Understanding the Many Book

	Preface
	Acknowledgments
	Introduction
1	Plural Quantifications	1
1.1	Singular Versus Plural Quantifications	2
1.2	Implication	7
1.3	Paraphrase	13
2	The Logic of Plurals	17
2.1	Language	17
2.2	Logic	38
App	Partial Axiomatization of the Logic of Plurals	57
3	Is Two a Property?	59
3.1	Why Property Two?	59
3.2	A Theory of Plural Properties	67
3.3	Two As an Intrinsic Plural Property	72
3.4	Concluding Remarks	75
4	What Numbers Should Be	77
4.1	Are Numbers Objects?	78
4.2	Plural Properties As Components of Numerical Facts	82
4.3	Analysis of Numerical Facts	86
4.4	Numbers Are Properties	90
5	How Sets Are Determined by Their Members	93
5.1	The Hierarchy of Sets and the Determination of Sets by Their Members	94
5.2	References of Set-like Objects	97
5.3	Plural Reference to Mundane Objects	98
5.4	Exclusive Reference to Mundane Objects	100
5.5	Concluding Remarks	101
	Bibliography	105
	Index	115