My research involves the extension of Peter Gärdenfors' conceptual spaces theory of concepts, attempting to fill in the gaps in his theory and show how it can provide a bridge not only between associationist and symbolic accounts of cognition (as he envisions it) but also between an atomistic theory of concepts qua Jerry Fodor and a non-atomistic theory qua Jesse Prinz. Fodor and Prinz present two of the currently more popular and debated theories of concepts that have sprung up as replacements for the discredited classical definitionist and imagist accounts. The incommensurability of their accounts is, I believe, only apparent. Not only are both views useful, I believe they (or something like them) are both necessary.
Per Fodor, I want to emphasize the centrality of an explicit and coherent theory of concepts to any work in cognitive science or AI. Too much of the time the theory of concepts underlying work in the field has been taken for granted if not simply implicitly assumed; and my suspicions are with Fodor that that theory has in many substantial ways been wrong.
My thesis revolves around four main points. First of all, any theory of concepts, to be complete, must reconcile contrasting theoretical understandings of concepts along at least two dimensions: concepts as conceptually atomistic vs. concepts as composites of other concepts, and concepts as shared entities in a public (social) space vs. concepts as private entities.
Of course, conceptually atomistic entities cannot be atomistic along all dimensions: i.e., they cannot be singularities. Whatever content they have must, however, be specified in terms of some kind of non-conceptual content. My intuition is that it is part of human cognition to toggle constantly between these two perspectives on concepts: conceptually atomistic and conceptually structured. When people think of concepts as concepts -- as, I believe, even lay persons do -- then it's natural (I argue) to understand them as complexly structured entities and specify their content conceptually. When people use concepts without thinking of them as concepts, then I think we, as philosophers of concepts, need means to specify the contents of those very same concepts non-conceptually, using methods e.g. suggested by synthetic phenomenology. Not only might this allow a nice continuity between non-conceptual and conceptual mental representations, it would also (I think) offer an escape from familiar self-referential paradoxes (e.g., Grelling's Paradox) that arise when one attempts to specify the contents of concepts purely with other concepts, without needing to take the drastic step of banishing those paradoxes altogether. (Note that the paradox is not eliminated. Rather, an alternative perspective is offered that is not subject to the paradox.)
Second, a theory of concepts grounded in the metaphor of geometry, in the style of Gärdenfors' conceptual spaces theory, can provide a means of bridging these divides, between the conceptually atomistic and the conceptually structured, and between the public and the private. Third, a single shape or a small set of shapes can provide perceptual primitives to ground conceptual spaces theory, giving common underlying form to all the concepts one has need to talk about. Fourth, a theory of concepts is best tested in some form of implementation that can then be used in refining the theory, creating a tight theory-implicit model-explicit model-implementation-theory loop.
The goal of my research is not just a refined theory of concepts but also a computational model that can be used to test the validity and practicality of that model with human subjects, offering them a virtual playground of conceptual building blocks in which to create an externalized model of some portion of their conceptual domain. If the theory does not explicitly violate anything we currently know from psychology or neuroscience, and if the test subjects find the test environment a natural or comfortable fit to their customary thought processes, that would provide support for the usefulness of the theory regardless of whether, in any useful sense, it is ultimately the "correct" explanation or not. Given my own pluralist perspective, useful seems to me more important than ultimately correct.