This paper defends the thesis of learning from non-causal models: viz. that the study of some model can prompt justified changes in one’s confidence in empirical hypotheses about a real-world target in the absence of any known or predicted similarity between model and target with regards to their causal features. Recognizing that we can learn from non-causal models matters not only to our understanding of past scientific achievements, but also to contemporary debates in the philosophy of science. At one end (...) of the philosophical spectrum, my thesis undermines the views of those who, like Cartwright (Erkenntnis 70:45–58, 2009), follow Hesse (Models and Analogies in Science, Notre Dame, University of Notre Dame Press, 1963) in restricting the possibility of learning from models to only those situations where a model identifies some causal factors present in the target. At the other end of the spectrum, my thesis also helps undermine some extremely permissive positions, e.g., Grüne-Yanoff’s (Erkenntnis 70(1):81–99, 2009, Philos Sci 80(5): 850–861, 2013) claim that learning from a model is possible even in the absence of any similarity at all between model and target. The thesis that we can learn from non-causal models offers a cautious middle ground between these two extremes. (shrink)

James Clerk Maxwell’s 1865 paper, “A Dynamical Theory of the Electromagnetic Field,” is usually remembered as replacing the mechanical model that underpins his 1862 publication with abstract mathematics. Up to this point historians have considered Maxwell’s usage of Lagrangian dynamics as the sole important feature that guides Maxwell’s analysis of electromagnetic phenomena in his 1865 publication. This paper offers an account of the often ignored mechanical analogy that Maxwell used to guide him and his readers in the construction of his (...) new electromagnetic equations. The mechanical system consists of a weighted flywheel geared into two independently driven crank wheels in what amounts to a mechanical differential. I will demonstrate how Maxwell made use of the analogy between his flywheel system and electromagnetic induction to ground his study of electromagnetism in clear mechanical conceptions and to structure the derivation of the equations that together are now recognized as Maxwell’s equations for electrodynamics. By reconceiving specific components of his model in electromagnetic terms, while at the same time retaining many of the relations between concepts in the mechanical case, Maxwell gradually assembled increasingly generalized equations for electromotive force. Maxwell thus realized a much sought after balance between physical analogy and abstract mathematics in this, the last of his three seminal papers on electromagnetism. (shrink)

The term “analogy” stands for a variety of methodological practices all related in one way or another to the idea of proportionality. We claim that in his first substantial contribution to electromagnetism James Clerk Maxwell developed a methodology of analogy which was completely new at the time or, to borrow John North’s expression, Maxwell’s methodology was a “newly contrived analogue”. In his initial response to Michael Faraday’s experimental researches in electromagnetism, Maxwell did not seek an analogy with some physical system (...) in a domain different from electromagnetism as advocated by William Thomson; rather, he constructed an entirely artificial one to suit his needs. Following North, we claim that the modification which Maxwell introduced to the methodology of analogy has not been properly appreciated. In view of our examination of the evidence, we argue that Maxwell gave a new meaning to analogy; in fact, it comes close to modeling in current usage. (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)

This paper argues that even when simple analogue models picture parallel worlds, they generally still serve as isolating tools. But there are serious obstacles that often stop them isolating in just the right way. These are obstacles that face any model that functions as a thought-experiment but they are especially pressing for economic models because of the paucity of economic principles. Because of the paucity of basic principles, economic models are rich in structural assumptions. Without these no interesting conclusions can (...) be drawn. This, however, makes trouble when it comes to exporting conclusions from the model to the world. One uncontroversial constraint on induction from special cases is to beware of extending conclusions to situations that we know are different in relevant respects. In the case of economic models it is clear by inspection that the unrealistic structural assumptions of the model are intensely relevant to the conclusion. Any inductive leap to a real situation seems a bad bet. (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)