Abstract

This chapter develops a model of cognitive accomplishment in logic and mathematics. The model is based on the idea that mathematical achievement is not just a matter of acquiring information but also a matter of acquiring the ability to use information already in one’s possession for new purposes. Accordingly, the model represents cognitive subjects as _fragmented_, that is, as having access to different pieces of information for different purposes. The chapter develops a formal framework for describing this idea, and shows how the framework can be used to account for important aspects of mathematical practice.