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Institute of Advanced Study

Mathematical Explanation and Complex Systems

Abstract

Complex systems present direct challenges to a number of positions in the philosophy of science on prediction, representation and explanation. Some examples of complex systems include stock markets, the weather and physical phenomena like superconductivity. The thematic goal of this paper involves examining the relation between the mathematics used to treat complex systems, understood as a formal representational tool, and its role in providing a ‘physical’ understanding of these systems. More specifically, I intend to address the way that a mathematical technique known as renormalization group (RG) methods can provide an explanatory foundation which highlights structural features that different complex systems have in common. What this suggests is that there is a fundamental level of explanation underlying complex systems which can be explicated via the mathematics of RG.

Insights Paper