Modal Logic as Metaphysics

481 Pages·2013·1.77 MB·English

by  Timothy Williamson

Modal Logic as Metaphysics
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Modal Logic as
Metaphysics
Timothy Williamson
Great Clarendon Street, Oxford, Ox2 6dp,
United Kingdom
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© Timothy Williamson 2013
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ISBN 978-0-19-955207-8
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To Ana
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Contents
Preface x
1 Contingentism and Necessitism 1
1.1 The question 1
1.2 Forms of necessitism 5
1.3 possible Fs 10
1.4 Unrestricted generality 14
1.5 Necessitism and Meinongianism 18
1.6 Actualism and possibilism 22
1.7 Identity and distinctness 25
1.8 dying and never being born 28
2 The Barcan Formula and its Converse: Early developments 30
2.1 The Barcan Formula 30
2.2 The Converse Barcan Formula 37
2.3 Ibn-Sina 45
2.4 Carnap 46
2.5 Barcan Marcus again 60
2.6 prior 64
2.7 Truth-value gaps 72
2.8 Logical modalities 75
3 possible Worlds Model Theory 81
3.1 Kripke 81
3.2 Kripke models for normal propositional modal logic 84
3.3 Metaphysical universality in propositional modal logic 92
3.4 Kripke models for first-order modal logic 119
3.5 The Barcan and converse Barcan formulas in Kripke’s model theory 124
3.6 Metaphysical universality in first-order modal logic 130
3.7 Intended inhabited model structures for necessitism 139
viii contents
4 predication and Modality 148
4.1 The being constraint 148
4.2 Stalnaker’s quantified modal logic with identity: orthodox
semantics 159
4.3 Stalnaker’s quantified modal logic with identity: unorthodox
semantics 163
4.4 The significance of Stalnaker’s results 167
4.5 Abstraction and the qualified converse Barcan formula 172
4.6 Variables and constants in Stalnaker’s system 177
4.7 Abstraction and the necessity of distinctness 179
4.8 Abstraction and necessitism 183
4.9 Stalnaker’s criterion of representational significance 188
5 From First-Order to Higher-Order Modal Logic 195
5.1 Methodological preliminaries 195
5.2 Lewis and Langford: propositional quantification in modal logic 198
5.3 Second-order modal logic in Barcan and Carnap: identity,
individual concepts, and semantic uniformity 203
5.4 Montague’s intensional logic 216
5.5 The system ML of higher-order modal logic 221
p
5.6 Necessitist and contingentist versions of ML 230
p
5.7 The challenge of interpreting higher-order quantification 235
5.8 plural quantification in modal logic 241
5.9 Non-plural interpretations of higher-order modal logic 254
6 Intensional Comprehension principles and Metaphysics 262
6.1 Comprehension and higher-order necessitism 262
6.2 Individuals and their haecceities 267
6.3 Non-modal comprehension 277
6.4 Non-singular comprehension 282
6.5 From properties to propositions 288
6.6 Truth in a world and truth of a world 296
6.7 Appendix 301
7 Mappings between Contingentist and Necessitist discourse 305
7.1 Communication between contingentists and necessitists 305
7.2 Mapping contingentist talk to neutral talk 313
7.3 Mapping necessitist talk to neutral talk 323
7.4 Modalism and anti-modalism 332
contents ix
7.5 The problem of incompossibles 335
7.6 Extending the framework to plurals 340
7.7 Infinitary languages 352
7.8 Further applications 365
7.9 Appendix 369
8 Consequences of Necessitism 376
8.1 The necessary framework of objects 376
8.2 Supervenience in question 380
8.3 No truthmakers 391
8.4 Contingency, change, and difference 403
Methodological Afterword 423
Bibliography 430
Index 451