Part II: Suppes and the mature theory. Representation and uniqueness.

It has become customary to locate the origins of modern measurement theory in the works of Helmholtz and Hölder. If by ‘modern measurement theory’ is meant the representational theory, then this may not be an accurate assessment. Both Helmholtz and Hölder present theories of measurement which are closely related to the classical conception of measurement. Indeed, Hölder can be interpreted as bringing this conception to fulfilment in a synthesis of Euclid, Newton, and Dedekind. The first explicitly representational theory appears to (...) have been Russell's. He rejected the traditional concept of quantity and its connection to number, making the use of number in quantitative science problematical. He solved the problem via representationalism. (shrink)

The direct use of a physical law for the purpose of measurement creates a problem of circularity: the law needs to be empirically tested in order to ensure the reliability of measurement, but the testing requires that we already know the value of the quantity to be measured. This problem is discussed through some detailed examples of energy measurements in quantum physics; three major methods are analyzed in their interrelation, with a focus on the method of “material retardation.” It seems (...) that the only reasonable solution is to establish the law needed for the measurement by relying on an alternate method of measurement. This solution is also circular, since it amounts to letting different measurement methods justify each other. However, this circularity can be fruitful for the process of concept building; meaning can be created in a web of interconnected measurement methods. (shrink)

ArgumentHermann von Helmholtz’s distinction between “pure intuitive” and “physical” geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant’s claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it (...) followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz’s understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz’s development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz’s arguments concerning geometry. (shrink)