On effective dualities

In this paper, we will develop a novel philosophical account of effective dualities. Building on De Haro and Butterfield’s schema for duality, we will present our notion of effective duality using the concepts of an approximate isomorphism and a limiting operation. We define these concepts on the space of models by adopting the similarity space approach to analysing intertheoretic concepts developed in Fletcher (forthcoming). In doing so, we will discuss the notion of mathematical structure, and discuss the properties of this notion of effective duality. From our account of effective dualities we will see that there emerges a typology of effective dualities. We will present and discuss this typology. Next, we will present two case studies of effective dualities to illustrate how our framework can be used to find effective dualities: (1) the effective duality between high-energy quantum field theories and effective field theories, and (2) the effective duality between finite information quantity classical mechanics and $$\mathbb{R}$$ classical mechanics. Finally, we will discuss what the heuristic function of effective dualities is, and compare it to the heuristic function of approximate dualities as outlined in De Haro (2017, 2019a).