Understanding the Many

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ISBN: 9780415938648 | 0415938643
Cover: Hardcover
Copyright: 5/31/2002

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This book presents a mathematically and logically sophisticated analysis of the "many," or the "more than one." Covering issues of natural numbers, facts and their proper analysis, properties and their instantiation, as well as the logic of sets, this book elucidates one of the most debated concepts of the century.

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Introduction
Plural Quantifications
Singular Versus Plural Quantifications
Implication
The Implication Argument
On the Three Theses on Implications
Implication Versus Metaphysical Necessity
Paraphrase
The Logic of Plurals
Language
Elementary Notation
The Term Connective "and"
Predicates
Singular, Plural, and Neutral Predicates
Neutral Expansions and Singular Reducts
Logical Predicates
Quantifiers and Variables
Singular and Plural Quantifiers
Paraphrasing Plural Quantifiers
Singularizable Plural Quantifications
The Canonical Notation for the Logic of Plurals
Terms
Predicates and Simple Sentences
Quantifiers and Complex Sentences
Logic
The Logic of Plurals: Partial Axiomatization
System A
System B
System C
System D
The Logic of Plurals: Model Theory Appendix: Partial Axiomatization of the Logic of Plurals
Is Two a Property?
Why Property Two?
What Is It to Be a Property?
Irregularities of Numerical Facts
Why Not the Set Analysis?
A Theory of Plural Properties
The Predicative Part
The Subject Part
Instantiation
Various Kinds of Plural Properties
Two As an Intrinsic Plural Property
Concluding Remarks
What Numbers Should Be
Are Numbers Objects?
Plural Properties As Components of Numerical Facts
Analysis of Numerical Facts
Numbers Are Properties
How Sets Are Determined by Their Members
The Hierarchy of Sets and the Determination of Sets by Their Members
Reference to Set-like Objects
Plural Reference to Mundane Objects
Exclusive Reference to Mundane Objects
Concluding Remarks
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Understanding the Many

Summary

Table of Contents

Supplemental Materials