David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophy of Science 38 (2):157-169 (1971)
Using H. Whitney's algebra of physical quantities and his definition of a similarity transformation, a family of similar systems (R. L. Causey  and ) is any maximal collection of subsets of a Cartesian product of dimensions for which every pair of subsets is related by a similarity transformation. We show that such families are characterized by dimensionally invariant laws (in Whitney's sense, , not Causey's). Dimensional constants play a crucial role in the formulation of such laws. They are represented as a function g, known as a system measure, from the family into a certain Cartesian product of dimensions and having the property gφ =φ g for every similarity φ . The dimensions involved in g are related to the family by means of certain stability groups of similarities. A one-to-one system measure is a proportional representing function, which plays an analogous role in Causey's theory, but not conversely. The present results simplify and clarify those of Causey
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Marc Lange (2009). Dimensional Explanations. Noûs 43 (4):742-775.
Brent Mundy (1987). Faithful Representation, Physical Extensive Measurement Theory and Archimedean Axioms. Synthese 70 (3):373 - 400.
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