This thesis confronts a fundamental shortcoming in cognitive science research: a failure to be explicit about the theory of concepts underlying cognitive science research and a resulting failure to justify that theory philosophically or otherwise. It demonstrates how most contemporary debates over theories of concepts divide over whether concepts are best understood as (mental) representations or as non-representational abilities. It concludes that there can be no single correct ontology, and that both perspectives are logically necessary. It details three critical distinctions that are frequently neglected: between concepts as we possess and employ them non-reflectively, and concepts as we reflect upon them; between the private (subjective...