Abstract
Abstract This chapter introduces the representational theory of measurement as the relevant formal framework for a metaphysics of quantities. After presenting key elements of the representational approach, axioms for different measurement structures are presented and their representation and uniqueness theorems are compared. Particular attention is given to Hölder’s theorem, which in the first instance describes conditions for quantitativeness for additive extensive structures, but which can be generalized to more abstract structures. The last section discusses the relationship between uniqueness, the hierarchy of scales, and the measurement-theoretic notion of meaningfulness. This chapter provides the basis for Chapter 6, which makes use of more abstract results in measurement theory.
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