Formal logic. Its scope and limits

This book deals with an elementary exposition of propositional and quantificational logic, and gives a detailed elementary completeness proof. The tree method tests validity of inferences by a systematic search for counterexamples, using easy formal techniques related in a natural way to the semantical interpretation. Church’s undecidability theorem and a version of Gödel’s incompleteness theorem are proved in the final chapter. Numerous worked examples are included where techniques are to be acquired. – Part One, «Compound Statements» : 1, Introduction; 2, Logical equivalence; 3, Truth-functions; 4, Truth trees; 5, Adequacy of the method. Trees and proofs. – Part Two, «Quantification» : 6, Inference rules for quantifiers; 7, Multiple quantification. Translation; 8, Adequacy of the tree method; 9, Identity. Functions; 10, Undecidability. Incompleteness. – Guide to further study. M.-M. V.