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)

Der Begriff ‘Modell’ leitet sich vom Lateinischen ‘modulus’ (das Maß) ab, im Italienischen existiert seit dem 16. Jh. ‘modello’ und R. Descartes verwendet im 17. Jh. ‘modèlle’. Während der Begriff in Architektur und Kunst schon seit der Renaissance gängig ist, wird er in den Naturwissenschaften erst im 19. Jh. verwendet.1 Dort greifen wissenschaftliche Modelle die für eine gegebene Problemstellung als wesentlich erachteten Charakteristika (Eigenschaften, Beziehungen, etc.) eines Untersuchungsgegenstandes heraus und machen diesen so einem Verständnis bzw. einer weiterführenden Untersuchung zugänglich. Es (...) ist üblich, zwischen Skalenmodellen, Analogmodellen und theoretischen Modellen zu unterscheiden. (shrink)

Making sense of modeling: beyond representation Content Type Journal Article Category Original paper in Philosophy of Science Pages 335-352 DOI 10.1007/s13194-011-0032-8 Authors Isabelle Peschard, Philosophy Department, San Francisco State University, 1600 Holloway Ave, San Francisco, CA 94132, USA Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 3.

This paper explores varieties of scientific structuralism. Central to our investigation is the notion of `shared structure'. We begin with a description of mathematical structuralism and use this to point out analogies and disanalogies with scientific structuralism. Our particular focus is the semantic structuralist's attempt to use the notion of shared structure to account for the theory-world connection, this use being crucially important to both the contemporary structural empiricist and realist. We show why minimal scientific structuralism is, at the very (...) least, a powerful methodological standpoint. Our investigation also makes explicit what more must be added to this minimal structuralist position in order to address the theory-world connection, namely, an account of representation. (shrink)

The use of fictional models is extensive and rewarding in modern science. This fact captured the attention of philosophers of science, who are focusing on questions such as the following: is it possible for a fictional model to be explanatory? And, if so, in virtue of what is such a fictional model explanatory? In this paper, I discuss these questions in relation to the realism vs. anti-realism debate in philosophy of science. I focus on work developed by Alisa Bokulich who (...) has argued for the explanatory role played by fictional models, claiming that it can be accommodated by realism in ‘a broad sense’. To this end, Bokulich introduced what she called ‘an eikonic conception’ of explanation, as opposed to the so-called ‘ontic’ conception. This move, Bokulich claims, allows non-causal explanations to be acceptable to a modified version, as opposed to a ‘naïve’ brand of realism. Roughly, a fictional model can capture aspects of reality if it manages to act as a proxy for a theory targeting a physical system. As Bokulich explains with the example of James Clerk Maxwell’s use of mechanical models, this is due to structural correspondences between a model and a theory at a certain level of abstraction. However, Bokulich does not explain how the model grasps reality. In this paper, I fill this missing piece of the puzzle. While I agree with Bokulich on the explanatory function of fictional models, I shall invoke her reading of Maxwell’s work to draw a different conclusion. Specifically, I argue that structural correspondences at various levels form what I call ‘a ladder of abstractions’ which connects aspects of a target system to the corresponding depths of descriptions. Modifying in these terms the scope of ‘representing a system’, I suggest that Bokulich’s proposed modification of realism is obviated. (shrink)

The focus of this paper is the recent revival of interest in structuralist approaches to science and, in particular, the structural realist position in philosophy of science . The challenge facing scientific structuralists is three-fold: i) to characterize scientific theories in ‘structural’ terms, and to use this characterization ii) to establish a theory-world connection (including an explanation of applicability) and iii) to address the relationship of ‘structural continuity’ between predecessor and successor theories. Our aim is to appeal to the notion (...) of shared structure between models to reconsider all of these challenges, and, in so doing, to classify the varieties of scientific structuralism and to offer a ‘minimal’ construal that is best viewed from a methodological stance. (shrink)