From rudimentary to classical logic

Abstract

AbstractRudimentary logic falls short of classical logic in a number of ways. To bridge the gap, the Second Philosopher follows Frege and imposes a number of restrictions and idealizations: she treats only well-functioning language, where terms refer and paradoxical predicates don't arise; vagueness is idealized away with the assumption that all properties and relations have sharp boundaries; complex ground-consequent dependencies are replaced by a material conditional. Many deviant logics (free logic, logics of vagueness, relevance logic) are then straightforwardly understood as rejections of one or another of these simplifications. As with any scientific modeling, the question is whether or not those simplifications are effective and benign in a given application; these are the proper terms of debate between these deviant logicians and the classicist. Other deviant logics (intuitionism, quantum logic, dialetheism) go deeper, rejecting elements of rudimentary logic itself. The Second Philosopher finds no evidence that any of these are viable candidates for the underlying logic of the world.