Higher-order metaphysics / edited by Peter Fritz and Nicholas K. Jones.

Format:

Book

Contributor:

Fritz, Peter, 1984- editor.

Jones, Nicholas, editor.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Logic.

Metaphysics.

Physical Description:

1 online resource : illustrations.

Place of Publication:

Oxford : Oxford University Press, [2024]

Summary:

Explores the use of higher-order logics in metaphysics. Seventeen original essays trace the development of higher-order metaphysics, discuss different ways in which higher-order languages and logics may be used, and consider their application to various central topics of metaphysics.

Contents:

Cover

Higher-Order Metaphysics

Copyright

Contents

List of Contributors

Part 1: Introduction

1: Higher-Order Metaphysics: An Introduction

1. Motivation and Meaning

1.1 Motivation

1.2 Meaning

2. Pure Higher-Order Metaphysics

2.1 Type Theories

2.2 Relational Type Theories

2.3 Functional Type Theories

2.4 Type-Theoretic Diversity

2.5 Logical Questions

3. Applied Higher-Order Metaphysics

4. The History of Higher-Order Metaphysics

5. Debating Higher-Order Metaphysics

Acknowledgements

Bibliography

2: A Case for Higher-Order Metaphysics

1. Higher-Order Generalizations

2. Propositions, Properties, and Relations

3. Property-Theoretic and Second-Order Questions Are Not the Same

4. Higher-Order Questions Are Closer to the Action than Property-Theoretic Questions

5. Some Remarks on Framework Choice

6. Conclusion

3: Higher-Order Logic as Metaphysics

1. First-Order Preliminaries

1.1 Defining Predicates

1.2 First-Order Logic as Metaphysics

2. Predicate Abstraction

2.1 Abstraction as Definition: Motivating -conversion

2.2 Higher-Order Abstraction and Open -terms

3. Higher-Order Quantification

3.1 Universal Instantiation and Comprehension

3.2 "Propositions", "Properties", and Pronunciation

3.3 Properties and Paradox

3.4 Separating Variable Binding and Generalization

4. Grain Science

5. -terms in Higher-Order Metaphysics

5.1 Against Structure

5.2 Objectual Aboutness: Singularity without Structure

Part II: Pure

4: Classicism

1. Classicism

1.1 Higher-Order Logic

1.2 Booleanism

1.3 Classicism

1.4 Axiomatizations with New Rules

2. Extensions of Classicism

2.1 Towards Extensionalism I: Coarse-Grainedness Principles

2.2 Towards Extensionalism II: Lattice-Theoretic Principles

2.3 Towards Extensionalism III: Comprehension Principles

2.4 Finer-Grained Strengthenings: Maximalist Classicism

2.5 Finer-Grained Strengthenings: Non-Logical Constants and Fundamentality

2.6 Finer-Grained Strengthenings: Beyond Maximalist Classicism

3. Model Theory for Classicism

3.1 BBK-Models

3.2 Henkin Models

3.3 Categories of BBK-Models

3.4 Action Models

3.5 Exploring Action Models

3.6 The Consistency of Maximalist Classicism

Appendices

A. Closure of Classicism under Equivalence

B. Axiomatizations in Terms of Entailment

C. Soundness and Completeness of Action Models for Classicism

D. Consistency Results Using Non-Full Action Models

E. Coalesced Sums and Maximalist Classicism

5: Reality as Tall and Fine, Not Flat and Coarse

1. The Ontological Question Generalized

2. Classical Higher-Order Logic and Type Theory

3. Some Generalizations of Cantor's Theorem

4. Russell-Myhill and the Possibility of Fine Structure

Notes:

Also issued in print: 2024.

Includes index.

Includes bibliographical records and index.

Description based on online resource and publisher information; title from PDF title page (viewed on February 5, 2024).

Other Format:

Print version :

ISBN:

0-19-264788-1

0-19-191576-9

OCLC:

1419961040