Generality and the limits of model-based science

Abstract

This dissertation is concerned with the in-principle limitations on mathematical modelling in science. I argue that multiple modelling approaches are required to optimally represent particular types of systems, and so the best modelling strategy in particular scientific domains is a pluralistic one. This is because the amount of detailed information contained in a model and the generality of that model interact in a negative way: they trade off against one another. I present two such trade-offs, and claim they are of particular significance in scientific domains where the entities studied are heterogeneous. My primary examples come from population biology, but the core points of the dissertation apply to mathematical models in any branch of science. Chapter 1 develops and defends a view of scientific models and their use, and examines how an understanding of modelling practice illuminates the ontology of scientific models. I show that the current debate regarding whether these models are mathematical objects or more akin to literary fictions is largely misguided, and that many of the apparent problems here can be successfully defused. In chapter 2 I critically assess the literature regarding trade-offs between the properties of scientific models. I argue that in order to understand the trade-offs faced by modelers in any particular field, we must pay close attention to the properties of the systems typically studied by that field. I also point out that this focus has been largely absent in previous philosophical work. The next chapter argues that there is an in-principle trade-off between the generality of a model and the precision of that model, and develops the idea that this trade-off has a greater effect when the systems being modelled are highly heterogeneous. The different categories of trade-off that can occur, and how they are interrelated, is also explored. In chapter 4 I show that there is a trade-off between the generality of a model and the amount of causal detail it represents. I argue that whenever a specific type of multiple realisability obtains, any increase in the causal detail represented by a model will decrease that model's generality. Chapter 5 serves to emphasize the significance of the trade-offs discussed above. I give an analysis of the type of generality that improves a model's explanatory efficacy. I conclude that multiple modelling approaches are required in order to optimally explain a phenomenon whenever the specific circumstances outlined in chapters 3 and 4 arise. Finally, I argue that these trade-offs are important for modelers in population biology, because this branch of science must deal in heterogeneous groups. The first part of the chapter discusses what it takes for the entities in a domain to vary in a way that really matters for scientific practice. The second part provides an analysis of the unit ""population"". Together these show that modelling in population biology will often require the use of multiple modelling approaches. The same will hold true for any science that seeks to explain the behavior of heterogeneous entities. -- provided by Candidate. Show more