Ira Kiourti - University of St Andrews

214 Pages·2010·0.98 MB·English

REAL IMPOSSIBLE WORLDS : THE BOUNDS OF POSSIBILITY
Ira Georgia Kiourti
A Thesis Submitted for the Degree of PhD
at the
University of St. Andrews
2010
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Real Impossible Worlds: The Bounds of
Possibility

Ira Georgia Kiourti

Submitted for the Degree of PhD in Philosophy
University of St. Andrews
th
18 December 2009
Abstract
Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to
accommodate impossible worlds and reap the benefits that these bestow to rival theories.
This thesis explores two alternative extensions of GR into the terrain of impossible worlds.
It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for
impossible worlds, and the central problem that such worlds present for GR: How can GR
even understand the notion of an impossible world, given Lewis’ reductive theoretical
framework? Since the desideratum is to incorporate impossible worlds into GR without
compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis
against (old and new) objections. The rest of the thesis is devoted to incorporating
impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the
form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI
venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against
such worlds, to the effect that contradictions true at impossible worlds amount to true
contradictions tout court. I argue that even if so, the relevant contradictions are only ever
about the non-actual, and that Lewis’ argument relies on a premise that cannot be non-
question-beggingly upheld in the face of genuine impossible worlds in any case. Chapter
V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine
impossibilia, if we differentiate the impossible from the possible by means of accessibility
relations, understood non-modally in terms of similarity. Finally, Chapter VI counters
objections to the effect that there are certain impossibilities, formulated in Lewis’
theoretical language, which genuine impossibilia should, but cannot, represent. I
conclude that Genuine Realism is still very much in the running when the discussion turns
to impossible worlds.
Ira Georgia Kiourti 040011301
Declarations

I, Ira Georgia Kiourti, hereby certify that this thesis, which is approximately 81000 words
in length, has been written by me, that it is the record of work carried out by me and that it
has not been submitted in any previous application for a higher degree.

I was admitted as a research student in September 2005 and as a candidate for the degree
of PhD in September 2005; the higher study for which this is a record was carried out in
the University of St Andrews between 2005 and 2009.

Date: .................................... Signature of candidate ....................................

I hereby certify that the candidate has fulfilled the conditions of the Resolution and
Regulations appropriate for the degree of PhD in the University of St Andrews and that the
candidate is qualified to submit this thesis in application for that degree.

Date .................................... Signature of supervisor ....................................

In submitting this thesis to the University of St Andrews we understand that we are giving
permission for it to be made available for use in accordance with the regulations of the
University Library for the time being in force, subject to any copyright vested in the work
not being affected thereby. We also understand that the title and the abstract will be
published, and that a copy of the work may be made and supplied to any bona fide library
or research worker, that my thesis will be electronically accessible for personal or research
use unless exempt by award of an embargo as requested below, and that the library has the
right to migrate my thesis into new electronic forms as required to ensure continued access
to the thesis. We have obtained any third-party copyright permissions that may be required
in order to allow such access and migration.

The following is an agreed request by candidate and supervisor regarding the electronic
publication of this thesis:

Access to Printed copy and electronic publication of thesis through the University of St
Andrews.

Date ………… Signature of candidate ………... Signature of supervisor …..……...
Acknowledgements

My gratitude goes, first and foremost, to my supervisors Katherine Hawley and
Graham Priest, for their seemingly infinite patience, unfailing support and intellectual
inspiration over the years, and for going far beyond the call of duty to help me complete
this study. I thank them for believing in me when I did not, for beckoning my thought to
distant shores, and for inspiring me as shining examples of everything that is of value in
the profession. Much that is of value in this dissertation, I owe to them.
I have also had the great pleasure of working with Stephen Read during the final years
of my research, and I am very grateful for the interest he has shown in my work, for his
painstakingly questioning of my ideas, and for always providing me with a fresh
perspective. My work was much improved as a direct result of my interactions with him.
During the decisive first year of my research, I was, moreover, lucky enough to work
under the supervision of Daniel Nolan, who inspired me and led me through some of the
bewildering topics, for which I am very grateful. My thanks also go to Patrick Greenough,
who also stimulated my thoughts and defiantly encouraged their pursuit during that first
decisive year. I am also grateful to Crispin Wright for giving me the opportunity, in 2005,
to carry out my doctoral research within the rich philosophical environment that is the
Arché Philosophical Research Centre, in St Andrews. Finally, I wish to thank the
Philosophy Department at the University of Glasgow for their excellent conversion course,
and in particular Bob Hale, Gary Kemp, Dudley Knowles, Philip Percival and Adam
Rieger for giving me a chance, guiding my first steps in philosophy, and inspiring in me
the desire for further research.
Earlier drafts of chapters have been presented on various occasions. I am grateful to
friends and colleagues for being present and for their lively discussion at various Arché
and Departmental seminars at the University of St. Andrews, as well as the 2008 Leeds
Graduate Conference, the Fourth World Congress on Paraconsistency in Melbourne, the
AAP 2008, and the University of Kyoto. A special thanks goes to John Divers for his
helpful comments and his support over the years. I would also like to acknowledge, for
their helpful suggestions, Jacob Busch, Ross Cameron, Colin Caret, Peter Clark, Mike De,
Philip Ebert, Ole Hjortland, Lloyd Humberstone, Carrie Jenkins, Charles Pigden, Simon
Prosser, Denis Robinson, Marcus Rossberg, Jeremy Seligman, Jonathan Shaffer, Peter
Simons, Martin Smith, Crispin Wright and Elia Zardini.
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I have also been fortunate to travel and draft parts of this thesis in Japan, Australia and
New York. Here, I am deeply grateful to Graham Priest for giving me the opportunity for
such travel, to Katherine Hawley and Peter Clark for encouraging me to go, to Yasuo
Deguchi and the wonderful students at the University of Kyoto for their overwhelming
hospitality and for making my stay in Japan magical, and to the Arts and Humanities
Research Council, the Philosophy Departments at the University of St. Andrews and the
Arché Philosophical Research centre for their financial help in actualising these trips.
Equally, I have been exceedingly fortunate to receive a Doctoral Award by the Arts
and Humanities Research Council and a Research Scholarship by the University of St
Andrews. This work could not have been written without the generous financial support of
these institutions, for which am truly grateful.
Last, but not least, I heartily thank the lovely crew at Apostrophe in London’s
Brunswick Centre for their exceedingly good cheer and coffee, my friends, especially
Katerina and Dagmar, who offered their support from afar, my devoted family, whose
unfailing love provides a bedrock for my creativity and, above all, I thank my partner Matt
without whose love, support, vision and encouragement, in more ways than I can say, none
of this would be, even remotely, possible.

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Contents
Acknowledgements iii
Introduction 1
I Genuine Realism and Impossible Worlds: Setting Things Up 5
1.1 Introduction 5
1.2 Impossible Worlds: Why This Topic? 5
1.2.1 What are Impossible Worlds? 5
1.2.2 Why Bother with Impossible Worlds? 8
1.2.3 Squaring Impossible Worlds with GR: The Good Reasons 13
1.2.4 And the Bad... 14
1.3 Genuine Realism about Possible Worlds 16
1.3.1 The GR Basics 16
1.3.2 A Brief Defence 21
1.4 Making Room for the Concept of an Impossible World in GR 23
1.4.1 The Central Puzzle 23
1.4.2 Concreteness and Absoluteness: Two Alternative Solutions 25
1.4.3 An Existing Concretist Proposal 26
1.4.4 A Role for Impossible Worlds in the Analysis of Modality? 28
1.5 The Many Obstacles to Concrete Impossibilia 30
1.5.1 Literally True Contradictions and Other Logical Worries 31
1.5.2 Representational Challenges 32
1.5.3 The Question of Logical Laws 33
1.5.4 The Competition with Ersatz Constructions 34
1.6 Conclusion 35
II Genuine Realism and the Reduction of Modality: A Defence 36
2.1 Introduction 36
2.2 The Reduction of Possibility, Its Value and the Accuracy Challenge 36
2.2.1 The Value of (P) 37
2.2.2 The Accuracy Challenge 39
2.2.3 Recombination 40
2.3 Accuracy and Epistemic Circularity 41
2.3.1 Modal Beliefs and Analysis Construction 41
2.3.2 Modal Beliefs and Recombination 43
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2.3.3 Methodological Circularity Worries 44
2.4 Accuracy, Arbitrariness and Metaphysical Circularity 46
2.4.1 Arbitrariness 47
2.4.2 Ontological Priority 48
2.4.3 Modal Conditions on (P)’s Accuracy? 49
2.5 Conceptual Circularity & Inconsistency: Impossible Individuals 51
2.6 Conceptual Circularity & Incompleteness: The Plenitude of Alien Properties 54
2.6.1 The Argument 54
2.6.2 What is Wrong with the Divers-Melia Argument: An Overview 55
2.6.3 Plenitude, Model Theoretic Completeness and Axiomatic Theories 59
2.6.4 Plenitude –‘Guarantee’ as Axiomatic Entailment 63
2.6.5 Plenitude, Arbitrariness and (P)’s Conditions of Accuracy 65
2.6.6 Plenitude and Recombination 68
2.6.7 Summary 69
2.7 Conclusion 70
III Genuine Realism with Impossible Worlds On The Cheap 71
3.1 Introduction 71
3.2 Abandoning Concreteness 72
3.3 Ersatz Impossible Worlds: Exploring Alternative Constructions 74
3.3.1 Sets of Ways 74
3.3.2 Sets of Propositions 79
3.3.3 Sets of Finer Propositional Structures 83
3.3.4 Properties? 89
3.3.5 Summary 91
3.4 Pros and Cons: Ontology, Methodology and Justification 92
3.4.1 No Inconsistency Threat 92
3.4.2 Ad Hoc Ontological Distinctions? 93
3.4.3 A New Hybrid View? 96
3.5 Why Still Bother with Concrete Impossibilia? 97
3.6 Conclusion 98
IV Genuine Impossible Worlds and Contradiction 100
4.1 Introduction 100
4.2 Lewis against Impossible Worlds 100
4.3 Classical Logic and Truth Simpliciter 103
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4.3.1 Truth about the Actual 104
4.3.2 Actual Truth, Necessary Truth and Truth Simpliciter 105
4.3.3 Why the New Theory Ought to Allow Contradiction 108
4.3.4 Classical Logic: Loss of Generality 109
4.3.5 Reasoning from GR’s Hypotheses 111
4.3.6 Summary 115
4.4 The Question of Negation Commutation 116
4.4.1 Questioning (CP) 116
4.4.2 (CP), Negation and Negation-at-w 120
4.4.3 (CP) and Representation: The Metaphysics Behind (CP) 121
4.4.4 Summary 128
4.5 Applications: Yagisawa and the Identity of Properties 128
4.5.1 The Actual-Truth-versus-Truth-Simpliciter-Approach 130
4.5.2 The Amended-Truth-at-w-Conditions-for-Negation Approach 131
4.6 Conclusion 132
V Genuine Impossible Worlds and Relative Modalities 133
5.1 Introduction 133
5.2 Abandoning Absoluteness 134
5.3 The Paradigm: Nomological Modalities 137
5.3.1 The Notion of a Natural Law 138
5.3.2 Nomological Similarity 139
5.4 Extension: Logical Modalities 141
5.4.1 The Appropriate Notion of a Logical Law 143
5.4.2 Logical Similarity Relations on Worlds? 147
5.4.3 Summary 153
5.5 Further Questions 154
5.5.1 Questions of Meaning 154
5.5.2 Characterising the Ontology 156
5.5.3 Metaphysical Necessity 157
5.5.4 Modality as World-Similarity 158
5.6 Conclusion 159
VI The Representational Power of Concrete Impossibilia 160
6.1 Introduction 160
6.2 Why Bother with GR-Theoretical Representation Objections 161
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6.3 GR-Impossibilities about Worlds: The Proper Response to Vander Laan 163
6.3.1 Reply to Vander Laan 164
6.3.2 Inconsistency and Representational Power 165
6.4 Transworld GR-Impossibilities: The Proper Response to Nolan 167
6.4.1 Reply to Nolan 170
6.4.2 Applications to GR-theoretical Impossibilities 177
6.4.3 Objections and Replies 184
6.5 Conclusion 189
Conclusion 191
References 192

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