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)

In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the (...) very idea of using this principle as a constructive tool were born in this context. The consequences of Poincaré’s and Einstein’s awareness of this approach are analyzed. Lastly, the legitimacy and significance of a relativity-based derivation of Newton’s second law are briefly discussed in a more philosophical vein. (shrink)

In this paper I examine the notion and role of metaphors and illustrations in Maxwell's works in exact science as a pathway into a broader and richer philosophical conception of a scientist and scientific practice. While some of these notions and methods are still at work in current scientific research-from economics and biology to quantum computation and quantum field theory-, here I have chosen to attest to their entrenchment and complexity in actual science by attempting to make some conceptual sense (...) of Maxwell's own usage; this endeavour includes situating Maxwell's conceptions and applications in his own culture of Victorian science and philosophy. I trace Maxwell's notions to the formulation of the problem of understanding, or interpreting, abstract representations such as potential functions and Lagrangian equations. I articulate the solution in terms of abstract-concrete relations, where the concrete, in tune with Victorian British psychology and engineering, includes the muscular as well as the pictorial. This sets the basis for a conception of understanding in terms of unification and concrete modelling, or representation. I examine the relation of illustration to analogies and metaphors on which this account rests. Lastly, I stress and explain the importance of context-dependence, its consequences for realism-instrumentalism debates, and Maxwell's own emphasis on method. (shrink)

Historians of the sciences have paid great attention to the ways that faith in what has been called the quantitative spirit emerged as a dominant feature of the politics of science, a theme of obvious salience in current epidemiological and climate crises. There are instructive connexions between measurement practices and orientation towards other cultures—as though scientific modernity somehow appeared through the primacy of robust quantification over subaltern, past, and exotic worlds, where merely provisional judgment allegedly still operated. This highly simplistic (...) Orientalist distinction accompanied assumptions that the remote was best understood as the ancient, a viewpoint common at the same late Enlightenment moment as the apparent institutionalisation of the regime of the exact sciences within European polities. Under this regime, precision surveys—the way the state saw—have often been understood as integral for European societies and even more so in colonised territories. This version of what might be called metrological Orientalism can be disoriented through excellent recent scholarship that explores complex entanglements of measurement practices circulating across very different scientific cultures, which shows how precision devices that claimed merely to represent phenomena often helped produce them. Studies of select cases of relations between European practitioners and indigenous experts, in fields such as Egyptian hydraulics or South Pacific surveys, can reveal even more: the role that judgment and exactitude played in forging very different, politically significant versions of the past history of the sciences. These disorientations can aid novel forms of historical understanding of the politics of science. (shrink)

The ArgumentIt has long been apparent that in the nineteenth century, mathematics in France and England developed along different lines. The differences, which might well be labelled stylistic, are most easy to see on the foundational level. At first this may seem surprising because it is such a fundamental area, but, upon reflection, it is to be expected. Ultimately discussions about the foundations of mathematics turn on views about what mathematics is, and this is a question which is answered by (...) a variety of different groups including mathematicians, students, curricular planners, parents, etc. Mathematical practice rests on some kind of mixture of the answers to this fundamental question which come from these diverse groups. Comparing the cultural matrices which supported mathematics in France and Britain in the first decades of the nineteenth century sheds light on the real though often subtle differences in the ways the subject was pursued in the two countries. (shrink)

The ArgumentThis paper deals with the achievements of those French mathematicians active in the period 1800–1830 who oriented their work specifically around the needs of engineering and technology. In addition to a review of their achievements, the principal organizations and institutions are noted, as is their importance as sources of employment and influence.The argument is centered on the word ‘neglected“ in the title. A case is made that a mass of work was produced which made considerable impact at the time (...) but has been overlooked or even completely ignored by historians since. The paper begins with a general discussion of the notion of context, both for the historical figures and for their supposed historians, and several examples of historical distortion are given.Regarding France itself, we see a professional and research profile rather different from that in other countries. The question of national differences in the organization and prosecution of science is thereby sharply exposed. (shrink)