Biologism - the idea that the science of biology supplies the means to exhaustively explain psychological processes - has become vastly popular in recent decades. It can be shown that the idea is illusory on fundamental and a-priori grounds. Several fields of inquiry are described, where the biologistic project has demonstrably failed, like, for example, heritability estimates for mental traits (like intelligence). It is argued as well that biologism is just a further instance of an older, more comprehensive and equally illusory concept: psychology as a natural science (a science that produces generally accepted basic facts, for example the creation of a psychological risk factor for coronary disease). It is shown that psychology, masquerading as a natural science, as it largely does, may create serious societal problems like, for example, its misuse for racist purposes. The peculiar use of methodology in psychology is also documented.