Ideology is a systemic property of cognition central to the transmission and actualization of beliefs. Ideologies take many forms including religious, philosophical, popular and scientific. They play a central role in both personal identity and in the way society holds itself together. Therefore, it is important to understand how to model identities. The article introduces ideologies as a function of cognition that have been described by political scientists and critical theorists. There follows a typology of ideologies that shows their increasing complexity as societies develop. These considerations lead to the identification of key elements and variables in an ideology that can be expressed mathematically together with some of their syste...