Abstract
In the philosophy of mathematics, ontological and epistemological questions have been discussed for centuries. These two set of questions span out a two-dimensional philosophy of mathematics. I find it important to establish a four dimensional philosophy of mathematics by adding two more dimensions, namely a sociological and an ethical dimension. The sociological dimension addresses the social formation of mathematics, while the ethical dimension addresses the mathematical formation of the social. In this article, I concentrate on exploring the ethical dimension by showing the broad range of social implications set in motion through bringing mathematics into action. These implications I illustrate in terms of quantifying, digitalising, serialising, categorising, and imagining. By the banality of mathematical expertise, I refer to the phenomenon that the formation of this expertise takes place in an ethical vacuum. To me this is a devastating feature of mathematical research and application practices. It is important that a philosophy of mathematics brings mathematics out of this vacuum.
