The metaphysics of quantities / J. E. Wolff.

Format:

Book

Author/Creator:

Wolff, John Eliot, 1857-1940, author.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Metaphysics.

Physical constants--Philosophy.

Physical constants.

Physical Description:

1 online resource (x, 213 pages).

Edition:

First edition.

Place of Publication:

Oxford, England : Oxford University Press, [2020]

Summary:

What are physical quantities, and in particular, what makes them quantitative? This text presents an original answer to this question through the novel position of substantival structuralism, arguing that quantitativeness is an irreducible feature of attributes, and quantitative attributes are best understood as substantival structured spaces.

Contents:

Machine generated contents note: 1. Introduction

1.1. What is a Metaphysics of Quantities?

1.2. Three Cross-Cutting Disputes about Quantities

1.3. Scientific Theories of Quantities

1.4. Metaphysical Landscape

1.5. Organization of the Book

2. Quantities as Determinables

Synopsis

2.1. Quantities as Variable Attributes

2.1.1. Intuitive Distinctions

2.1.2. Determinable/Determinate Model

2.1.3. Applying the Determinable/Determinate Model to Quantities

2.2. Awkward Fit

2.2.1. Some Initial Observations

2.2.2. Horizontal vs. Vertical Relations

2.2.3. Challenge of the Single Value Principle

2.2.4. Conclusion

3. Quantities as Numerical Attributes

3.1. Restrictive and Permissive Views of Quantities

3.1.1. Restrictive Empiricism: Carnap's Division of Scientific Concepts

3.1.2. Restrictive Realism: Numbers are Hard

3.1.3. Permissivism: Numbers are Easy

3.2. Difference in Strength, not in Numbers

3.2.1. Numbers: Neither Necessary nor Sufficient

3.2.2. Why Draw a Distinction at all?

3.2.3. Summary and Outlook

4. Quantitative Attributes or Measurable Concepts

4.1. Measurement Realism

4.1.1. Naive View of Measurement

4.1.2. Measurement Realism Today

4.2. Measurement Realism under Attack

4.2.1. Line of Attack

4.2.2. Problem of Nomic Measurement

4.2.3. Establishing Constancy

4.2.4. Extending Scales

4.2.5. How Far to the True Value?

4.3. Operationalism

4.3.1. Traditional Operationalism

4.3.2. Sophisticated Operationalism

4.4. Defending Quantitativeness

4.4.1. Measurability vs. Quantitativeness

4.4.2. Attributes Matter: Hardness

4.5. Measurement Realism as Scientific Realism

5. Representational Theory of Measurement

5.1. Preliminaries

5.1.1. Origins of Representationalism

5.1.2. Basic Principles of Representationalism

5.2. Additive Extensive Structures

5.2.1. Representation and Uniqueness Theorems for Additive Extensive Structures

5.2.2. Holder's Theorem

5.3. Other Important Types of Measurement Structures

5.3.1. Difference Structures

5.3.2. Additive Conjoint Measurement

5.3.3. Types of Quantities and Types of Measurement Structures

5.4. Uniqueness and the Hierarchy of Scales

5.4.1. Permissible Transformations and the Hierarchy of Scales

5.4.2. Uniqueness and Conventionality

6. Representationalism as a Basis for Metaphysics

6.1. Representationalism and its Critics

6.1.1. Representational Theory of Measurement as a Mathematical Framework

6.1.2. Is Representationalism Sufficiently Realist?

6.2. When is an Attribute Quantitative?

6.2.1. Uniqueness, not Representation

6.2.2. Intuitive Difference

6.2.3. Formal Difference

6.2.4. Criterion in Terms of the Structure Itself

6.3. How RTM Constrains the Metaphysics of Quantities

6.3.1. Role of Structure

6.3.2. Invarianceas Meaningfulness

6.3.3. Conclusion

7. Ontologies for Quantities

7.1. Universals as Relata

7.1.1. Aristotelian Universals

7.1.2. Platonic Universals

7.1.3. Hybrid Views of Quantities as Universals

7.2. Particulars as Relata

7.2.1. Objects as Relata

7.2.2. Space-Time Points as Relata

7.2.3. Points beyond Space-Time: Limitations and Modifications of Field's Programme

7.3. Quantity Substantivalism

7.3.1. Substantivalism

7.3.2. Locationism

8. Questions of Priority: Relations or Relata?

8.1. Debate between Absolutists and Comparativists

8.1.1. Prelude

8.1.2. Contenders

8.1.3. Initial Victory for Absolutism

8.2. Why we should not be Absolutists

8.2.1. Scalings and Non-trivial Automorphisms

8.2.2. Homogeneity and Quiddities

8.3. Sophisticated Substantivalism as an Alternative

8.3.1. Sophisticated Substantivalism

8.3.2. Background Structure: The Response of Sophisticated Substantivalism

8.3.3. Are Sophisticated Substantivalists Cheating?

9. Fundamental Structure for Quantities

9.1. Invariantism: Intrinsicalism or Quotienting?

9.1.1. Introduction

9.1.2. Intrinsic Explanations and Fundamental Theories

9.1.3. Fundamentalism and Quotienting

9.2. Representational Theory as Fundamental Theory

9.2.1. Fundamental Mass Facts and Representational Axioms

9.2.2. Preferred Interpretations

9.2.3. Group Structure as Fundamental Structure?

9.3. Classifying Structures and Levels of Determinacy

9.3.1. Legacy of the Erlanger Programme

9.3.2. Quantitativeness and Determinacy

10. Structuralist View of Quantities

10.1. Threads of Structure

10.1.1. What is Structuralism?

10.1.2. Homogeneous Relational Structures

10.1.3. Structure of an Archimedean Ordered Group

10.2. Mathematical or Physical Structure?

10.2.1. Reductionist and Non-Reductionist Views of Quantities

10.2.2. Structuralism as Non-Reductionism

10.2.3. Final Thoughts.

Notes:

This edition also issued in print: 2020.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-19-189588-1

0-19-257393-4

0-19-257394-2