In this paper I briefly outlined what I see as an important deficiency in the attempts to explain religion simply in terms of the cognitive capacities of the human mind, focusing attention in this regard primarily on the work of Pascal Boyer and Justin Barrett. I have shown that neither of these scholars actually provided clear, coherent and persuasive grounds for believing that ordinary everyday cognitive capacities of the human mind can, of themselves, "motivate" the mind's creation of the "supernatural" which is an essential aspect of religion. I then argued that David Lewis-Williams' neuropsychological theory of the origin of religion that takes seriously the alternate states of consciousness and weird experiences that early Homo sapiens would have had to deal with, both psychologically and socially, provided a sound basis on which our ordinary cognitive capacities could create a non-natural world inhabited by "supernatural beings and forces" that could influence life.