Philosophy of Science 45 (1):1-16 (1978)

Abstract
In formal theories of measurement meaningfulness is usually formulated in terms of numerical statements that are invariant under admissible transformations of the numerical representation. This is equivalent to qualitative relations that are invariant under automorphisms of the measurement structure. This concept of meaningfulness, appropriately generalized, is studied in spaces constructed from a number of conjoint and extensive structures some of which are suitably interrelated by distribution laws. Such spaces model the dimensional structures of classical physics. It is shown that this qualitative concept corresponds exactly with the numerical concept of dimensionally invariant laws of physics
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DOI 10.1086/288776
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References found in this work BETA

Introduction to Logic.Roland Hall - 1960 - Philosophical Quarterly 10 (40):287-288.
On the Notion of Invariance in Classical Mechanics.J. C. C. Mckinsey & Patrick Suppes - 1955 - British Journal for the Philosophy of Science 5 (20):290-302.
Similar Systems and Dimensionally Invariant Laws.R. Duncan Luce - 1971 - Philosophy of Science 38 (2):157-169.

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On the Space-Time Ontology of Physical Theories.Kenneth L. Manders - 1982 - Philosophy of Science 49 (4):575-590.

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