Understanding the Many

Byeong-uk Yi

Introduction

1. Plural Quantifications
1. Singular Versus Plural Quantifications
2. Implication
2.a The Implication Argument
2.b On the Three Theses on Implications
2.c Implication Versus Metaphysical Necessity
3. Paraphrase

2. The Logic of Plurals
1. Language
1.a Elementary Notation
*1.b. The Term Connective and
1.c. Predicates
1.c.i. Singular, Plural, and Neutral Predicates
1.c.ii. Neutral Expansions and Singular Reducts
1.c.iii. Logical Predicates
1.d. Quantifiers and Variables
1.d.i. Singular and Plural Quantifiers
1.d.ii. Paraphrasing Plural Quantifiers
1.d.iii. Singularizable Plural Quantifications
1.e. The Canonical Notation for the Logic of Plurals
1.e.i. Terms
1.e.ii. Predicates and Simple Sentences
1.e.iii. Quantifiers and Complex Sentences
2. Logic
2.a. The Logic of Plurals: Partial Axiomatization
2.a.i. System A
2.a.ii. System B
2.a.iii. System C
2.a.iv. System D
*2.b. The Logic of Plurals: Model Theory
Appendix: Partial Axiomatization of the Logic of Plurals

3. Is Two a Property?
1. Why Property Two?
1.a. What Is It to Be a Property?
1.b. Irregularities of Numerical Facts
1.c. Why Not the Set Analysis?
2. A Theory of Plural Properties
2.a. The Predicative Part
2.b. The Subject Part
2.c. Instantiation
2.d. Various Kinds of Plural Properties
3. Two As an Intrinsic Plural Property
4. Concluding Remarks

4. What Numbers Should Be
1. Are Numbers Objects?
2. Plural Properties As Components of Numerical Facts
3. Analysis of Numerical Facts
4. Numbers Are Properties

5. How Sets Are Determined by Their Members
1. The Hierarchy of Sets and the Determination of Sets by Their Members
2. Reference to Set-like Objects
3. Plural Reference to Mundane Objects
4. Exclusive Reference to Mundane Objects
5. Concluding Remarks
References
Index