In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics, on the possibility of quantitative psychology, and on the meaning of temperature measurement. Late nineteenth-century scrutinisers of the foundations of mathematics made little of Helmholtz’s essay. Yet it inspired two mathematicians with an eye on physics, and a few philosopher-physicists. The aim of the present paper is to situate Helmholtz’s contribution (...) in this complex array of nineteenth-century philosophies of number, quantity, and measurement.Author Keywords: Helmholtz; Measurement; Arithmetic; P. Du Bois-Reymond; H. and R. Grassmann; J. von Kries. (shrink)

The kinds of models discussed in this paper function as measuring instruments. We will concentrate on two necessary steps for measurement: (1) the search of a mathematical representation of the phenomenon; (2) this representation should cover an invariant relationship between the properties of the phenomenon to be measured and observable accociated attributes of a measuring instrument. Therefore, the measuring instrument should function as a nomological machine. However, invariant relationships are not necessarily ceteris paribus regularities, but could also occur when the (...) influence of the environment is negligible. Then we are able to achieve accurate measurements outside the laboratory. (shrink)

In 1870, Hermann von Helmholtz criticized the Kantian conception of geometrical axioms as a priori synthetic judgments grounded in spatial intuition. However, during his dispute with Albrecht Krause (Kant und Helmholtz über den Ursprung und die Bedeutung der Raumanschauung und der geometrischen Axiome. Lahr, Schauenburg, 1878), Helmholtz maintained that space can be transcendental without the axioms being so. In this paper, I will analyze Helmholtz’s claim in connection with his theory of measurement. Helmholtz uses a Kantian argument that can be (...) summarized as follows: mathematical structures that can be defined independently of the objects we experience are necessary for judgments about magnitudes to be generally valid. I suggest that space is conceived by Helmholtz as one such structure. I will analyze his argument in its most detailed version, which is found in Helmholtz (Zählen und Messen, erkenntnistheoretisch betrachtet 1887. In: Schriften zur Erkenntnistheorie. Springer, Berlin, 1921, 70–97). In support of my view, I will consider alternative formulations of the same argument by Ernst Cassirer and Otto Hölder. (shrink)

Hermann von Helmholtz has been widely acknowledged as one of the forerunners of contemporary theories of measurement. However, his conception of measurement differs from later, representational conceptions in two main respects. Firstly, Helmholtz advocated an empiricist philosophy of arithmetic as grounded in some psychological facts concerning quantification. Secondly, his theory implies that mathematical structures are common to both subjective experiences and objective ones. My suggestion is that both of these differences depend on a classical approach to measurement, according to which (...) the arithmetic laws of addition define what is measurable as a particular domain for their application, and, at the same time, the extensibility of these laws to all known physical processes works as a heuristic principle for empirical research. Such an approach is worth reconsidering, not only because it lends plausibility to some of the controversial aspects of Helmholtz’s theory, but also because it offers a philosophical perspective on quantification problems that originated in the nineteenth-century.This paper draws insights on Helmholtz’s philosophical views from his engagement with the measurability of sensations via Fechner’s psychophysical law. This seems to be in contrast with the fact that the reception of Helmholtz’s theory culminated with the formulation of the theory of extensive measurement. I will contend that Helmholtz reached a no less important standpoint in the nineteenth-century debate on whether sensations are different (i.e., intensive) kinds of magnitudes and on how, if at all, they can be measured. (shrink)

Ernest Nagel played a key role in bridging the gap between American philosophy and logical empiricism. He introduced European philosophy of science to the American philosophical community but also remained faithful to the naturalism of his teachers. This paper aims to shed new light on Nagel’s intermediating endeavors by reconstructing his philosophical development in the late 1920s and 1930s. This is a decisive period in Nagel’s career because it is the phase in which he first formulated the principles of his (...) naturalism and spent a year in Europe to visit the key centers of logical empiricism. Building on a range of published and unpublished papers, notes, and correspondence—including hundreds of pages of letters to his close friend Sidney Hook—I reconstruct Nagel’s philosophical development, focusing especially on the philosophical influence of John Dewey, Morris R. Cohen, Rudolf Carnap, and Hans Reichenbach. (shrink)

Psychometrics and the representational theory of measurement are widely used in social scientific measurement. They are currently pursued largely in isolation from one another. I argue that despite their separation in practice, RTM and psychometrics are complementary approaches, because they can contribute in complementary ways to the establishment of what I argue is a crucial measurement property, namely, representational interpretability. Because RTM and psychometrics are complementary in the establishment of representational interpretability, the current separation of measurement approaches is unfounded. 1Introduction2Two (...) Approaches to Measurement 2.1Representational theory of measurement2.2Psychometrics2.3Representational interpretability3Complementarity, Conceptually 3.1Representational theory of measurement: Conditions of representational interpretability3.2Psychometrics: Evidence of representational interpretability4Complementarity in Action 4.1What is the Rasch model?4.2Rasch and conjoint measurement5Conclusion: Critics and Fruits of Complementarity. (shrink)

As an aspiring science in the nineteenth and early twentieth centuries, psychology pursued quantification. A problem was that degrees of psychological attributes were experienced only as greater than, less than, or equal to one another. They were categorised as intensive magnitudes. The meaning of this concept was shifting, from that of an attribute possessing underlying quantitative structure to that of a merely ordinal attribute . This fluidity allowed psychologists to claim that their attributes were intensive magnitudes and measurable . This (...) claim was supported by an argument that order entails quantity. As adapted by psychometricians, the argument was that if an attribute is ordered, then the differences between its degrees are quantitative and, therefore, measurable. However, in a paper ignored in psychology for six decades, the issue was resolved mathematically and the resolution implies that the psychometricians’ argument was fallacious. (shrink)