 Defining measurement as numerical assignment raises the question: which assignments are adequate, and under what conditions? Early measurement theorists like Helmholtz (1887), Hölder (1901) and Campbell (1920) argued that numbers are adequate for expressing magnitudes insofar as algebraic operations among numbers mirror empirical relations among magnitudes. For example, the qualitative relation “longer than” among rigid rods is (roughly) transitive and asymmetrical, and in this regard shares structural features with the relation “larger than” among numbers. Moreover, the end-to-end concatenation of rigid rods shares structural features—such as associativity and commutativity—with the mathematical operation of addition. A similar situation holds for the measurement of weight with an equal-arms balance. Here deflection of the arms provides ordering among weights and the heaping of weights on one pan constitutes concatenation.