Abstract

This is a textbook in symbolic logic comprising sentential and quantificational theory only. The logic of the propositional calculus is developed in a natural-deduction form reminiscent of Fitch's technique; therefore, most of the theorems take the form of metamathematical assertions and possess corresponding meta-proofs. The classical propositional calculus SCc is then formulated in the Hilbert-style axiomatic way which naturally leads to consistency, completeness, and decidability theorems for the system. The theory of quantifiers is also first set up in natural deduction form, and then reformulated classically. Leblanc spends considerable time in a careful treatment of satisfiability and validity in first-order logic, this leading naturally to the Löweheim-Skolem [[sic]] theorem and related completeness results. There is an appendix containing some relevant results from set theory. In general this is a most thorough and neat job which succeeds admirably in giving in semantical form a rigorous introduction to logic.—P. J. M.