Theory Reduction in Physics: A Model-Based, Dynamical Systems Approach

Joshua Rosaler (Pittsburgh) gives a talk at the MCMP conference "Reduction and Emergence in the Sciences" (14-16 November, 2013) titled "Theory Reduction in Physics: A Model-Based, Dynamical Systems Approach". Abstract: I elaborate an approach to reduction in physics that is distinct from the Nagelian and limit-based approaches that have been discussed most widely in the philosophical literature. This approach, which I call ‘Dynamical Systems (DS) Reduction’, is intended to apply to the reduction of theories whose models can be formulated as dynamical systems models. Importantly, this is the case with most physical theories, including classical mechanics, classical field theory, quantum mechanics and quantum field theory. After setting out the basic elements of DS reduction, I compare this approach with the limit-based and Nagelian approaches, arguing in each case that the DS approach does better. In particular, I highlight a number of significant parallels between the DS and Nagelian approaches, specifically relating to their use of special correspondences between theories (what are most commonly called ‘bridge laws’ in Nagelian approaches) to identify those elements of the low-level theory that emulate the behavior of certain elements in the high-level theory. Despite these similarities, I argue that DS reduction, in its use such correspondences (which I call ‘bridge maps’) does not face the ambiguities or difficulties that are often associated with Nagelian bridge laws: in particular, I argue that it avoids ambiguities as to whether these correspondences are to be regarded as conventions or empirically substantive claims, as well addressing concerns about multiple realisability.