The Politics of Disjunction

At the center of the rise of modern logic in the twentieth century was an unquestioned commitment to the idea that inclusive disjunction and negation were the fundamental logical operations. Lost in the development of this logic was an alternative starting point proposed by earlier idealist logicians taking exclusive disjunction and negation as fundamental. This paper considers the logical system of Josiah Royce as a development of the idealist version and argues that it has the potential to account both for modern logical systems and for the place of agency and purpose in logic. I will briefly present the late twentieth century effort to settle on a single concept of disjunction in logic in order to reveal the issues at work. This late debate over the nature of disjunction follows an earlier one in which the leading British idealists were challenged by a variety of philosophers who sought to separate formal systems from conscious agency. Once I have set out the debate, I present a reformulation of Royce’s System ∑ that shows how it takes up the conception of disjunction as it developed in idealist logic and uses it to reconnect agency and formal logic.