Mathematical constructs developed to advance knowledge in one discipline are sometimes applied to study new phenomena and answer different questions in other disciplines. Using game theory and formal language theory as examples, this project will develop a conceptual framework to analyze the epistemic impacts of the cross-disciplinary use of mathematical constructs in science. Game theory was developed to model strategic interaction between rational agents, but it has been borrowed to study biological evolution. Similarly, formal language theory was developed to study natural languages,  yet it has become the theoretical backbone of computer science4 and recently applied to study the cognitive capacity of animals. Concerning these theories and their novel applications, my research questions are:

(1) To researchers from different—and not directly related—scientific contexts, what epistemic opportunities may make these mathematical constructs attractive?

(2) What are the epistemic risks involved in producing knowledge associated with the aid of borrowed mathematical constructs in particular?

In this project, I confine my philosophical analysis to focus on these two theories’ features and their applications in multiple disciplinary contexts. I will begin by investigating the kind of questions these theories were conceived to answer in their initial disciplinary contexts, such as economics and linguistics respectively. I will then compare and contrast these with their various novel applications in evolutionary biology, computer science, the social sciences, and most recently cognitive biology. The primary goal of this project is two-fold: it aims to understand both the positive and negative impacts of the cross-disciplinary use of formal constructs in the sciences, and to disseminate the research results among scholars of science. To this end, this project will produce two conference presentations6 and two manuscripts to be submitted for peer-reviewed journals for publication.