The cognitive neurosciences are based on the idea that the level of neurons or neural networks constitutes a privileged level of analysis for the explanation of mental phenomena. This paper brings to mind several arguments to the effect that this presumption is ill-conceived and unwarranted in light of what is currently understood about the physical principles underlying mental achievements. It then scrutinizes the question why such conceptions are nevertheless currently prevailing in many areas of psychology. The paper argues that corresponding conceptions are rooted in four different aspects of our common-sense conception of mental phenomena and their explanation, which are illegitimately transferred to scientific enquiry. These four aspects pertain to the notion of explanation, to conceptions about which mental phenomena are singled out for enquiry, to an inductivist epistemology, and, in the wake of behavioristic conceptions, to a bias favoring investigations of input–output relations at the expense of enquiries into internal principles. To the extent that the cognitive neurosciences methodologically adhere to these tacit assumptions, they are prone to turn into a largely a-theoretical and data-driven endeavor while at the same time enhancing the prospects for receiving widespread public appreciation of their empirical findings.