Arbitrary Reference in Logic and Mathematics (Synthese Library, 490)

Preface
Contents
1 On Arbitrary Reference
	1.1 Introduction
	1.2 On PAR
	1.3 Is PAR a Semantic Principle?
	1.4 PAR and Game-Theoretical Semantics
	1.5 The Principle of Arbitrary Choice (PAC)
	1.6 PAC and the Axiom of Choice
	1.7 Arbitrary Reference and Impredicativity
	References
2 On Plural Arbitrary Reference
	2.1 Introduction
	2.2 Boolos on Second Order Monadic Logic
	2.3 Plural Reference: Some Background
	2.4 Plural Arbitrary Reference
	2.5 A Team of Agents Making Choices for a Semantics of Acts of Choices (SAC). How Plural Arbitrary Reference Works
	2.6 A Fictional Constructivism About Acts of Choice
	2.7 On the Ideal Agent, Again
	2.8 On Our Fictionalism
	References
3 On Arbitrary Fictional Models
	3.1 Introduction
	3.2 On Epistemic Validity, Epistemic Truth, and Epistemic Completeness
	3.3 The Unprovability of Consistency
	3.4 On Löb\'s Theorem
	3.5 Conclusions
	References
4 On the Logicality of Second-Order Logic in Terms of Plural Arbitrary Reference
	4.1 Introduction
	4.2 Linnebo\'s Objections to Boolos\' Plural Quantification
	4.3 Is Second-Order Logic Logic at All?
	4.4 Conclusions
	References
5 A Notion of Logical Concept Based on Plural Arbitrary Reference
	5.1 Introduction
	5.2 The Formal Language
	5.3 The Intended Model
	5.4 Formal Semantics
		5.4.1 Logical Principles
	5.5 The Consistency of the Theory
	5.6 Relations and Sets
	5.7 Natural Numbers
	5.8 Russell\'s Paradox
	5.9 The Logicist Flavor of the Theory of Logical Concepts
	5.10 Conclusions
	References
6 Plural Arbitrary Reference and Mereology
	6.1 Introduction
	6.2 Arguments for a Fictional Ontological Commitment
	6.3 Arbitrary Plural Choices for a Second Order Logic
	6.4 Virtual Mereology (VM): An Informal Exposition
	6.5 The Calculus of Individuals with Atoms (CG)
	6.6 Conclusions
	References
7 Grounding Megethology on Plural Arbitrary Reference
	7.1 Introduction
	7.2 Lewis\' Megethology in a Nutshell
	7.3 Megethology with Choices
	7.4 An Interpretation of ZFC Set Theory
	7.5 Categoricity
	7.6 Concluding Remarks
	References
8 The Mereological Foundation of Megethology
	8.1 Introduction
	8.2 Mereological Axioms
	8.3 Axioms on the Size of the Universe
	8.4 An Interpretation of Set Theory
	8.5 Categoricity
	8.6 Consistency of Megethology
	8.7 A Mereological Codification of Ordered Pairs
	8.8 On the Infinite in Lewis\' Mereology
	8.9 Conclusions
	References
9 Final Ruminations
Author Index
Subject Index