Philosophical Logic

George Englebretsen is Professor Emeritus at Bishop's University, Canada. He is the author of a large number of works dealing with topics in the philosophy of logic and language, metaphysics and the history of logic. Charles Sayward is Professor of Philosophy at the University of Nebraska-Lincoln, USA. He is a much-published author of works in the philosophy of logic and the philosophy of mathematics, most recently Dialogues Concerning Natural Numbers.

"Englebretsen and Sayward's book fills a gap in the current array of logic textbooks available. It starts from the beginning, thus allowing students to gain the first rudiments of symbolization; yet, it covers areas usually neglected in introductory logic textbook such as set theory and modal logic. Finally, it presents a constructivist approach in contrast to the point of view of classical logic usually tacitly assumed in logic textbooks and a substitutional rather than an objectual interpretation of quantification. This is truly a logic textbook for philosophers." - Pieranna Garavaso, University of Minnesota, Morris, USA

• 1. Introduction / Sentences / Truth and Falsity / Defense and Refutation / Inference, Form and Implication / Formally Valid Inference / Conjunctions / Inference with Conjunctions / Negation / Inference with Negation / Truth-Functionality and Negation / Grouping / 2. Sentential Logic / Simple Sentences / Sentences / Derivations: A First Look / A Note on Sets / Lines / Derivations Again / Theorems / Truth Sets / Soundness / Completeness / Extensions of SL / Conditionalization / Model Sets / Syntax and Semantics / 3. Quantificational Logic / Singular Terms / Predicates / Some Symbolic Conventions / Some / The Language QL / Derivations / Truth Sets / All / Further Extensions of QL / Model Sets / Identity / Model Sets for QL / 4. Sentential Modal Logic / Non-Truth-Functional Sentential Operators / Sentential Modal Operators / Derivations / S5, S4, T, and B / Possible Worlds / At a World and In a World / Model Sets and Model Systems / Deontic Logic and Model Sets / 5. Quantification and Modality / Some Derivations / Model Sets and Systems / An Alternative / 6. Set Theory / The Axiom of Extensionality / Axioms of Separation / Pairing Axiom and Rule U / The Restriction on the A2 Axiom / The Null Set / An Interpretation / More Axioms / General Intersection Operation / Order and Relations / Functions / Sizes of Sets / The Power Set Axiom / A Basic Theorem / 7. Incompleteness / The Language of Arithmetic / Three Key Concepts / Three Key Theorems / The Core Argument / Concluding Observations / 8. An Introduction to Term Logic / Syllogistic / The Limits of Syllogistic / Term Functor Logic / Singular Terms and Identity in TFL / Relationals in TFL / The Logic of Sentences in TFL / Rules of Inference for Derivations in TFL / Derivation in TFL / The Bridge to TFL / 9. Modal Term Logic / Modal Operators on Terms / Modal Operators on Sentences / Rules of Derivation for Modal TFL / Modal Inference in TFL / Rules, Axioms and Principles / List of Symbols / Glossary / Index.