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UC San Diego UC San Diego Electronic Theses and Dissertations UC San Diego UC San Diego Electronic Theses and Dissertations Title An actualist ontology for counterfactuals Permalink https://escholarship.org/uc/item/3z28m2v8 Author Peñafuerte, Araceli Sandil Publication Date 2008 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, SAN DIEGO An Actualist Ontology for Counterfactuals A Dissertation submitted in partial satisfaction of the Requirements for the degree Doctor of Philosophy in Philosophy by Araceli Sandil Peñafuerte Committee in charge: Professor Gila Sher, Chair Professor Samual Buss Professor Patricia Churchland Professor Philip Kitcher Professor Alfred Manaster 2008 SIGNATURE PAGE The Dissertation of Araceli Sandil Peñafuerte is approved, and it is acceptable in quality and form for publication on microfilm: Chair University of California, San Diego 2008 iii TABLE OF CONTENTS SIGNATURE PAGE .........................................................................................................iii TABLE OF CONTENTS................................................................................................... iv VITA…….......................................................................................................................... vi ABSTRACT OF THE DISSERTATION ......................................................................... vii CHAPTER ONE INTRODUCTION: THEORETICAL VIRTUES ................................. 1 1 The Ontological Question Reformulated............................................................ 1 2 Ontological Commitments in Mathematics and Modal Theories ....................... 6 CHAPTER TWO COUNTERFACTUALS AND POSSIBLE WORLDS....................... 11 1 Kinds of Conditional Statements ...................................................................... 12 2 Early Analysis of Counterfactuals .................................................................... 20 3 Propositional Modal Logic ............................................................................... 36 4 Semantics for Modal Systems........................................................................... 42 CHAPTER THREE REALISM VS. CONSTRUCTIVISM............................................ 52 1 Platonist Interpretation of Mathematics............................................................ 54 2 An Alternative to Platonism.............................................................................. 61 3 Problems with Platonism .................................................................................. 66 CHAPTER FOUR A REALIST VIEW OF POSSIBLE WORLDS ............................... 72 1 Counterpart Theory and an Indexical Notion of Actuality ............................... 74 2 Truth Conditions for Counterfactuals (Lewis).................................................. 79 3 Advantages of Lewis’ Theory........................................................................... 87 iv 4 Lewis’ Quantified Modal Logic........................................................................ 89 5 The Lack of Empirical Data.............................................................................. 95 CHAPTER FIVE NICHOLAS RESCHER: A CONSTRUCTIVIST VIEW................... 99 1 Mind-Dependent Existence of Possible Objects............................................... 99 2 Construction of Preferred Maximal Mutually Consistent Sets....................... 103 3 Kinds of Properties and Essentialism ............................................................. 108 4 Rescher’s Quantified Modal Logic................................................................. 115 5 Truth Condition for Counterfactuals (Rescher) .............................................. 124 CHAPTER SIX AN ONTOLOGY OF IDEAL CONSTRUCTIONS........................... 132 1 Theoretical Virtues of Realism ....................................................................... 132 2 Objections to Realism..................................................................................... 135 3 Objections to an Ontology of Idealized Operations?...................................... 142 4 The Choice between Rival Theories ............................................................... 151 BIBLIOGRAPHY........................................................................................................... 160 v VITA 1989 Bachelor of Arts, University of California, Irvine 1993 Master of Arts, University of California, San Diego 1993-1996 Lecturer, Cuyamaca College 1996-1997 Lecturer, Palomar College 1995-2000 Lecturer, University of California, San Diego 1996-2007 Lecturer, University of San Diego 1997-2008 Lecturer, San Diego State University 2008 Doctor of Philosophy, University of California, San Diego HONORS Special San Diego Fellowship, UC San Diego 1990-1994 Graduated Cum Laude, UC Irvine, 1989 Phi Beta Kappa Honor Society, 1988 Regents Scholar, UC Irvine, 1985-1989 Joy Industries Scholarship, 1985-1989 Humanities Honors Program 1988-1989 FIELDS OF STUDY AOS METAPHYSICS & EPISTEMOLOGY philosophy of possible worlds, the philosophy of language (counterfactuals), ontology, the philosophy of mathematics, analytic philosophy (Quine, Frege) AOC LOGIC (critical thinking, symbolic logic, modal logic, mathematical logic) ETHICS (biomedical, utilitarian, Kantian, existentialist) ASIAN PHILOSOPHY (Confucianism, Taoism, Zen Buddhism) vi ABSTRACT OF THE DISSERTATION An Actualist Ontology for Counterfactuals by Araceli Sandil Peñafuerte Doctor of Philosophy in Philosophy University of California, San Diego, 2008 Professor Gila Sher, Chair What theory along with its ontological commitments should we adopt? David Lewis and Nicholas Rescher offer competing theories for the interpretation of counterfactuals and modality involving statements. Using Quine’s criterion for theory selection, this paper will argue that, when one weighs the various merits and difficulties of vii these two theories, it appears that a constructivist theory like Nicholas Rescher’s offers a greater balance of theoretical advantages than does David Lewis’ realist view. I begin by surveying the early attempts made by logicians to understand counterfactuals and modal statements and then proceed with a similar inquiry into a mathematician’s efforts at interpreting mathematical statements. I try to show how similar ontological problems arise in the histories of both disciplines and how both disciplines first attempt to meet these difficulties by espousing a realist perspective, that of mathematical Platonism and David Lewis’ possibilism. I then argue that a host of problems may be avoided and a number of metaphysical questions may be answered if we adopt a constructivist approach to modal and mathematical statements. With respect to mathematical statements, Philip Kitcher offers a constructivist theory which interprets mathematical statements as referring to idealized constructions of an ideal mind rather than to abstract Platonic entities. This paper concludes that we should adopt Rescher’s actualist theory over David Lewis’ possibilism and shift our ontological commitments from possible worlds to ideal constructions. Accordingly, modal statements are true in virtue of the constructions which the mind is ideally able to perform upon the actual physical world. Among its theoretical virtues, Rescher’s theory explains the truth of counterfactuals in connection with ordinary experience, allows for the continued use of a uniform semantics for modal discourse, and avoids certain epistemological problems which rival theories face. viii CHAPTER ONE INTRODUCTION: THEORETICAL VIRTUES 1 The Ontological Question Reformulated What kinds of objects are there? It’s less problematic to be a realist about physical objects such as tables and chairs. Through our sense perception of the world, we have evidence that such macroscopic, material things exists. It is a more challenging task, however, to be a realist with respect to the kinds of objects our scientific, mathematical, and modal theories suppose. Is science right to assume the existence of unobserved entities such as quarks and electron-spins? Do numbers or sets actually exist as some mathematicians may presume? Along similar lines, we may also question our various modal theories and their ontological commitments to the existence of possible worlds. Ontological claims about the existence of abstract objects like numbers or possible worlds are neither directly verifiable nor falsifiable. We cannot simply check to see whether such objects really do exist. Nor can we gather physical evidence to prove the contrary. Notwithstanding, our theories, even our best scientific ones, may sometimes allow for the existence of unobservable objects. Scientists have proposed the existence of entities that cannot be directly seen nor detected and about which they know very little. For example, physicists consider whether their theories should include quarks. Our best theories of the proton and neutron, they argue, indicate that there are three particles inside every proton and neutron. Although these particles cannot be observed, their existence accords with the evidence we do have and reference to ‘quarks’ would help to explain 1 2 various other phenomena. It has been argued that an object’s explanatory power is reason enough to suppose that such an object exists. Scientific explanation also makes use of ideal models that offer a more simplified and orderly system of the world than may actually exist. Newton recognized the operations
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