The important role of mathematical representations in scientific thinking has received little attention from cognitive scientists. This study argues that neglect of this issue is unwarranted, given existing cognitive theories and laws, together with promising results from the cognitive historical analysis of several important scientists. In particular, while the mathematical wizardry of James Clerk Maxwell differed dramatically from the experimental approaches favored by Michael Faraday, Maxwell himself recognized Faraday as “in reality a mathematician of a very high order,” and his (...) own work as in some respects a re‐representation of Faraday’s field theory in analytic terms. The implications of the similarities and differences between the two figures open new perspectives on the cognitive role of mathematics as a learned mode of representation in science. (shrink)

It is demonstrated that Maxwellian electrodynamics was created as a result of the old pre-Maxwellian programmes’s reconciliation: the electrodynamics of Ampère–Weber, the wave theory of Young–Fresnel and Faraday’s programme. Maxwell’s programme finally superseded the Ampère–Weber one because it assimilated the ideas of the Ampère–Weber programme, as well as the presuppositions of the programmes of Young–Fresnel and Faraday. Maxwell’s victory became possible because the core of Maxwell’s unification strategy was formed by Kantian epistemology. Maxwell put forward as a basic synthetic principle (...) an idea that radically differed from that of rival approaches by its open, flexible and contra-ontological character. “Action at a distance”, “incompressible fluid”, “molecular vortices” were contrived analogies for Maxwell, capable only of directing the researcher to the “right” mathematical relations Kantian epistemology subsequently enabled Helmholtz and Hertz to arrive at a version of Maxwell’s theory that served as a heuristical basis for the discovery of radio waves. Finally, though neither of Einstein’s relativistic ideas came directly from Kant, they were made possible by the Kantian worldview that had permeated Einstein’s thinking. The Maxwellian revolution can be described in terms of Habermas’s communicative rationality encouraging the establishment of mutual understanding between the various scientific communities. Maxwell’s programme constituted a progressive step in respect to its rivals because it constituted a basis of communication and interpenetration between the main paradigms of 19th century physics. (shrink)

Key words: rationality, communication, maxwellian revolution, Ampere-Weber research programme, synthesis, Kantian epistemology.. Why did Maxwell’s programme supersede the Ampere-Weber one? – To answer the question one has to consider the intertheoretic context of maxwellian electrodynamics genesis and development. It is demonstrated that maxwellian electrodynamics was created as a result of the old pre-maxwellian programmes reconciliation: the electrodynamics of Ampere-Weber, the wave theory of Young-Fresnel and Faraday’s programme. The programmes’ meeting led to construction of the hybrid theory at first with an (...) irregular set of theoretical schemes. However, step by step, on revealing and gradual eliminating the contradictions between the programmes involved, the hybrid set is “put into order”.A hierarchy of theoretical schemes starting from the crossbreeds and up to usual hybrids is set up. And after the displacement current construction the interpenetration of the pre-maxwellian programmes begins that markes the commencement of theoretical schemes of optics and electromagnetism real unification. Maxwell’s programme did supersede the Ampere-Weber one because it did assimilate the ideas of the Ampere-Weber programme, as well as the presuppositions of the programmes of Young-Fresnel and Faraday properly co-ordinating them with each other. But the opposite proposition is not true. Ampere-Weber programme did not assimilate the propositions of the Maxwellian programme. Maxwell’s victory became possible because the core of Maxwell’s unification strategy was formed by Kantian epistemology looked through the prism of William Whewell and such representatives of Scottish Enlightenment as Thomas Reid and William Hamilton. Maxwell did put forward as a basic synthetic principle the idea that radically differed from that of Ampere-Weber approach by its open, flexible and contra-ontological, strictly epistemological, Kantian character. For Maxwell, ether was not the last building block of physical reality, from which all the charges and fields should be constructed. “Action at a distance”, “incompressible fluid”, “molecular vortices” were contrived analogies for Maxwell, capable only to direct the researcher at the “right” mathematical relations. Namely the application of Kantian epistemology enabled Hermann von Helmholtz and his pupil Heinrich Hertz to arrive at such a version of Maxwell’s theory that served a heuristical basis for the radio waves discovery. (shrink)

Stein has raised a fundamental problem for any attempt to characterize instrumentalism and realism as substantive alternatives. This is the distinguishability problem, which consists in the problem of developing a form of instrumentalism that is substantially different from a plausible realist alternative and the problem of showing that this form of instrumentalism does justice to actual scientific practice. Using Stein’s own discussion of Maxwell, I formulate instrumentalism and realism as a scientist’s attitudes toward models, where an attitude is understood to (...) be a complex of the scientist’s belief and intention regarding models. Developing a case study of Benzer’s modeling practice, I show that each attitude can structure inquiry differently and argue that to understand certain aspects of scientific practice, such as the practice of genetic mapping in Benzer’s work, we sometimes need to appeal to the coexistence of these attitudes. (shrink)

I want to combine two hitherto largely independent research projects, scientific understanding and mechanistic explanations. Understanding is not only achieved by answering why-questions, that is, by providing scientific explanations, but also by answering what-questions, that is, by providing what I call scientific descriptions. Based on this distinction, I develop three forms of understanding: understanding-what, understanding-why, and understanding-how. I argue that understanding-how is a particularly deep form of understanding, because it is based on mechanistic explanations, which answer why something happens in (...) virtue of what it is made of. I apply the three forms of understanding to two case studies: first, to the historical development of thermodynamics and, second, to the differences between the Clausius and the Boltzmann entropy in explaining thermodynamic processes. (shrink)

Any advanced theory of physics contains modules defined as essential components that are themselves theories with different domains of application. Different kinds of modules can be distinguished according to the way in which they fit in the symbolic and interpretive apparatus of a theory. The number and kind of the modules of a given theory vary as the theory evolves in time. The relative stability of modules and the variability of their insertion in other theories play a vital role in (...) the application, comparison, construction, and communication of theories. Modularity conveys some global unity to physics through the sharing of modules by diverse theories. This alternative to rigid hierarchies and holistic totalities permits a dynamical, plastic, and symbiotic approach to physical theory. (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)

The relativistic revolution led to varieties of neo-Kantianism in which constitutive principles define the object of scientific knowledge in a domain-dependent and historically mutable manner. These principles are a priori insofar as they are necessary premises for the formulation of empirical laws in a given domain, but they lack the self-evidence of Kant’s a priori and they cannot be identified without prior knowledge of the theory they purport to frame. In contrast, the rationalist endeavors of a few masters of theoretical (...) physics have led to comprehensibility conditions that are easily admitted in a given domain and yet suffice to generate the theory of this domain. The purpose of this essay is to compare these two kinds of relativized a priori, to discuss the nature of the comprehensibility conditions, and to demonstrate their effectiveness in a modular conception of physical theories. (shrink)

John Herschel's discussion of hypotheses in the Preliminary Discourse on Natural Philosophy has generated questions concerning his commitment to the principle that hypothetical speculation is legitimate only if warranted by inductive evidence. While Herschel explicitly articulates an inductivist philosophy of science, he also asserts that “it matters little how {a hypothesis or theory} has been originally framed” when it can withstand extensive testing and empirical scrutiny. This evidence has convinced some that Herschel endorses an early form of hypothetico-deductivism. I aim (...) to clarify this interpretive puzzle and adduce evidence in support of the inductivist interpretation of Herschel's philosophy of science by examining his published account of a series of experiments in the domain of electromagnetism. (shrink)

Cet article vise à éclairer le contexte universitaire et éditorial qui favorisa la publication du Treatise on electricity and magnetism de James Clerk Maxwell afin de mieux cerner la nature de cette entreprise scientifique. Le projet fut formé en 1867 à l'occasion d'une réforme introduisant l'étude de l'électricité et du magnétisme dans l'enseignement délivré à Cambridge et s'inscrivait dans un mouvement plus vaste qui développait l'enseignement de ces disciplines dans les universités britanniques. L'étude des relations entre le projet de Maxwell (...) et d'autres ouvrages contemporains indique que le Treatise était en situation de devenir un ouvrage de référence en Grande-Bretagne. Ainsi, le livre de Maxwell était-il l'instrument d'une très ambitieuse tentative de transformation de l'électromagnétisme, indissociable de son contexte et conforme à sa fonction pédagogique. (shrink)

Prompted by Hasok Chang’s conception of the history and philosophy of science (HPS) as the continuation of science by other means, I examine the possibility of obtaining scientific knowledge through philosophical criticism and reflection, in the light of four historical cases, concerning (i) the role of absolute space in Newtonian dynamics, (ii) the purported contraction of rods and retardation of clocks in Special Relativity, (iii) the reality of the electromagnetic ether, and (iv) the so-called problem of time’s arrow. In all (...) four cases it is clear that a better understanding of such matters can be achieved —and has been achieved— through conceptual analysis. On the other hand, however, it would seem that this kind of advance has more to do with philosophical questions in science than with narrowly scientific questions. Hence, if HPS in effect continues the work of science by other means, it could well be doing it for other ends than those that working scientists ordinarily have in mind. (shrink)