actual microscopic duplicates: perhaps pairs of duplicate electrons. And surely every object, microscopic or macroscopic, has a duplicate in some other possible world.1 One reason for the importance of the concept of duplication is that ‘in- trinsic’ may be de ned in terms of ‘duplicate’, as David Lewis has proposed:2 (D1) Property P is intrinsic iff for any possible individuals x and y, if x and y are duplicates then x has P iff y has P In fact, the direction of de nition can be reversed: ‘duplicate’ is de nable in terms of ‘intrinsic’: (D2) Possible individuals x and y are duplicates iff for any intrinsic property P, x has P iff y has P 1 I ignore sets, numbers, and the like.
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