It is widely accepted in cognitive science that cognition can be understood at two levels: a cognitive level and a neural level. This position has been challenged by Bennett and Hacker who claim that attempts at cognitive-level explanations of behavioural phenomena are always mere re-descriptions of these phenomena, and hence are never of any explanatory value. For them, only explanations at the neural (brain) level are acceptable. They accept that currently nothing is known about the neural bases of many of the behavioural phenomena they consider. Hence for them, these behavioural phenomena are completely inexplicable at present. I argue that the cognitive-level explanations that have been offered for such phenomena cannot be mere re-descriptions since (1) they are falsifiable by experiment; and (2) there are often mutually incompatible cognitive-level explanations being offered for a particular phenomenon, explanations between which adjudication is possible by further experimentation. Such explanations are therefore scientifically acceptable rather than being empty, and they provide us with understandings of many behavioural phenomena that are utterly mysterious to Bennett and Hacker.