Metaphysics of Quantities

Quantities are ubiquitous in science and especially in the physical sciences. My project aims to provide a comprehensive metaphysical account of quantities. A metaphysical account of quantities must address three key questions:

  1. What distinguishes quantities from other attributes like qualities and kinds?
  2. What ontology is needed for quantities?
  3. What is the relationship between quantities, theory, and measurement?

In this project I develop and defend a systematic answer to all three questions. The resulting view of quantities is (cautiously) realist in the sense of scientific realism, structuralist, substantivalist, and non-reductionist.

Select draft chapters are available below.

Table of Contents


1. Introduction 

1.1. Who needs a metaphysics of quantities?

1.2. The philosophical challenges of quantities

1.3. Structure of the book

2. Realism about Quantities

2.1. Empiricism and realism about measurement

2.2. Operationalism

2.3. Coherentism

2.4. Realism about quantities as an aspect of scientific realism

3. The representationalist theory of measurement

3.1. Theories of measurement

3.2. Representationalism and the Foundations of Measurement

3.3. Representationalism and empiricism

3.4. Representationalism as a form of structuralism

4. When is an attribute quantitative?

4.1. Numbers: neither necessary nor sufficient for quantities

4.2. No sharp distinction between quantities and qualities?

4.3. Different types of quantities and their representations

4.4. Where to draw the line

5. Counting and measuring

5.1. Dimensions, units, quantities

5.2. Case study: The SI-base quantity amount of substance

5.3. Counting is not measuring

6. Against the determinable/determinate model

6.1. Determinables and Determinates

6.2. General problems with the model as applied to quantities

6.3. Case study: spin as a determinable

6.4. Conclusion

7. Ontologies for quantities

7.1. Universals as relata

7.2. Particulars as relata

7.3. Quantity substantivalism

8. Comparative and absolute quantities

8.1. The debate: absolutism vs. comparativism

8.2. Are absolutism and comparativism empirically equivalent?

8.3. Comparativism for quantities and relationalism for spacetime

8.4. Different types of quantities and the prospects for comparativism

9. Intrinsicalism vs. Structuralism

9.1. Field’s intrinsicalism

9.2. Meta-metaphysical interlude

9.3. Representationalism: Fundamentalism or Quotienting?

9.4. Representationalism as Structuralism?

10. So what are quantities, then?

10.1. The picture so far

10.2. The mathematical structure of physical quantities

10.3. The final view




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