In this thesis, I defend the explanatory force of algorithmic information processing models in cognitive neuroscience. I describe the algorithmic approach to cognitive explanation, its relation to Shea’s theory of cognitive representation, and challenges stemming from neuronal population analysis and dimensionality reduction. I then consider competing interpretations of some neuroscientific data that have been central to the debate. I argue in favor of a sequenced computational explanation of the phenomenon, contra Burnston. Finally, I argue that insights from theoretical neuroscience allow us to understand why dimensionality reduction does not militate against localizing distinct contents to distinct components of functioning brain systems.