Mathematical models and their modeling frameworks developed to advance knowledge in one discipline are sometimes sourced to answer questions or solve problems in another discipline. Studying this aspect of cross-disciplinary transfer of knowledge objects, philosophers of science have weighed in on the question of whether knowledge about how a mathematical model is previously applied in one discipline is necessary for the success of reapplying said model in a different discipline. However, not much has been said about whether the answer to (...) that epistemological question applies to the reapplication of a modeling framework. More generally, regarding the nature of the production of knowledge in science, a metaphysical question remains to be explored whether historical contingencies associated with a mathematical construct have a genuine impact on the nature—as opposed to sociological practices or individual psychology—of advancing scientific knowledge with said construct. Focusing on this metaphysical question, this paper analyzes the use of mathematical logic in the development of the Chomsky hierarchy and subsequent reapplications of said hierarchy; with these examples, this paper develops the notion of “spillovers” as a way to detect cross-disciplinary justifications for better understanding the relations between reapplications of the same mathematical construct across disciplines. (shrink)

The omnipresence of the same basic equations, function forms, algorithms, and quantitative methods is one of the most spectacular characteristics of contemporary modeling practice. Recently, the emergence of the discussion of templates and template transfer has addressed this striking cross-disciplinary reach of certain mathematical forms and computational algorithms. In this paper, we develop a notion of a model template, consisting of its mathematical structure, ontology, prototypical properties and behaviors, focal conceptualizations, and the paradigmatic questions it addresses. We apply this notion (...) to three widely disseminated and powerful model templates: the Sherrington-Kirkpatrick model of spin glasses, scale-free networks, and the Kuramoto model of synchronization. We argue that what appears to be an interdisciplinary model transfer between different domains turns out, from a broader perspective, to be the application of transdisciplinary model templates across a multitude of domains. We also point out a further feature of template-based modeling that so far has not been discussed: template entanglement. Such entanglement enhances and makes manifest the conceptual side of model templates. (shrink)

I propose an approach that expands philosophical views of scientific change, on the basis of an analysis of contemporary biomedical research and recent developments in the philosophy of scientific change. Focusing on the establishment of the exposome in epidemiology as a case study and the role of data as a context for contrasting views on change, I discuss change at conceptual, methodological, material, and social levels of biomedical epistemology. Available models of change provide key resources to discuss this type of (...) change, but I present the need for an approach that models transfer, alignment, and influence as key processes of change. I develop this as a pragmatic approach to scientific change, where processes might change substantially depending on specific circumstances, thus contributing to and complementing the debate on a crucial epistemological issue. (shrink)

In this chapter, we discuss a specific kind of progress that occurs in most branches of economics today: progress involving the repeated use of mathematical models. We adopt a functional account of progress to argue that progress in economics occurs through the use of what we call “common recipes” and model templates for defining and solving problems of relevance for economists. We support our argument by discussing the case of 20th century business cycle research. By presenting this case study in (...) detail, we show how model templates are not only reapplied to different phenomena. We also show how scientists first develop them and how, once they are considered less useful, they are replaced with new ones. Finally, our case also illustrates that it is not only the mathematical structure that is reused but that such reuse also requires a shared conceptual vision of the core properties of the phenomenon to be studied. If that vision is no longer shared among economists, a model template can become useless and has to be replaced, sometimes against resistance, with a different one. (shrink)