Colin Howson

Logic with Trees (eBook, PDF)

An Introduction to Symbolic Logic

• Format: PDF

Produktbeschreibung

Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 212
• Erscheinungstermin: 11. Oktober 2005
• Englisch
• ISBN-13: 9781134785513
• Artikelnr.: 42710570

Autorenporträt

Howson, Colin

Inhaltsangabe

Introduction. Part 1: Truth-Functional Logic Chapter 1. The Basics 1.
Deductively Valid Inference 2. Syntax: Connectives and the Principle of
Composition 3. Semantics: Truth-Functionality 4. Negation and Conjunction
5. Disjunction 6. Truth-Functional Equivalence 7. The Conditional 8. Some
Other Connectives, and the Biconditional Chapter 2. Truth Trees 1.
Truth-Functionally Valid Inference 2. Conjugate Tree Diagrams 3. Truth
Trees 4. Tautologies and Contradictions Chapter 3. Propositional Languages
1. Propositional Languages 2. Object Language and Metalanguage 3. Ancestral
Trees 4. An Induction Principle 5. Multiple Conjunctions and Disjunctions
6. The Disjunctive Normal Form Theorem 7. Adequate Sets of Connectives 8.
The Duality Principle 9. Conjunctive Normal Forms Chapter 4. Soundness and
Completeness 1. The Standard Propositional Language 2. Truth Trees Again 3.
Truth-Functional Consistency, Truth-Functionally Valid Inferences, and
Trees 4. Soundness and Completeness Part 2: First Order Logic Chapter 5.
Introduction 1. Some Non-Truth-Functional Inferences 2. Quantifiers and
Variables 3. Relations 4. Formalising English Sentences Chapter 6. First
Languages: Syntax and Two More Trees Rules 1. First Order Languages 2. Two
More Tree Rules 3. Tree Proofs Chapter 7. First Order Languages: Semantics
1. Interpretations 2. Formulas and Truth 3. The Tree Rules Revisited 4.
Consistency and Validity 5. Logical Truth and Logical Equivalence Chapter
8. Soundness and Completeness 1. Applying the Tree Rules 2. Branch Models
3. Soundness and Completeness Theorems 4. Compactness Chapter 9. Identity
1. Identity 2. Tree Rules For Identity 3. Some Arithmetic 4. Functions and
Function Symbols 5. Working with Equations 6. Is Identity Part of Logic?
Chapter 10. Alternative Deductive Systems for First Order Logic 1.
Introduction 2. H 3 ND 4. Comparisons 5. Intuitionism Chapter 11. First
Order Theories 1. First Order Theories 2. Infinite Cardinals 3.
Lowenheim-Skolem Theorems 4. Second O