Nguồn ngoài

A Modern Formal Logic Primer

This text is a primer that presents the basic elements of logic.

Philosophy Humanities

Tác giả: Paul Teller
Nhà xuất bản: UC Davis
Nguồn: LibreTexts
Ngôn ngữ: EN

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Mục lục· 119 mục

01: Preface- A Guide to the Primer
02: Volume I- Sentence Logic
2.01: Basic Ideas and Tools
2.1.01: Logic As the Science of Argument
2.1.02: Sentences and Connectives
2.1.03: Truth Tables and the Meaning of '' 'and' and 'v'
2.1.04: Truth Functions
2.1.05: Compounding Compound Sentences
2.1.06: Rules of Formation and Rules of Valuation
2.1.S: Basic Ideas and Tools (Summary)
2.02: Transciption Between English and Sentence Logic
2.2.01: Grouping in Transcription
2.2.02: GROUPING IN TRANSCRIPTION
2.2.03: Adequacy of Transcriptions
2.03: Logical Equivalence Logical Truths and Contradictions
2.3.01: Logical Equivalence
2.3.02: Substitution of Logical Equivalents and Some More Laws
2.3.03: Logical Truths and Contradictions
2.3.04: Disjunctive Normal Form and the Sheffer Stroke
2.04: Validity and Conditionals
2.4.01: Validity
2.4.02: Invalidity and Counter Examples
2.4.03: Soundness
2.4.04: The Conditional
2.4.05: The Biconditional
2.05: Natural Deduction for Sentence Logic - Fundamentals
2.5.01: The Idea of Natural Deduction
2.5.02: Subderivations
2.5.03: The Complete Rules of Inference
2.06: Natural Deduction for Sentence Logic - Strategies
2.6.01: Constructing Correct Derivations
2.6.02: Recognizing the Main Connective
2.6.03: Derivations- Overview Definitions and Points to Watch out for
2.07: Natural Deduction for Sentence Logic - Derived Rules and Derivations without Premises
2.7.01: Derived Rules
2.7.02: Argument by Cases
2.7.03: Further Derived Rules
2.7.04: Derivations without Premises
2.08: Truth Trees for Sentence Logic - Fundamentals
2.8.01: Proving Validity with Truth Trees
2.8.02: The General Strategy for the Rules
2.8.03: Proving Invalidity with Truth Trees
2.8.04: The Complete Rules for the Connectives
2.8.05: In Which Order Should You Work on the Sentences in a Tree
2.09: Truth Trees for Sentence Logic - Applications
2.9.01: Application of the Rules to Complex Sentences
2.9.02: Other Uses for Truth Trees
03: Volume II- Predicate Logic
3.01: Predicate Logic - Syntax
3.1.01: We Need More Logical Form
3.1.02: Quantifiers and Variables
3.1.03: The Sentences of Predicate Logic
3.02: Predicate Logic - Semantics and Validity
3.2.01: Interpretations
3.2.02: Truth in an Interpretation
3.2.03: Validity in Predicate Logic
3.03: More about Quantifiers
3.3.01: Some Examples of Multiple Quantification
3.3.02: Quantifier Scope Bound Variables and Free Variables
3.3.03: Correct Definitions of Substitution Instance and Truth in an Interpretation
3.3.04: Some Logical Equivalences
3.04: Transcription
3.4.01: Restricted Quantifiers
3.4.02: Transcribing from English into Logic
3.4.03: Transcription Strategies
3.05: Natural Deduction for Predicate Logic - Fundamentals
3.5.01: Review and Overview
3.5.02: The Universal Elimination Rule
3.5.03: The Existential Introduction Rule
3.5.04: The Existential Elimination and Universal Introduction Rules- Background in lnformal Argument
3.5.05: The Universal Introduction Rule
3.5.06: The Existential Elimination Rule
3.06: More on Natural Deduction for Predicate Logic
3.6.01: Multiple Quantification and Harder Problems
3.6.02: Some Derived Rules
3.6.03: Logical Truth Contradictions Inconsistency and Logical Equivalence
3.07: Truth Trees for Predicate Logic - Fundamentals
3.7.01: The Rule for Universal Quantification
3.7.02: The Rule for Existential Quantification
3.7.03: Applying the Rules
3.7.04: Negated Quantified Sentences
3.08: More on Truth Trees for Predicate Logic
3.8.01: Contradictions Logical Truth Logical Equivalence and Consistency
3.8.02: Truth Trees with Multiple Quantifiers
3.8.03: Three Shortcuts
3.8.04: Infinite Trees
3.09: Identity Functions and Definite Descriptions
3.9.01: Identity
3.9.02: Inference Rules for Identity
3.9.03: Functions
3.9.04: Definite Descriptions
3.10: Metatheory - The Basic Concepts
3.10.01: Object Language and Metalanguage
3.10.02: Syntax and Semantics
3.10.03: Soundness and Completeness
3.10.04: Some Further Notation and Definitions
3.11: Mathematical Induction
3.11.01: Informal Introduction
3.11.02: The Principle of Weak Induction
3.11.03: Strong Induction
3.12: Soundness and Completeness for Sentence Logic Tree
3.12.01: Preliminaries
3.12.02: Soundness and Completeness of the Tree Method- Informal Statement
3.12.03: Soundness and Completeness for Sentence Logic Trees- Formal Details
3.13: Soundness and Completeness for Sentence Logic Derivation
3.13.01: Soundness for Derivations- Informal Introduction
3.13.02: Soundness for Derivations- Formal Details
3.13.03: Completeness for Derivations- Informal Introduction
3.13.04: Completeness for Derivations- Formal Details
3.14: Compactness and Generalization to Infinite Sets of Premises
3.14.01: Koenig's Lemma
3.14.02: Compactness and Infinite Sets of Premises
3.15: Interpretations Soundness and Completeness for Predicate Logic
3.15.01: Interpretations
3.15.02: Soundness and Completeness for Tree
3.15.03: Soundness for Predicate Logic Derivations
3.15.04: Completeness for Predicate Logic Derivations
3.15.05: Compactness Identity and Functions
3.15.06: Conclusion