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)

Computer models and simulations have become, since the 1960s, an essential instrument for scientific inquiry and political decision making in several fields, from climate to life and social sciences. Philosophical reflection has mainly focused on the ontological status of the computational modeling, on its epistemological validity and on the research practices it entails. But in computational sciences, the work on models and simulations are only two steps of a longer and richer process where operations on data are as important as, (...) and even more time and energy-consuming than modeling itself. Drawing on two study cases—computational embryology and computational epidemiology—this article contributes to filling the gap by focusing on the operations of producing and re-using data in computational sciences. The different phases of the scientific and artisanal work of modelers include data collection, aggregation, homogenization, assemblage, analysis and visualization. The article deconstructs the ideas that data are self-evident informational aggregates and that data-driven approaches are exempted from theoretical work. More importantly, the paper stresses the fact that data are constructed and theory laden not only in their fabrication, but also in their reusing. (shrink)