Mathematics in Physics

As part of Establishing the Nordic Network for Philosophy of Physics, a workshop on Mathematics in Physics will be hosted at The University of Oslo.

Mathematical and formal properties are used heavily as guides to theory development, and means of theory confirmation in current physics. That a theory-in-development satisfies particular mathematical constraints or principles is standardly taken as necessary in order that the theory be accepted (or deemed worthy of pursuit), and an established theory’s failure to exemplify particular mathematical features can motivate the search for a new theory. For instance, the search for a theory of quantum gravity can be seen as motivated by the desire for a singularity-free, unified, and mathematically consistent theory that applies in the regimes where we expect a quantum theory of gravity to be necessary. 

What is the connection between these features and truth, or acceptability? Why are they taken as necessary, or even useful in particular theoretical contexts? A promising and novel approach towards answering this question lies in these features’ connections to theoretical virtues. Theoretical virtues in physics often take the form of specific mathematical features. The virtue of simplicity, for example, is embodied in symmetry constraints, including more specific principles such as background independence, which feature prominently as guides, and means of confirmation in current theories. Recently, current physics’ use of particular mathematical or formal features falling under the category of “beauty principles” has been challenged, several of which (e.g., naturalness, unification) are already recognised as of philosophical interest. Yet, this area of research has not gone deep enough to consider the more widespread and basic mathematical features taken as constraints in current physics, e.g., symmetries, singularity resolution, correspondence/reduction, and mathematical consistency.

This workshop will explore the use of particular mathematical or formal features—construed as theoretical virtues—as non-empirical guides and means of theory confirmation in physics. In particular, we are interested in exploring whether, or how, the use of these features in theory-assessment is related to mathematical explanation and indispensability arguments. The workshop’s aim is novel and exploratory in tying together these debates in the philosophy of mathematics with those regarding theoretical virtues in the philosophy of science, and non-empirical confirmation in the philosophy of physics.

Speakers 

• Sorin Bangu (Bergen)
• Neil Barton (Oslo)
• Katharine Brading (Duke)
• Otavio Bueno (Miami)
• Hans Halvorson (Princeton)
• Saakshi Dulani (Geneva)
• Pablo Ruiz de Olano (MPIWG)
• James Fraser (Wuppertal)
• Radin Dardashti (Wuppertal)
• Samuel Fletcher (Minnesota)
• John Wigglesworth (York)
• Keizo Matsubara (Uppsala)

Organizer

Karen Crowther and Øystein Linnebo

Committee

• Karen Crowther (Oslo)
• Richard Dawid (Stockholm)
• Øystein Linnebo (Oslo)
• Samuel Schindler (Aarhus)
• Harald Wiltsche (Linköping)

For schedule and Zoom link please see the Workshop's webpage.