What can we mean? On practices, norms and pluralisms

Last century, Michael Dummett argued that the principles of intuitionistic logic are semantically neutral, and that classical logic involves a distinctive commitment to realism. The ensuing debate over realism and anti-realism and intuitionistic logic has now receded from view. The situation is reversed in mathematics: constructive reasoning has become more popular in the twenty-first century with the rise of proof assistants based on constructive type theory. In this paper, I revisit Dummett’s concerns in the light of these developments, arguing that both constructive and classical reasoning are recognizable and coherent assertoric and inferential practices.