Abstract
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.
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- 1.
“[A] categorial framework is a set of fundamental metaphysical assumptions about what sorts of entities and what sorts of processes lie within the theory’s domain” (Hughes 1989b, p. 175).
- 2.
For what the definition of the models utilized in SE is concerned, a ‘mathematical model’ is a set-theoretic structure (Suppes 1967). A set-theoretic structure S = < U, O, R > is a triple consisting of (i) a non-empty set U of individuals called the domain (or universe) of the structure S, (ii) an indexed set O (i.e., an ordered list) of operations on U (which may be empty), and (iii) a non-empty indexed set R of relations on U. The fact that M is the model of a theory, in the sense that the theory of reference must be true of it, guarantees that the explanation is anchored to the actual scientific knowledge, and is not an arbitrary invention.
- 3.
In (Hughes 1989a) Hughes proposes a presumed SE of the EPR correlations which, however, necessarily hinges on an interpretation à la Bub of quantum mechanics, where measurements are ultimately treated as black boxes. Hughes’ example is therefore bound to this interpretation of quantum mechanics.
- 4.
One could counter at this point that in this way SE looses its peculiarity and it is not clear whether there is the need of a theory of SE in contrast to a theory of causal explanation. However, the non trivial question we want to face here is, again, if mathematical models, not supported by an underlying categorial framework, can be explicative towards physical phenomena. A specific account of SE (as one of causal explanation) has then the aim of clarifying when and why mathematical models can be explicatively effective in physics and what kind of understanding of the physical world mathematical modelling provides us with.
- 5.
If some affinity is to be found between structural (and theoretical) explanation and another account of explanation, this is surely with Nancy Cartwright’s simulacrum account of explanation.
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Acknowledgments
My research has been funded by a grant from the Master and Back program of Regione Sardegna. I am extremely grateful to Mauro Dorato, who has provided me with guidance throughout this project. I am also extremely grateful to Angelo Cei, Marco Giunti and Matteo Morganti for their comments on a previous version of this paper.
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Felline, L. (2010). Remarks on a Structural Account of Scientific Explanation. In: Suárez, M., Dorato, M., Rédei, M. (eds) EPSA Philosophical Issues in the Sciences. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3252-2_5
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