While initial musings (and some early theories) on Categorization come from Philosophy (think Categories by Aristotle), most modern research on Categorization which adheres to the scientific method comes from Psychology (Concept Learning on Wikipedia). Two popular models which originate from Psychology literature are Prototype Theory and Exemplar Theory. Summarizing briefly, categories in Prototype Theory are abstractions which summarize a category while categories in Exemplar Theory are represented nonparametrically. While I'm personally a big proponent of Exemplar Theory (see my Recognition by Association CVPR2008 paper), I'm not going to discuss the details of my philosophical stance in this post. I want to briefly point out the shortcomings of these two simplified views of concepts.
Researchers focusing on Categorization are generally dealing with a very simplified (and overly academic) view of the world -- where the task is to categorize a single input stimulus. The problem is that if we want a Theory of Concepts that will be the backbone of intelligent agents, we have to deal with relationships between concepts with as much fervor as the representations of concepts themselves. While the debate concerning exemplars vs. prototypes has been restricted to these single stimulus categorization experiments, it is not clear to me why we should prematurely adhere to one of these polarized views before we consider how we can make sense of inter-category relationships. In other words, if an exemplar-based view of concepts looks good (so-far) yet it is not as useful for modeling relationships as a prototype-view, then we have to change our views. Following James' pragmatic method, we should evaluate category representations with respect to a larger system embodied in an intelligent agent (and its ability to cope with the world) and not the overly academic single-stimulus experiments dominating experimental psychology.
On another note, I submitted my most recent research to NIPS last week (supersecret for now), and went to a few Phish concerts. I'm driving to California next week and I start at Google at the end of June. I also started reading a book on James and Wittgenstein.