Metalogic

Geoffrey Hunter’s text provides a rigorous technical introduction to the metatheory of first-order logic, focusing on the formal properties of logical systems rather than just how to use them. The book delivers step-by-step proofs for the consistency, completeness, and decidability of propositional logic before transitioning into the complexities of predicate logic. Hunter details Henkin’s proof of the completeness theorem and provides a thorough explanation of Church’s Theorem regarding the undecidability of first-order logic. By establishing a foundation in set theory and formal languages, the text demonstrates how mathematical methods verify that a logical system captures all valid truths without contradiction.

This volume serves students of philosophy and mathematics who require a bridge between basic symbolic logic and advanced model theory. It is designed for readers who lack a deep background in formal mathematics but want to understand the mechanical proofs behind logical consistency. Readers finish the book with a functional grasp of how Gödel’s findings and recursive functions define the limits of mechanical calculation. The inclusion of worked exercises and answers allows for independent verification of these abstract proofs.

Deep, outward-looking and clear-cut; a demanding read.

Best for readers like The Systems Thinker. Which reader are you?