Remarks on a Structural Account of Scientific Explanation (original) (raw)

The problems that exist in relating quantum mechanical phenomena to classical concepts like properties, causes, or entities like particles or waves are well-known and still open to question, so that there is not yet an agreement on what kind of metaphysics lies at the foundations of quantum mechanics. However, physicists constantly use the formal resources of quantum mechanics in order to explain quantum phenomena. The structural account of explanation, therefore, tries to account for this kind of mathematical explanation in physics, and hinges on the following claims: i) scientific models are central in scientific explanation; ii) in some cases the relevant information for the explanation/understanding of a phenomenon P consists in the sole structural properties of the (models displayed by the) theory; iii) in these cases, the interpretation of the formalism in terms of a categorial framework is unessential for the explanation of P and a mathematical model can be at the base of an objective and effective scientific explanation. The present paper will carry a reflection about some issues arising from R.I.G. Hughes and Robert Clifton's works in the attempt to outline some details of structural explanation. § 1 Introduction The pervasive role of mathematics in modern science has cross-fertilized the philosophy of science in many ways. Among them, a topic of growing interest is the epistemological status of mathematical explanations of natural phenomena. An extensive literature can be found on this subject, for instance in cognitive science – concerning the so-called computational explanations (McCulloch and Pitts 1943, Piccinini 2006), where the mental capacities of the brain are explained by its computations – and in more recent times a significant number of papers have investigated the role of mathematical explanations also in biology (Berger 1998). Since the role that mathematics plays in the explanation of natural phenomena can hardly be overrated, it seems remarkably odd that such a topic has been hitherto neglected in the philosophy of physics, the mathematised science par excellence. The current state of scientific knowledge and within it of the relationship between mathematics and explanation is well illustrated by Ruth Berger: " Today's science is often concerned with the behavior of extremely complicated physical systems and with huge data sets that can be organized in many different ways. To deal with this, scientists increasingly rely on mathematical models to process, organize, and generate explanatory information. Since much of the understanding produced by contemporary science is gathered during the process of mathematical modelling, it is incumbent upon philosophical accounts of explanation to accommodate modelling explanations. This is recognized by the semantic view of theories, which identifies mathematical modelling as one of the mains explanatory engines of science. " (Berger 1998, p.308) But the acknowledgement of the central role of models in science did not correspond to the recognition of a similar role in the more restricted field of scientific explanation: " Although many philosophers accept the basic features of the semantic view of theories, there have been surprisingly few attempts to reconcile it with our best philosophical accounts of scientific explanation. […] [C]ausal accounts cannot illuminate precisely those explanatory features of science which the semantic view deems most important. Specifically, causal accounts of explanation cannot accommodate, and often obscure, the crucial role which mathematical modelling