The Metaphysics of Quantities

Research output: Book/ReportBook


This book articulates and defends a new and original answer to two questions: What are physical quantities and what makes them quantitative? This novel position—substantival structuralism—says that quantitativeness is an irreducible feature of attributes, and quantitative attributes are best understood as substantival structured spaces. Physical quantities like mass, momentum, or temperature play an important role in formulating laws of nature and in testing scientific theories. It is therefore important to have a clear philosophical understanding of what makes these attributes special. Traditional views of quantities have either suggested that quantities are determinables, that is, attributes that require determination by magnitudes, or that quantities are in some sense numerical, but neither view is satisfactory.
The book shows how to use the representational theory of measurement to provide a better, more abstract criterion for quantitativeness: only attributes whose numerical representation has a high degree of uniqueness are quantitative. The best ontology for quantities is offered by a form of sophisticated substantivalism applied to quantities as structured spaces. Substantivalism, because an infinite domain is required to satisfy the formal requirements of quantitativeness; structured spaces, because they contain fundamental relations; sophisticated substantivalism because the identity of positions in such spaces is irrelevant. The resulting view is a form structuralism about quantities. The topic of the book falls squarely in the metaphysics of science, with contributions to general metaphysics and philosophy of science.
Original languageEnglish
Place of PublicationOxford
PublisherOxford University Press
Number of pages240
ISBN (Electronic)9780191895883, 9780192573940
ISBN (Print)9780198837084
Publication statusPublished - 28 May 2020


  • physical quantities
  • magnitudes
  • structuralism
  • philosophy of science
  • metaphysics
  • substantivalism
  • quantitativeness
  • representational measurement theory
  • ontology
  • metaphysics of science


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