Post-Classical Logic?

Abstract

The project of formalizing natural argumentation is an old one, and has long been
dominated by classical logic (henceforth K). However, non-classical logics, which are
non-conservatively revisionary of K, have increasingly come to threaten this
hegemony. Non-conservative revisions of logic may proceed by several strategies. The
least revisionary is simple restriction: adoption of a new logic which lacks
previously valid inferences and theorems. However, circumstances which motivate
restriction characteristically result in more wholesale revision: features of the
logic beyond its formal calculus are exposed to criticism, and reformulated in
response. Thus judicious restriction can initiate clarification and disambiguation of
confused metalogical concepts, including the nature of consequence, and what it
should preserve (the inferential goal). For example, relevant logic exposes the
contrast between intensional and extensional constants, obscured in K, and permits a
restatement of the consequence relation.