Predicate Logic

Abstract

In this chapter we extend the language of propositional logic to the one of predicate logic, in which we also can analyse arguments containing subjects and predicates, such as in, for example: All men are mortal; therefore: Socrates is mortal; and in: Socrates is a philosopher; therefore: someone is a philosopher. These simple arguments cannot be adequately dealt with in propositional logic. The semantic notions of logical consequence and logical validity and the syntactic notions of (logical) deducibility and provability are adapted to the language of predicate logic, and again it turns out that these two notions are extensionally equivalent (soundness and completeness).