Philosophical Logic: An Introduction to Advanced Topics
George Englebretsen, Charles W. Sayward · 2011
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.