The Logic of Number

Cover
Title Page
Contents
Acknowledgments
Part I: Natural Logicism
	1 What is Natural Logicism?
	2 Before and After Frege
	3 After Gentzen
	4 Foundations After Gödel
	5 Logico-Genetic Theorizing
Part II: Natural Logicism and the Naturals
	6 Introduction, with Some Historical Background
	7 Denoting Numbers
	8 Exact Numerosity
	9 The Adequacy Condition Involving Schema N
	10 The Rules of Constructive Logicism
	11 Formal Results of Constructive Logicism
	12 Reflections on Counting
	13 Formal Results about the Inductively Defined Numerically Exact Quantifiers
Part III: Natural Logicism and the Rationals
	14 What Would a Gifted Child Need in Order to Grasp Fractions? The Case of Edwin
	15 Past Accounts of the Rationals as Ratios
	16 Mereology and Fraction Abstraction
	17 Taking Stock and Glimpsing Beyond
Part IV: Natural Logicism and the Reals
	18 The Trend toward Arithmetization
	19 Resisting the Trend toward Arithmetization
	20 Impurities and Incompletenesses
	21 The Concept of Real Number
	22 Geometric Concepts and Axioms
	23 Bicimals
	24 Uncountability
	25 Back to Bicimals
Appendix A: Proof of the Non-Compossibility Theorem
Appendix B: Formal Proof of a Geometric Inference
Bibliography
Index