Our aim in this article is to show how the theory of conceptual spaces can be useful in describing diachronic changes to conceptual frameworks, and thus useful in understanding conceptual change in the empirical sciences. We also compare the conceptual space approach to Moulines’s typology of intertheoretical relations in the structuralist tradition. Unlike structuralist reconstructions, those based on conceptual spaces yield a natural way of modeling the changes of a conceptual framework, including noncumulative changes, by tracing the changes to the (...) dimensions that reconstitute a conceptual framework. As a consequence, the incommensurability of empirical theories need not be viewed as a matter of conceptual representation. (shrink)

Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

This article provides a spatial analysis of the conceptual framework of fluid dynamics during the nineteenth century, focusing on the transition from the Euler equation to the Navier–Stokes equation. A dynamic version of Peter Gärdenfors's theory of conceptual spaces is applied which distinguishes changes of five types: addition and deletion of special laws; change of metric; change in importance; change in separability; addition and deletion of dimensions. The case instantiates all types but the deletion of dimensions. We also provide a (...) new view upon limiting case reduction at the conceptual level that clarifies the relation between the predecessor and successor conceptual framework. The nineteenth-century development of fluid dynamics is argued to be an instance of normal science development. (shrink)

The late nineteenth century gradually witnessed a liberalization of the kinds of mathematical object and forms of mathematical reasoning permissible in physical argumentation. The construction of theories of units illustrates the slow and difficult spread of new “algebraic” modes of mathematical intelligibility, developed by leading mathematicians from the 1830s onwards, into elementary arithmetical pedagogy, experimental physics, and fields of physical practice like telegraphic engineering. A watershed event in this process was a clash that took place during 1878 between J. D. (...) Everett and James Thomson over the meaning and algebraic manipulation of dimensional formulae. This precipitated the emergence of rival “Maxwellian” and “Thomsonian” approaches towards interpreting and applying “dimensional” equations, which expressed the relationship between derived and fundamental units in an absolute system of measurement. What at first looks like a dispute over a seemingly esoteric mathematical tool for unit conversion turns out to concern Everett’s break with arithmetical algebra in the representation and manipulation of physical quantities. This move prompted a vigorous rebuttal from Thomsonian defenders of an orthodox “arithmetical empiricism” on epistemological, semantic, or pedagogical grounds. Their resistance in Victorian Britain to a shift in mathematical intelligibility is suggestive of the difficult birth of theoretical physics, in which the intermediate steps of a mathematical argument need have no direct physical meaning. (shrink)

This paper offers a novel way of reconstructing conceptual change in empirical theories. Changes occur in terms of the structure of the dimensions—that is to say, the conceptual spaces—underlying the conceptual framework within which a given theory is formulated. Five types of changes are identified: (1) addition or deletion of special laws, (2) change in scale or metric, (3) change in the importance of dimensions, (4) change in the separability of dimensions, and (5) addition or deletion of dimensions. Given this (...) classification, the conceptual development of empirical theories becomes more gradual and rationalizable. Only the most extreme type—replacement of dimensions—comes close to a revolution. The five types are exemplified and applied in a case study on the development within physics from the original Newtonian mechanics to special relativity theory. (shrink)

Academia’s mathematical metaphysics are briefly explored en route to an elaboration of the qualitatively rigorous requirements underpinning the calibration and unambiguous interpretation of quantitative instrumentation in any science. Of particular interest are Gadamer’s emphases on number as the paradigm of the noetic, on the role of play in interpretation, and on Hegel’s sense of method as the activity of the thing itself that thought experiences. These point toward and overlap with (1) Latour’s study of the metrological social networks through which (...) technological phenomena are brought into language as modes of being that can be understood, and (2) the way that Rasch’s models for measurement comprise a potential beginning for metaphysically astute, qualitatively and quantitatively integrated, mathematical methods in the social sciences. The paper closes with observations on the general problem that is philosophy, the need to remain open to multiplicities of meaning even as clear understandings are sought and obtained. (shrink)

The philosophical significance attached to the construction of systems of units has traditionally been confined to the notion of convention, while their adoption was considered to be the exclusive province of the history and sociology of science. Against this tradition, a close articulation between history, philosophy, and sociology of science is needed in order to analyse the recent reform of the International system of units. In the new SI, units are redefined on the basis of certain fundamental constants of nature, (...) established by physical theories, whose values are fixed without uncertainty. The purpose of this article is to show that the redefinition of SI units, far from being a convention, involves a holistic reconstruction of our concepts of quantities from accepted theoretical laws. Fixing the values of the defining constants stabilizes these laws within the framework of physics through a twofold adjustment procedure that ensures both a semantic coordination between theory and world and an intersubjective coordination between human agents required by social activities. This double adjustment implies a treatment of uncertainties that results in closely entwining the pursuit of truth as correspondence and truth as coherence which turn out to be complementary, thus highlighting the anthropological underpinnings of scientific realism. (shrink)

The guest editors would like to thank the University of Paris and the ENSA Paris-Val de Seine for having provided premises to successfully host the 2018 "Measurement at the Crossroads" conference in Paris.Our thanks extend to our funding sources: the conference was made possible thanks to the generous support of the Institut Humanités, Sciences et Sociétés, the SPHERE laboratory and the Laboratoire Matériaux et Phénomènes Quantiques of the University of Paris, the department of History and Philosophy of Science of the (...) University of Paris, the Laboratoire National de métrologie et d'Essais, and the University of Geneva.We would like to thank the many people who contributed to the organization of... (shrink)

Euclidean geometry, statics, and classical mechanics, being in some sense the simplest physical theories based on a full-fledged mathematical apparatus, are well suited to a historico-philosophical analysis of the way in which a physical theory differs from a purely mathematical theory. Through a series of examples including Newton’s Principia and later forms of mechanics, we will identify the interpretive substructure that connects the mathematical apparatus of the theory to the world of experience. This substructure includes models of experiments, models of (...) measurement, and modular connections with partial theories. It evolves during the life of a theory as physicists learn how to apply it in various contexts. It should nevertheless be regarded as an integral part of a genuine physical theory since the theory would otherwise degenerate into pure mathematics. (shrink)