Logic with Trees: An Introduction to Symbolic Logic

by Howson; Colin

• ISBN13: 9780415133418
• ISBN10: 0415133416
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-03-21
• Publisher: Routledge

Summary

Logic With Treesis a new and original introduction to modern formal logic. It contains discussions on philosophical issues such as truth, conditionals and modal logic, presenting the formal material with clarity, and preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and exercises guide beginners through the book, with answers to selected exercises enabling readers to check their progress. Logic With Treesequips 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.

Author Biography

Colin Howson is Reader in Logic at the London School of Economics and Political Science.

Table of Contents

Introduction

Truth-Functional Logic Chapter

The Basics

Deductively Valid Inference

Syntax: Connectives and the Principle of Composition

Semantics: Truth-Functionality

Negation and Conjunction

Disjunction

Truth-Functional Equivalence

The Conditional

Some Other Connectives, and the Biconditional Chapter

Truth Trees

Truth-Functionally Valid Inference

Conjugate Tree Diagrams

Truth Trees

Tautologies and Contradictions Chapter

Propositional Languages

Propositional Languages

Object Language and Metalanguage

Ancestral Trees

An Induction Principle

Multiple Conjunctions and Disjunctions

The Disjunctive Normal Form Theorem

Adequate Sets of Connectives

The Duality Principle

Conjunctive Normal Forms Chapter

Soundness and Completeness

The Standard Propositional Language

Truth Trees Again

Truth-Functional Consistency, Truth-Functionally Valid Inferences, and Trees

Soundness and Completeness

First Order Logic Chapter

Introduction

Some Non-Truth-Functional Inferences

Quantifiers and Variables

Relations

Formalising English Sentences Chapter

First Languages: Syntax and Two More Trees Rules

First Order Languages

Two More Tree Rules

Tree Proofs Chapter

First Order Languages: Semantics

Interpretations

Formulas and Truth

The Tree Rules Revisited

Consistency and Validity

Logical Truth and Logical Equivalence Chapter

Soundness and Completeness

Applying the Tree Rules

Branch Models

Soundness and Completeness Theorems

Compactness Chapter

Identity

Identity

Tree Rules For Identity

Some Arithmetic

Functions and Function Symbols

Working with Equations

Is Identity Part of Logic? Chapter

Alternative Deductive Systems for First Order Logic

Introduction

H 3 ND

Comparisons

Intuitionism Chapter

First Order Theories

First Order Theories

Infinite Cardinals

Lowenheim-Skolem Theorems

Second Order Languages

Completeness

The Liar Paradox Chapter

Beyond the Fringe

Counterfactual Conditions

Modal Propositional Logic

Indicative Conditionals and ->

Conclusion

List of Notation

Answers to Selected Exercises

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