Chapter 9: Predicate Logic

9.1 Introduces predicate letters and quantifiers into the formal language and explains how these can be used to translate English statements into symbolic formulas.

9.2 Explains how to the Finite Universe Method can be used to demonstrate the invalidity of many arguments within predicate logic.

9.3 Building on the system of natural deduction developed in chapter 8, this section adds the first set of rules for predicate logic: universal instantiation, existential instantiation, universal generalization, and existential generalization.

9.4 Adds an equivalence rule, Quantifier Negation, to the system of predicate logic. Also explains how Conditional Proof and Reductio ad Absurdum may be employed within predicate logic.

9.5 Introduces the logic of relations and explains how to translate English statements into the formal language, using polyadic predicate letters.

9.6 Discusses proofs within the logic of relations, drawing attention to errors that often occur when the inference rules of predicate logic are applied to statements involving relations.

9.7 Introduces the logic of identity and explains how to translate English statements involving identity into the formal language.

9.8 Introduces three inference rules for the logic of identity: Leibniz' law, symmetry, and the identity rule. (The identity rule allows one to enter statements of self-identity, such as b = b, as lines in a proof).