The Foundations of Modality: From Propositions to Possible Worlds

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The Foundations of Modality: From Propositions to Possible Worlds
Copyright
Contents
Acknowledgements
Introduction
	The Ubiquity of Modalities
	Ideological Disputes
	Identity-First Metaphysics
	Outline
PART I: LANGUAGE
	1: Breaking the Domination of the Word over the Human Spirit
		1.1 Introduction
		1.2 Desiderata of Property Talk
		1.3 Inconsistency
		1.4 Metasemantics
		1.5 Going Higher Order
	2: A Formal Language
		2.1 Syntax
		2.2 A Proof System
		2.3 Identity
		2.4 Supplement: Possible Worlds Models
		2.5 Supplement: Relative Consistency
PART II: IDENTITY
	3: Attitudes and Structured Propositions
		3.1 Attitude Ascriptions
		3.2 Structure and the Russell-Myhill Argument
		3.3 Supplement: Logical Structure and Grounding
		3.4 Supplement: Closed Structure
	4: Classicism
		4.1 Extensionalism
		4.2 Boolean Connectives
		4.3 Quantifiers
		4.4 The Rule of Equivalence
		4.5 A Preliminary Assessment
		4.6 Supplement: Attitude Ascriptions and Attitudes
		4.7 Supplement: Identity
		4.8 Supplement: Schema vs Rule
PART III: NECESSITY
	5: Metaphysical Necessity
		5.1 Classicism and Intensionalism
		5.2 Metaphysical Necessity
		5.3 The Broadest Necessity
		5.4 An Objection
		5.5 The Logic of Necessity
		5.6 Supplement: Equivalence
		5.7 Supplement: Counterfactuals
	6: Actuality, and the Necessity of Distinctness and Possibility
		6.1 “Actually”
		6.2 The Necessity of Distinctness
		6.3 The Necessity of Possibility
		6.4 Strengthening Classicism
		6.5 The Logic of Necessity Revisited
		6.6 Supplement: Independence
		6.7 Supplement: Axioms for Actuality
PART IV: WORLDS
	7: A Theory of Possible Worlds
		7.1 Worlds as Propositions
		7.2 Formalizing World-Talk
		7.3 A Theory of Worlds
		7.4 Maximal Propositions
		7.5 Atomicity
		7.6 Supplement: Consistency Proofs Using Models
		7.7 Supplement: Deductions
	8: Plural Propositional Quantification
		8.1 Necessity without Worlds
		8.2 Adding Plural Quantifiers
		8.3 Worlds from Plural Quantification
		8.4 World-Propositions and World-Stories
		8.5 The Logic of Necessity, Once More
		8.6 Supplement: Independence
		8.7 Supplement: Informal Completeness
PART V: CONCLUSION
	9: A Coarse-Grained World-View
		9.1 Summing Up
		9.2 Open Questions
		9.3 Supplement: Challenges to Possible Worlds Accounts of Propositions
		9.4 Supplement: Challenges to Higher-Order Languages
		9.5 Supplement: Infinite Arity
	10: Looking Ahead
		10.1 Backtracking
		10.2 Metaphysics and Metasemantics
		10.3 Hyperintensional Metaphysics
		10.4 Models and Theories
Bibliography
List of Notation
	Logical Connectives
	Mathematical Notation
	Languages
	Proof Systems
	Labeled Principles
	Logics and Theories
	Model-Theoretic Notation
	Syntactic Mappings
Author Index
Subject Index