ABSTRACT
The propositional calculus (also called the sentential calculus, calculus of unanalysed propositions, calculus of truth values, or calculus of truth functions) concerns truth FUNCTIONS of propositions, but with the restriction that the propositions are regarded as either the same as each other or completely different. Partial similarities like that between ‘All cats are black’ and ‘Some cats are black’ are ignored. Its theorems are the relevant TAUTOLOGIES. When the restriction is lifted and the structure of propositions is taken into account, we have the functional or predicate calculus, or the calculus of relations. When the predicates are limited to MONADIC predicates we have the monadic predicate calculus. The predicate calculus is called extended or second-order when predicates are quantified over (see QUANTIFICATION). When only INDIVIDUALS are quantified over, it is called restricted or first-order. There is also an extended propositional calculus, where propositions are quantified over.
