ABSTRACT
The logical operators that come to us most naturally when we try to build a propositional logic by inspecting the ways in which sentences in natural language can be put together are conjunction, implication, negation, and disjunction. They are usually regimented by the well-known symbols. Conjunction can be easily characterized in terms of its role within arguments. The situation with implication is trickier, because its most straightforward characterization involves considering not only arguments but also steps from arguments to arguments (“metaarguments”); and similarly for disjunction. The situation is even more involved in the case of negation, where we may also want to take into account, aside from arguments and metaarguments, the fact that some sentences are incompatible with other sentences. The most straightforward characterizations of the roles of the operators lead us to the Gentzenian calculus for intuitionistic logic.
