This is an analytical study into how the new cognitive science of religion (CSR) relates to the classical but now lowly regarded "intellectualist" view of religion, according to which supernatural-agent concepts serve to explain the world. Could CSR be merely old intellectualist wine in new bottles? No, the central idea of the "standard model" of CSR, "minimal counterintuitiveness" (MCI), is not intellectualist --- yet for the phenomenon that motivates MCI theory a better account falls out of intellectualist work, five decades old, by the late anthropologist Robin Horton. Other CSR ideas include the "hyperactive agency detection device" (HADD), as well as two approaches that I classify as intellectualist. I argue that an agency bias is not needed to account for religion --- in fact, no type of bias is needed that could not be found in modern science as well --- and that old-fashioned intellectualism, which along the way I defend against objections, does a better job than the two CSR intellectualisms. (Although part of the CSR problem here turns out to be just odd prohibitions against the old-fashioned intellectualism.) Insight largely overlooked today, and applicable to the origin of religion and especially to the so-called Axial Age, can be found in work that is no less than three centuries old, by Bernard de Fontenelle.