Mathematisation and computation in philosophy and history of science

A variety of scientific fields have seen an increasing mathematisation throughout the last century. Driven by the construction of large-scale data processing facilities in the natural sciences and the introduction of digital tools and models in the human and social sciences, contemporary research practices are increasingly dependent on mathematics. In fields such as computer science, cognitive neuroscience, linguistics, climate science, economics and network science, research is being mediated through the development, integration and application of mathematical models. Yet, this dependency on applied mathematics – and more broadly on computation and digitalisation – has so far received little attention by philosophers of science. Debates continue to emerge around the role of representation in applied mathematics, the use of abstract models of empirical systems, inconsistent formal descriptions of empirical data etc. while discussions over instrumentation and genuine interdisciplinary encounters with mathematics tend to be largely absent.

This workshop explored the intersection of mathematics and other scientific disciplines, and in particular the interdisciplinary nature of applied mathematics and its entanglements with other disciplinary modes of research. How does mathematisation and computation change the methodological structure of science? Are mathematics, logic and coding merely auxiliary disciplines or should they be considered as genuinely intellectual endeavours with their own professional practices, standards and theoretical implications? Should we think of new computational tools as offering only provocations, surfacing evidence, suggesting patterns and structures and adumbrating trends, or should we consider computation as pointing towards a new way of working with representation and mediation, what might be called the mathematical ‘folding’ of reality, whereby the researcher is able to approach reality in entirely new ways?