This talk argues that hinge epistemology adds new insights which help us understand the role of certainties in mathematical practices. Subsequently, we employ these insights to account for disagreements on a local level coexisting with a high level of consensus in modern mathematics globally. We characterize mathematics as a set of partially overlapping practices instead of simply a tree or a building with secure foundations at the bottom. Explicit disagreements are often casted out of the forefront of mathematics and qualified as mere philosophical background of different practices, thus conventionally contributing to the prevalent image of mathematics as objective and uber-consensual. In a short excurse we also talk why this might have consequences for the idea of inner-mathematical explanations pushing a context-sensitive or even relativistic approach to the issue at hand.

This is jww: José Antonio Perez-Escobar and Jordi Fairhurst.