Philosophical Logic

ISBN-13: 9781441119117 / Angielski / Miękka / 2011 / 208 str.

George Englebretsen

Opis

Taking students beyond classical mathematical logic, Philosophical Logic is a wide-ranging introduction to more advanced topics in the study of philosophical logic.



Starting by contrasting familiar classical logic with constructivist or intuitionist logic, the book goes on to offer concise but easy-to-read introductions to such subjects as quantificational and syllogistic logic, modal logic and set theory.



Chapters include:



- Sentential Logic- Quantificational Logic- Sentential Modal Logic- Quantification and Modality- Set Theory- Incompleteness- An Introduction to Term Logic- Modal Term Logic



In addition, the book includes a list of symbols and a glossary of terms for ease of reference and exercises throughout help students master the topics covered in the book. Philosophical Logic is an essential, student-friendly guide for anyone studying these difficult topics as part of their Logic course.

Spis treści

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