This chapter develops the theory that there are two kinds of self-organizing, self-mending, self-reproducing structures in the world. The first is living organisms. The second is complex minds, or more precisely, worldviews: ways of seeing the world and being in the world, i.e., networks of memory and knowledge that constitute the content of complex minds. The chapter explores the role played by two forms of exaptation—biological and psychological—in the perpetuation of these self-organizing structures. Biological exaptation occurs when selective environmental pressures cause the exploitation of potentiality, while psychological exaptation involves the ability to modify/change a pattern of cognition to incorporate different perspectives, thereby increasing cultural variation. While the former is associated with survival, the latter has far-reaching consequences in terms of how humans view not only the world around them, but also their own place within it. Within psychological exaptation, the difference between generic and strategic exaptation has been drawn to illustrate the unique attributes of the exaptation process in humans. Strategic exaptation operates through a process of representational redescription, reflexivity, and autocatalysis, that allows for humans to use psychological exaptation for processes that are adaptive, open-ended, and cumulative. Towards the end of the chapter, a brief overview of a quantum model for exaptation has been provided.