Founding Mathematics on Semantic Conventions (Synthese Library, 446)

Founding Mathematics on Semantic Conventions
	Preface
	Contents
1 Introduction
	1.1 Overview and Guide to Partial Reading
2 Classical Mathematics and Plenitudinous Combinatorialism
	2.1 Large Cardinal Axioms and Theorems of Arithmetic
	2.2 Transfinite Ordinals
	2.3 Transfinite Cardinals
	2.4 The Continuum Hypothesis
3 Intuitionism and Choice Sequences
	3.1 General Introduction
	3.2 Brouwer on Freely Proceeding Choice Sequences
	3.3 Constitution of Free Choice Sequences
	3.4 Evaluation of Brouwer\'s Claim
	3.5 Verificationism and Intuitionistic Logic
4 From Logicism to Predicativism
	4.1 Frege
	4.2 Russell
	4.3 Weyl
	4.4 Weyl\'s Failure to Include All Real Numbers
5 Conventional Truth
	5.1 The Obvious Solution to the Liar Paradox
	5.2 Conventional Truth Conditions
	5.3 The Dogma
	5.4 Possible Language Conventions
	5.5 T-schemas and Expressive Strength
	5.6 Dialectical Situation
	5.7 The View from Nowhere
	5.8 Comparison with Chihara\'s Position
	5.9 Revenge
6 Semantic Conventionalism for Mathematics
	6.1 Needs Assessment
	6.2 Simple Arithmetic as a Conventional Language
	6.3 Quine\'s Anti-Conventionalism
	6.4 Rule-Following
	6.5 Choice of Logic
7 A Convention for a Type-free Language
	7.1 The Kripke Convention and Its Shortcomings
	7.2 Reformulating the Kripke Convention
		7.2.1 Collapsing Truth and Satisfaction of View-From-Nowhere Truth Conditions
		7.2.2 Kleenification
		7.2.3 Kripke Recursion
	7.3 Adding a Conditional with Supervaluational Semantics
		7.3.1 Supervaluation over All Possibilities
		7.3.2 View-From-Nowhere Truth Conditions for the Strong Conditional
		7.3.3 If the Supervaluation Criterion is Not Satisfied
		7.3.4 Ensuring Quantification over All Possibilities in the Presence of Supervaluation
		7.3.5 Iteration of the Strong Conditional
		7.3.6 Summary
	7.4 Denoting Terms for Applied Mathematics
	7.5 Meta-Theorems
8 Basic Mathematics
	8.1 Logic
	8.2 Natural Numbers
	8.3 Integers
	8.4 Rational Numbers
	8.5 Classicality So Far
	8.6 Classes
	8.7 An Example of Applied Mathematics
9 Real Analysis
	9.1 Functions
	9.2 Real Numbers
	9.3 Exponentiation
	9.4 Completeness
	9.5 Suprema, Infima, and Roots
	9.6 Continuity
	9.7 Operations on Functions
	9.8 Differentiation
		9.8.1 Calculating Derivatives
		9.8.2 Uniform Differentiability
	9.9 Integration
	9.10 Unbounded Intervals and Piecewise Continuity
	9.11 Completifications of Functions Generalized
	9.12 Another Example of Applied Mathematics
	9.13 Diagonalization
10 Possibility
	10.1 All Possible Real Numbers
	10.2 Modal Metaphysics
	10.3 Conclusion
References
Index of Symbols
General Index