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)

The fact that the same equations or mathematical models reappear in the descriptions of what are otherwise disparate physical systems can be seen as yet another manifestation of Wigner's “unreasonable effectiveness of mathematics.” James Clerk Maxwell famously exploited such formal similarities in what he called the “method of physical analogy.” Both Maxwell and Hermann von Helmholtz appealed to the physical analogies between electromagnetism and hydrodynamics in their development of these theories. I argue that a closer historical examination of the different (...) ways in which Maxwell and Helmholtz each deployed this analogy gives further insight into debates about the representational and explanatory power of mathematical models. (shrink)

Work on analogy has been done from a number of disciplinary perspectives throughout the history of Western thought. This work is a multidisciplinary guide to theorizing about analogy. It contains 1,406 references, primarily to journal articles and monographs, and primarily to English language material. classical through to contemporary sources are included. The work is classified into eight different sections (with a number of subsections). A brief introduction to each section is provided. Keywords and key expressions of importance to research on (...) analogy are discussed in the introductory material. Electronic resources for conducting research on analogy are listed as well. (shrink)

I survey a broad variety of models with an eye to asking what kind of model each is in the following sense: in virtue of what is each of them regarded as a model? It will be seen that when we classify models according to the answer to this question, it comes to light that the notion of model predominant in philosophy of science covers only some of the kinds of models used in scientific contexts. The notion of a model (...) predominant in philosophy of science requires that a model be related to something formal, such as equations or statements. Not all the examples provided in the brief survey in this paper fit that notion of a model. I identify another kind of model that ought to be included in philosophical and foundational studies of scientific models, which I call a “piece of the world” kind of model, to contrast with a “realm of thought” kind of model. These models also have formal methodologies associated with them, and, hence, analytic philosophers of science can embrace them without abandoning the rigor that has characterized the discipline. (shrink)

Sometimes instances of perceived causation turn out to lack causal relata. The reasons may vary. Causation may display itself as prevention, or as omission, and in some cases causation occurs within such complex environments that few of the things we associate with causes and effects are true of them, etc. But even then, there may be causal explanations to be had. This suggests that the explanatory power of causal reports have other sources than the relation between cause and effect. In (...) this paper it is argued that the causal mechanisms we allude to in explanations have relevant determinables other than the traditionally acknowledged ones. The traditional but in this aspect mistaken view of causation is to be blamed. Discernability, complexity of manifestation, originality, and even stability have often been overlooked. We know, that, in fact, heat is a constant attendant of flame; but what is the connexion between them, we have no room so much as to conjecture or imagine. (Hume 1777, VII. 2, 64). (shrink)

In the course of his researches in electromagnetism and the kinetic theory of gases, James Clerk Maxwell gave some thought to the nature of science itself. His observations in this field are of interest today not only because they are his, but because they are still instructive. Maxwell's views are to be found in the many asides with which he enlivened his scientific papers and treatises and in the various articles and reviews which he prepared for more popular consumption. The (...) topics discussed bear on his own contributions to physics; they include the logic of dynamical explanation, the method of physical analogy, and the perennial question of action at a distance versus contiguity. In the present essay, I wish to discuss Maxwell's views on dynamical explanation. (shrink)

This paper distinguishes in Maxwell’s thought between “atomic molecules” and “ultimate atoms,” and arrives at a set of properties that characterize each type of atom. It concludes that Maxwell is a mathematical atomist, an approach that entails the notion that although it is impossible to observe the ultimate atoms as free particles, we can nevertheless study them as mathematical observables, on the caveat that mathematical formalism remains tied to phenomenalism and to theoretical interpretations of such phenomena as, for example, mass (...) and force variations, gravitational pull, gas diffusion and viscosity, and heat conduction. (shrink)