DOCSLIB.ORG

Philosophical Reflections on Modern Quantum Gravity Research

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Philosophical Reflections on Modern Quantum Gravity Research Stringed along or caught in a loop? Stringed along or caught in a loop? Philosophical reflections on modern quantum gravity research Keizo Matsubara Dissertation presented at Uppsala University to be publicly examined in Geijersalen, Building 6, (Eng 6-1023), English Park Campus, Thunbergsvägen 3P, Uppsala, Friday, January 18, 2013 at 10:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Abstract Matsubara, K. 2013. Stringed along or caught in a loop?: Philosophical reflections on modern quantum gravity research. Filosofiska Institutionen. 139 pp. Uppsala. ISBN 978-91-506-2324-6. A number of philosophical questions, all connected to modern research in quantum gravity, are discussed in this dissertation. The goal of research in quantum gravity is to find a quantum theory for gravitation; the ot- her fundamental forces are already understood in terms of quantum physics. Quantum gravity is studied within a number of different research programmes. The most popular are string theory and loop quantum gravity; besides these a number of other approaches are pursued. Due to the lack of empirical support, it is relevant to assess the scientific status of this rese- arch. This is done from four different points of view, namely the ones held by: logical positi- vists, Popper, Kuhn and Lakatos. It is then argued that research in quantum gravity may be considered scientific, conditional on scientists being open with the tentative and speculative nature of their pursuits. Given the lack of empirical progress, in all approaches to quantum gravity, a pluralistic strategy is advised. In string theory there are different theoretical formulations, or dualities, which are physi- cally equivalent. This is relevant for the problem of underdetermination of theories by data, and the debate on scientific realism. Different views on the dualities are possible. It is argued that a more empiricist view on the semantics of theories, than what has been popular lately, ought to be adopted. This is of importance for our understanding of what the theories tell us about space and time. In physics and philosophy, the idea that there are worlds or universes other than our own, has appeared in different contexts. It is discussed how we should understand these different suggestions; how they are similar and how they are different. A discussion on, how and when theoretical multiverse scenarios can be empirically testable, is also given. The reliability of thought experiments in physics in general and in quantum gravity in par- ticular is evaluated. Thought experiments can be important for heuristic purposes, but in the case of quantum gravity, conclusions based on thoght experiments are not very reliable. Keywords: quantum gravity, string theory, loop quantum gravity, philosophy of physics, philosophy of science, scientific realism, structural realism, multiverse, thought experiments Keizo Matsubara, Uppsala University, Department of Philosophy, Logic and Metaphysics, Box 627, SE-751 26 Uppsala, Sweden. © Keizo Matsubara 2013 ISBN 978-91-506-2324-6 urn:nbn:se:uu:diva-185554 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-185554) Printed by Elanders Sverige AB, 2012 Dedicated to my parents, Akira and Carine Acknowledgements First of all I would like to thank Lars-Göran Johansson, my advisor and collab- orator. He has been very helpful and inspiring during the years we have been working together. Riksbankens Jubileumsfond funded the project, in which we started our joint work on philosophical issues regarding string theory. I am very grateful for the financial support they provided. In this project, I was hired as a researcher in my role as a theoretical physicist, since I already had a Ph.D. in theoretical physics. Shortly after being hired to work on this project, I finished my MA in philosophy. It was then decided that I was also going to be hired as a Ph.D.-student in philosophy, with the intention of using my work in the project as part of my dissertation. Lars-Göran supported this decision and for this I am very happy. When the project, financed by Riksbankens Jubileumsfond, was finished I went to the University of Toronto. This was made possible due to a gener- ous stipend which was given to me by The Sweden-America Foundation and donated by Borgrättsfonderna. I had a great time in Toronto, much due to my wonderful host Jim Brown. He introduced me to the interesting topic of study- ing thought experiments in science and philosophy for which I will be forever grateful. I would also like to acknowledge a number of people who have contributed to my research in various ways. They have helped me through valuable discus- sions, by giving comments to manuscripts, by writing letters of recommenda- tion etc. These people are: Ulf Danielsson, Richard Dawid, Sven Ove Hans- son, Sten Lindström, George Masterton, Chris Smeenk, Kim Solin, Mårten Stenmark and Harald Wiltsche. I would also like to thank all other friends and colleagues, in Uppsala, Toronto and elsewhere, who in a more indirect way have contributed to my research. They may mot have directly influenced the contents of this thesis. Instead they have all been very important in other ways namely by making my days more enjoyable, or by helping me in various practical matters. It is very many who fall into this category and I hope they will not be sad by the fact that I have decided not to include a list with all their names. With regards to this large group of people I use the old cliché; no one mentioned, no one forgotten. Finally I extend my deepest gratitude to my family and in particular my parents, Akira and Carine, for their constant support during all these years. I have dedicated this dissertation to them. Contents Acknowledgements ......................................................................................... vii 1 Introduction ................................................................................................ 13 2 Physics and Philosophy ............................................................................. 18 2.1 What physicists say about philosophy .......................................... 18 2.2 Why philosophy is relevant for physics ........................................ 20 3 Approaches to quantum gravity ................................................................ 22 3.1 Why do we need a theory of quantum gravity? ........................... 22 3.2 String theory ................................................................................... 24 3.3 Loop quantum gravity .................................................................... 27 3.4 Other approaches to quantum gravity ........................................... 28 4 Methodology and research in quantum gravity ....................................... 31 4.1 String theory ................................................................................... 31 4.2 String theory and philosophy of science ....................................... 33 4.2.1 String theory from a logical positivist’s perspective ..... 33 4.2.2 String theory from a Popperian perspective ................... 34 4.2.3 String theory from a Kuhnian perspective ..................... 37 4.2.4 String theory from a Lakatosian perspective ................. 39 4.3 Further remarks concerning string theory and scientific norms .. 43 4.3.1 Why are tests of string theory required? ........................ 45 4.3.2 String theory from an internalist perspective: explanations ..................................................................... 46 4.3.3 String theory from an externalist perspective ................ 50 4.4 Other approaches to quantum gravity ........................................... 51 4.5 Conclusions .................................................................................... 51 5 Realism, semantics and scientific theories ............................................... 56 5.1 Introduction .................................................................................... 56 5.2 Earlier views on scientific theories ............................................... 57 5.2.1 Logical positivism and verificationist semantics ........... 57 5.2.2 Quine and semantic holism ............................................. 58 5.2.3 Arguments for scientific realism ..................................... 59 5.2.4 Arguments for scientific anti-realism ............................. 60 5.3 A literal understanding of theories? .............................................. 62 5.4 Final comments .............................................................................. 63 6 Realism, underdetermination and string theory dualities ........................ 64 6.1 Introduction .................................................................................... 64 6.2 Underdetermination and scientific realism ................................... 64 6.2.1 Underdetermination ......................................................... 64 6.2.2 Scientific theories and realism ........................................ 66 6.3 Formalisms and physical content .................................................. 69 6.3.1 On how the word ‘duality’ will be used ......................... 69 6.3.2 Purported dualities outside of string theory ................... 70 6.4 Dualities in string theory ............................................................... 72 6.4.1 T-duality and mirror symmetry ....................................... 73 6.4.2 S-duality ........................................................................... 75
Load more

Recommended publications
  • Modalism and Theoretical Virtues: Toward an Epistemology of Modality
    This is a repository copy of Modalism and theoretical virtues: Toward an epistemology of modality. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/83720/ Version: Accepted Version Article: Bueno, O and Shalkowski, SA (2015) Modalism and theoretical virtues: Toward an epistemology of modality. Philosophical Studies, 172 (3). pp. 671-689. ISSN 0031-8116 https://doi.org/10.1007/s11098-014-0327-7 Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ Modalism and Theoretical Virtues: Toward an Epistemology of Modality1 Otávio Bueno Department of Philosophy University of Miami Coral Gables, FL 33124-4670, USA e-mail: [email protected] Scott A. Shalkowski Department of Philosophy University of Leeds Leeds LS2 9JT, UK e-mail: [email protected] ABSTRACT According to modalism, modality is primitive. In this paper, we examine the implications of this view for modal epistemology, and articulate a modalist account of modal knowledge.
    [Show full text]
  • Peircean Modal Realism?”
    Nordic NSP Studies in Pragmatism Helsinki | 2010 Sami Pihlstr¨om “Peircean Modal Realism?” In: Bergman, M., Paavola, S., Pietarinen, A.-V., & Rydenfelt, H. (Eds.) (2010). Ideas in Action: Proceedings of the Applying Peirce Conference (pp. 48–61). Nordic Studies in Pragmatism 1. Helsinki: Nordic Pragmatism Network. ISSN-L - ISSN - ISBN ---- Copyright c 2010 The Authors and the Nordic Pragmatism Network. This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. CC BY NC For more information, see http://creativecommons.org/licenses/by-nc/./ Nordic Pragmatism Network, NPN Helsinki 2010 www.nordprag.org Peircean Modal Realism? Sami Pihlstr¨om University of Helsinki 1. Introduction: the metaphysically realist assumptions of contem- porary modal realism1 The purpose of this paper is to critically compare Charles Peirce’s meta- physics of the modalities – or a “Peircean” approach to this metaphysical is- sue derived from his defense of scholastic realism – to the modal realist views defended by important twentieth century and contemporary philosophers. In this introductory section, I note that the contemporary discourse on modality is firmly rooted in metaphysical realism. In section 2, I suggest that the Peircean approach is closer to Kantian transcendental metaphysics. The contrast between metaphysical realism – or what Kant called “tran- scendental realism” – and the properly transcendental metaphysics in my view inherited by pragmatism turns out to be important, both generally and in the case of modality. Section 3 examines the possibility of inter- preting Peirce’s scholastic realism (a key doctrine in his modal theory) as 1 In addition to the Applying Peirce conference (Helsinki, June 2007), parts of this material were presented at the conference on Peirce’s normative thought in Opole, Poland (also June 2007).
    [Show full text]
  • Historical Parallels Between, and Modal Realism Underlying Einstein and Everett Relativities
    Historical Parallels between, and Modal Realism underlying Einstein and Everett Relativities Sascha Vongehr National Laboratory of Solid-State Microstructures, Nanjing University, Nanjing 210093, P. R. China A century ago, “ past ” and “ future ”, previously strictly apart, mixed up and merged. Temporal terminology improved. Today, not actualized quantum states, that is merely “ possible ” alternatives, objectively “exist ” (are real) when they interfere. Again, two previously strictly immiscible realms mix. Now, modal terminology is insufficient. Both times, extreme reactions reach from rejection of the empirical science to mystic holism. This paper shows how progress started with the relativization of previously absolute terms, first through Einstein’s relativity and now through Everett’s relative state description, which is a modal realism. The historical parallels suggest mere relativization is insufficient. A deformation of domains occurs: The determined past and the dependent future were restricted to smaller regions of space-time. This ‘light cone description’ is superior to hyperspace foliations and already entails the modal realism of quantum mechanics. Moreover, an entirely new region, namely the ‘absolute elsewhere’ was identified. The historical precedent suggests that modal terminology may need a similar extension. Discussing the modal realistic connection underlying both relativities, Popper’s proof of future indeterminism is turned to shatter the past already into many worlds/minds, thus Everett relativity is merely the
    [Show full text]
  • Quantum Gravity: a Primer for Philosophers∗
    Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts.
    [Show full text]
  • Subjectifying Objectivity: Delineating Tastes in Theoretical Quantum Gravity Research
    SSS0010.1177/0306312720949691Social Studies of ScienceGilbert and Loveridge 949691research-article2020 Article Social Studies of Science 1 –27 Subjectifying objectivity: © The Author(s) 2020 Article reuse guidelines: Delineating tastes in sagepub.com/journals-permissions https://doi.org/10.1177/0306312720949691DOI: 10.1177/0306312720949691 theoretical quantum gravity journals.sagepub.com/home/sss research Thomas Krendl Gilbert1 and Andrew Loveridge2 Abstract Research in theoretical quantum gravity has continued expansively even as it has become detached from classic arbiters of research such as direct empirical falsification. This makes it an interesting test case for theories of what motivates and mediates contemporary scientific research and of the nature of scientific objectivity. We conducted 50 semi-structured interviews with researchers in the rival camps of string theory and loop quantum gravity, coded a subset for reoccurring themes, and subjected the resulting data to statistical analysis. To delineate the subjective tastes and the related process of collective consensus-making in contemporary quantum gravity research, we mobilize aspects of Daston and Galison’s depiction of the scientific self and its relation to epistemic virtues, Bourdieu’s field-centered account of social space, and Kantian notions of aesthetics. We make two key contributions. First, our analysis sheds light on the inner workings of the field by connecting its internal epistemic struggles with approaches to understanding scientific fields. Second, our application of theories of social reproduction to the substance of scientific inquiry allows some substantive generalizations of Daston and Galison’s framework. Keywords objectivity, scientific self, social fields, Kantian aesthetics, quantum gravity, high energy physics 1University of California, Berkeley, USA 2University of Texas at Austin, USA Correspondence to: Thomas Krendl Gilbert, UC Berkeley Graduate Division, Berkeley, CA 94720-5900, USA.
    [Show full text]
  • Possible Worlds I: Modal Realism
    Possible Worlds I: Modal Realism May 31, 2009 It is difficult to wander far in contemporary metaphysics without bumping into talk of possible worlds. And reference to possible worlds is not confined to metaphysics. It can be found in contemporary epistemology and ethics, and has even found its way into linguistics and decision theory. But what are those possible worlds, the entities to which theorists in these disciplines all appeal? Call any attempt to answer this question a theory of possible worlds. This paper sets out and evaluates a leading contemporary theory of possible worlds. The view’s principal proponent is David Lewis, and his label for it is ‘Modal Realism,’ which I will abbreviate ‘MR.’1 The view accepts the following sys- tematic correspondence between certain modal facts and facts regarding the existence of possible worlds: (SC) it is possible that φ iff there is a w such that w is a possible world and ‘φ’ is true at w. Lewis proposes MR, in part, as an attempt to specify the nature of the possible worlds whose existence is required by (SC)’s instances. This paper outlines Lewis’s view and discusses some main lines of objection. I will start by noting two competing ambitions for a theory of possible worlds (§1): that a theory of possible worlds be reductive and user-friendly. I will then outline Lewis’s version of MR (§2), and consider objections on the grounds that MR is not reductive (§3) and not user-friendly (§4). 1 Two Ambitions for a Theory of Possible Worlds There are at least two ambitions one might have for a theory of possible worlds.
    [Show full text]
  • 22 Worlds Within Worlds: a Dilemma for Modal Realism
    Worlds within Worlds: 22 a Dilemma for Modal Realism Subrena E. Smith | University of New Hampshire. In this paper I will present an argument that David Lewis’ modal realism is self-refuting, and that the contradiction that makes it self-refuting can only be blocked by modifying certain other of Lewis’ philosophical commitments. My argument will proceed as follows. First, I will briefly describe the motivation for and the main components of Lewisian modal realism. Second, I will explain Lewis’ view of what it is for an individual or a set to exist in a world. Third, I go on to argue that Lewis’ position creates a dilemma for modal realism: either each world contains all the other worlds as parts, which violates the principle that worlds are spatiotemporally isolated, or worlds are reducible to sets, which violates the principle that worlds are individuals. Finally, I briefly discuss a suggestion by Divers that strongly bears on this problem. Modal Realism I begin with a summary description of modal realism. Modal realism is motivated by the broadly Quinean view that quantifying over possibilia provides us with the best way of making sense of modal claims, a position that Lewis (1986a) defends in considerable detail as “a philosopher’s paradise.” Lewis identifies possibilia with worlds. Worlds are concrete (“a big physical object” [Lewis, 1986b: 1]) and non-overlapping. They are non-overlapping because they are spatiotemporally, and therefore causally, segregated from one another. Items are spatiotemporally or causally related to one another just in case they are parts of the same world, and no two worlds share any parts.
    [Show full text]
  • Theorists Snap Over String Pieces
    NATURE|Vol 443|5 October 2006 NEWS JAVA MUD VOLCANO SEEMS UNSTOPPABLE Could Indonesia’s mud flow be put to good use? www.nature.com/news CRISP Theorists snap over string pieces Two recently published books are riling the Brian Greene’s 1999 bestseller The Elegant small but influential community of string Universe, which said that the approach might theorists, by arguing that the field is wandering unify the incompatible theories of gravity and D. F. GRASER F. D. dangerously far from the mainstream. quantum mechanics. The books’ titles say it all: Not Even Wrong, a phrase that physicist Wolfgang Pauli used Strung up to describe incomplete ideas, and The Trou- But the theory has its share of problems, and ble with Physics: The Rise of String Theory, the these are the focus of the new works. For one Fall of a Science, and What Comes Next. Both thing, recent calculations suggest that it gen- articulate a fear that the field is becoming too erates 10500 possible models of the Universe abstract and is focusing on aesthetics rather (see Nature 439, 10–12; 2006). This renders than reality. Some physicists even warn that the theory essentially meaningless, according the theory’s dominance could pose a threat to to critics. When these countless possibilities the scientific method itself (see page 507). were first announced, Lee Smolin was already Those accusations are vehemently denied working on the book that eventually became “None of the major string theory by string theorists, and the books — written by The Trouble With Physics. A physicist at the outsiders — have stirred deep resentment in the Perimeter Institute for Theoretical Physics groups has hired someone tight-knit community.
    [Show full text]
  • Primitive Modality and Possible Worlds
    CORE Metadata, citation and similar papers at core.ac.uk Provided by RERO DOC Digital Library Primitive Modality and Possible Worlds JAVIER KALHAT Abstract This paper sets out a number of reasons for thinking that the framework of possible worlds, even when construed non-reductively, does not provide an adequate basis for an explanation of modality. I first consider a non-reductive version of Lewis’ modal realism, and then move on to consider the ersatzist approach of Plantinga et al.My main complaint is that the framework of possible worlds gets the semantics and meta- physics of ordinary modal discourse wrong. That is, possible worlds do not give us an adequate answer to the semantic question of what ordinary modal claims mean, nor do they give us an adequate answer to the metaphysical question of what makes such claims true. There is a growing consensus among philosophers that modality cannot be reductively explained. Modal notions are to be accounted for, not by trying to reduce them to non-modal ones, but rather by tracing their complex interconnections with one another. The most prominent non-reductive approach to modality is what David Lewis calls ersatzism.1 Like Lewis, ersatzists attempt to explain modality in terms of possible worlds and their inhabitants. Unlike Lewis, they construe possible worlds as abstract representations of concrete worlds, rather than as concrete worlds themselves. And unlike Lewis, of course, they construe possible worlds as primitively modal in nature. Proponents of ersatzism include Adams, Kripke, Plantinga, and Stalnaker among others.2 1 David Lewis, On the Plurality of Worlds (Oxford: Blackwell, 1986), Ch.
    [Show full text]
  • Quantum Gravity: a Primer for Philosophers∗
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Philsci-Archive Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts.
    [Show full text]
  • Connecting Loop Quantum Gravity and String Theory Via Quantum Geometry
    SciPost Physics Submission Connecting Loop Quantum Gravity and String Theory via Quantum Geometry D. Vaid* Department of Physics, National Institute of Technology Karnataka (NITK), India * [email protected] January 9, 2018 Abstract We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macro- scopic geometry emerges and String Theory then becomes the effective theory which describes the dynamics of that exoskeleton. The core of the argument rests on the claim that the Nambu-Goto action of String Theory can be viewed as the expectation value of the LQG area operator evaluated on the string worldsheet. A concrete result is that the string tension of String Theory and the Barbero- Immirzi parameter of LQG turn out to be proportional to each other. Contents 1 Strings vs. Loops 2 2 LQG Area Operator 3 2.1 Minimum Area and Conformal Symmetry 6 3 String Theory and Quantum Geometry 7 3.1 Gravity From String Theory 7 3.2 Geometry vs. Pre-Geometry 8 arXiv:1711.05693v3 [gr-qc] 8 Jan 2018 4 Geometry from Pre-Geometry 9 4.1 Barbero-Immirzi parameter as String Tension 10 5 Discussion and Future Work 11 References 13 1 SciPost Physics Submission 1 Strings vs. Loops There are several competing candidates for a theory of quantum gravity. Two of the strongest contenders are Loop Quantum Gravity (LQG) [1{3] and String Theory [4{6]. Of these, string theory has been around for much longer, is more mature and has a far greater number of practitioners.
    [Show full text]
  • Is Really David Lewis a Realist?
    Ontology Studies 8, 2008 119 Is really David Lewis a realist? Sorin Costreie University of Western Ontario Department of Philosophy Talbot College University of Bucharest Department of Philosophy Resumen. ¿Es David Lewis realmente un realista? Paradoxically, concerning the structure of the world, David Lewis endorses a very nominalistic point of view, whereas he approaches possible worlds from an extreme realistic position. The aim of the present paper is exactly to analyze the relation between the ontology of actual world and the possible worlds ontology in the case of David Lewis, and to see whether or not this tension between the two irreconcilable positions is based on an inner contradiction in his philosophy. Key Words: nominalism, realism, possible worlds, actual world Abstract Paradoxically, concerning the structure of the world, David Lewis endorses a very nominalistic point of view, whereas he approaches possible worlds from an extreme realistic position. The aim of the present paper is exactly to analyze the relation between the ontology of actual world and the possible worlds ontology in the case of David Lewis, and to see whether or not this tension between the two irreconcilable positions is based on an inner contradiction in his philosophy. Key Words: nominalism, realism, possible worlds, actual world In assessing David Lewis’ ontology, one seems to be trapped in the following dilemma: on one hand, he holds a nominalistic position regarding the structure of the world, and, on the other hand, he is well-known for endorsing a realistic position concerning possible worlds. Lewis says explicitly: “That ontology, though Nominalistic, is in other respects generous.
    [Show full text]