Logic Works is a critical and extensive introduction to logic. It asks questions about why systems of logic are as they are, how they relate to ordinary language and ordinary reasoning, and what alternatives there might be to classical logical doctrines.
The book covers classical first order logic and alternatives, including intuitionistic, free, and many-valued logic. It also considers how logical analysis can be applied to carefully represent the reasoning employed in academic and scientific work, better understand that reasoning, and identify its hidden premises. Aiming to be as much a reference work and handbook for further, independent study as a course text, it covers more material than is typically covered in an introductory course. It also covers this material at greater length and in more depth with the purpose of making it accessible to those with no prior training in logic or formal systems.
A companion website contains a detailed student solutions manual with a running commentary on all starred exercises and a set of editable slides for instructors to customize their courses.
Key Features
- Introduces an unusually broad range of topics, allowing instructors to craft courses to meet a range of various objectives
- Adopts a critical attitude to certain classical doctrines, exposing students to alternative ways to answer philosophical questions about logic
- Carefully considers the ways natural language both resists and lends itself to formalization
- Makes objectual semantics for quantified logic easy, with an incremental, rule-governed approach assisted by numerous simple exercises
- Makes important metatheoretical results accessible to introductory students through a discursive presentation of those results and by using simple case studies
Author(s): Lorne Falkenstein, Scott Stapleford, Molly Kao
Edition: 1
Publisher: Routledge
Year: 2021
Language: English
Pages: 576
Tags: logic; deductive demonstration; inductive demonstration;
Cover
Half Title
Endorsement
Title Page
Copyright Page
Table of Contents
Preface
Instructors’ Preface
Acknowledgements
Symbol Summary
1 Introduction to the Study of Logic
1.1 Demonstration and Interpretation
1.2 Deductive and Inductive Demonstrations
1.3 The Principle of Noncontradiction
1.4 Abstraction, Variables, and Formalization; Logical and Nonlogical Elements; Formal Contradiction
1.5 A Fundamental Problem
1.6 Chapter Outline
Technical Appendix: Elements of a Theory of Demonstrative Logic
Notes
References
Part I Sentential Logic
2 Vocabulary and Syntax
2.1 Introduction
2.2 Conventions
2.3 Syntactic Demonstrations and Trees
2.4 Scope; Main Connective and Immediate Components; Named Forms
2.5 Formal Properties
Note
3 Semantics
3.1 Semantics for ⊥ and the Sentence Letters
3.2 Semantics for the Connectives
3.3 Semantics for Compound Sentences
3.3.1 Extensional Meaning
3.3.2 Intensional Meaning
3.4 Intensional Concepts
Appendix Expressive Adequacy; Disjunctive Normal Form; The Lean Language
Notes
4 Formalization
4.1 Looseness of Fit
4.1.1 Formalization of Sentences as Sentence Letters
4.1.2 Formalization of Connective Expressions
4.2 Conditional Sentences of English
4.3 Necessary Conditions
4.4 Sufficient Conditions
4.5 Necessary and Sufficient Conditions; The Principle of Charity
4.6 Formalizing Necessary and Sufficient Conditions
4.7 Exceptions and Strong Exceptions
4.8 Disjunction
4.9 Negations and Conjunctions
4.10 Punctuation
4.11 Limits of Formalization
4.12 Formalizing Demonstrations
Notes
References
5 Working With SL Semantics
5.1 Identifying and Verifying Interpretations
5.2 Demonstrating That There Is No Interpretation
5.3 Demonstrating General Principles
5.4 Falsifying General Claims
5.5 Relations Between Intensional Concepts; Models; Entailment; Biconditional Proof
Appendix Alternatives to Bivalence
Appendix 5.1 Supervaluations
Appendix 5.2 Three-Valued Logic
Appendix 5.3 Paraconsistent Logic
Notes
References
A-1: Advanced Topics Concerning SL Semantics
A-1.1 Mathematical Induction
A-1.2 Bivalence
A-1.3 Extensionality
A-1.4 Compactness
Note
References
6 Derivations
6.1 DL: A Lean Derivation System
6.2 Strategies for Doing Derivations in DL
6.3 Ds: A Derivation System for SL
6.4 Strategies for Doing Derivations in Ds
6.5 Extensions of Ds; Bracket Free Notation
6.5.1 Systematic Overview; Adequacy of DL
6.5.2 Metatheorems and Derived Rules for Ds
6.5.3 Substitution Principles
6.5.4 Disjunctive Normal Form
6.5.5 Relations Between Intensional Concepts
6.5.6 Bracket Free Notation
6.6 Intuition and “Intuitionism”: Derivation in Intuitionistic Logic
Notes
References
A-2: Advanced Topics Concerning the Soundness and Completeness of Ds
A-2.1 Soundness
A-2.2 Corollary Results
A-2.3 Henkin Completeness
A-2.4 Demonstration of the Lindenbaum Lemma
A-2.5 Demonstration of Lemma 2
A-2.6 Demonstration of Lemma 3
A-2.7 Corollary Results
A-2.8 Post/Hilbert–Ackermann Completeness
7 Reduction Trees
7.1 Method and Strategies
7.2 Using Trees to Determine Derivability
7.2.1 Theorems; Inconsistent and Contingent Sentences
7.2.2 Demonstrations
7.2.3 Interderivability
7.3 Theory and Definitions
Appendix Trees for Three-Valued and Paraconsistent Logic
Notes
References
A-3: Advanced Topics Concerning the Soundness and Completeness of Ts
A-3.1 Soundness of Ts
A-3.2 Completeness of Ts
A-3.3 Decidability of Ts
A-3.4 Tree Conversion; Completeness and Decidability of Ds
Part II Modal Sentential Logic
8 Vocabulary, Syntax, Formalization, and Derivations
8.1 Vocabulary and Syntax
8.2 Formalization
8.3 Derivations
Notes
9 Semantics and Trees for Modal and Intuitionistic Sentential Logic
9.1 Semantics for Modal Sentential Logic
9.1.1 Discovering Interpretations
9.1.2 Demonstrating That There Is No Interpretation
9.2 Reduction Trees for Modal Sentential Logic
9.3 Semantics for Intuitionistic Sentential Logic
9.4 Reduction Trees for Intuitionistic Sentential Logic
References
A-4: Advanced Topics Concerning the “Soundness” and “Completeness” of Dm and Tm
A-4.1 “Soundness” of Dm
A-4.2 Completeness of Tm
A-4.3 Tree Conversions
A-4.4 Adequacy of Dm and Tm
Notes
References
Part III Predicate Sentential Logic
10 Vocabulary, Syntax, Formalization, and Derivations
10.1 English Predication
10.2 Simple Terms
10.2.1 Vocabulary and Syntax of Predicate Sentential Logic
10.2.2 Formalization
10.2.3 Derivations
10.3 Complex Terms
10.3.1 Functional Terms
10.3.2 Vocabulary and Syntax of PLf; Formalization
10.3.3 Dpf
10.3.4 Definite Descriptions
10.3.5 Vocabulary and Syntax of PL1; Formalization
11 Semantics and Trees
11.1 Interpretations
11.1.1 Domains
11.1.2 Names
11.1.3 Predicates and Satisfaction
11.1.4 Identity
11.2 Valuation Rules
11.3 Working With the Semantics
11.4 Tp
11.5 Semantics for Functional Terms
11.6 Tpf
11.6.1 Systematic Paths
11.6.2 Decidability
11.7 Semantics for PL1
11.7.1 Variable Assignments
11.7.2 Denotation for Variables
11.7.3 Satisfaction
11.7.4 Denotation for Proper Descriptions
11.7.5 Truth Conditions
11.7.6 Denotation for Improper Descriptions
11.7.7 Free Description Theory
Notes
References
A-5: Advanced Topics for PSL
A-5.1 Extensionality and Variance
A-5.1.1 Extensionality
A-5.1.2 Variance
A-5.1.2.1 The Variant Interpretation Principle
A-5.1.2.2 The Variant Name Principle
A-5.2 Soundness of Dp
A-5.3 Completeness of Tp
A-5.4 Tree Conversion; Soundness of Tp; Completeness of Dp
Note
Part IV Quantified Predicate Logic
12 Vocabulary, Syntax, and Formalization
12.1 Informal Vocabulary and Syntax
12.1.1 Symbols for Objects
12.1.2 Symbols for Quantities of Objects
12.1.3 Informal Syntax
12.2 Formal Vocabulary and Syntax
12.3 Formalizing English Sentences in Quantified Predicate Logic
12.3.1 Simply Quantified Sentences; Scope
12.3.2 Multiply Quantified Sentences; Scope Ambiguity
12.3.3 Negations of Quantified Claims; Duality; The Square of Opposition; “Any”
12.3.4 Formalizing Relations Between Predicates
12.3.5 A, E, I, and O Sentences; Existential Import
12.3.6 Predicate Descriptions; Changing Scope
12.3.7 Quantities and Superlatives
12.3.8 Definite Descriptions
12.3.9 Bare Existence; Limits of Formalization
Notes
References
13 Derivations
13.1 Dq
13.2 Extensions of Dq
13.2.1 Functional Terms
13.2.2 Intuitionistic Logic
13.2.3 Free Logic
13.2.4 Free Description Theory
Notes
References
14 Trees and Tree Model Semantics for Quantified Predicate Logic
14.1 Rules
14.2 Method
14.3 Tree Model Semantics
14.4 Extensions of Tq
14.4.1 Functional Terms
14.4.2 Semantics and Trees for Intuitionistic Logic
14.4.3 Semantics and Trees for Free Logic
14.4.4 Semantics and Trees for Free Description Theories
Notes
References
15 Semantics for QPL Without Mixed Multiple Quantification
15.1 Objectual Semantics
15.2 Denotation
15.2.1 Variable Assignments
15.2.2 Names
15.3 Satisfaction
15.3.1 Satisfaction Conditions for Predicate and Identity Formulas
15.3.2 Satisfaction Conditions for ., Zero-Place Predicates, and Connective Compounds
15.3.3 Satisfaction Conditions for Singly Quantified Formulas
15.4 Truth
15.5 Working With the Semantics
15.5.1 Discovering Interpretations
15.5.2 Discovering Contradictions
15.6 Demonstrating General Principles
15.6.1 Extensionality
15.6.2 Variance
Notes
16 Semantics for QPL With Mixed Multiple Quantification
16.1 Variants On Variable Assignments; Denotation of Variables
16.2 Satisfaction Conditions for Quantified Formulas
16.3 (P) and (=) Applications
16.4 Truth Conditions for Sentences
16.5 Working With the Semantics
16.5.1 Order of List Items
16.5.2 Embellishing the Variant List
16.5.3 Describing the Model at a More Abstract Level
16.5.4 Avoiding Inversion
Appendix Demonstration of the Exclusivity Principle
A-6: Advanced Topics for QPL
A-6.1 Extensionality and Variance
A-6.1.1 Name Extensionality
A-6.1.2 Variable Extensionality
A-6.1.3 Formula Extensionality
A-6.1.4 Variance
A-6.2 Soundness of Dq
A-6.3 Completeness of Tq
A-6.4 Tree Conversion; Soundness of Tq; Completeness of Dq
Appendix Quantified Modal Logic
A-6.A.1 Objects and Worlds
A-6.A.1.1 Counterpart Theory
A-6.A.1.2 Haecceity Theory
A-6.A.2 Names and Predicates
A-6.A.3 Quantifier Domains and the Barcan Formulas
A-6.A.4 Derivation and Tree Rules
A-6.A.5 Substances
Reference
17 Higher-Order Logic
17.1 Vocabulary and Syntax
17.2 Formalization; Definitions of Higher-Order Predicates
17.3 Syntax II: Instances
17.4 Derivations
17.5 Semantics
17.6 Trees and Incompleteness
Notes
References
Main Appendix: Rule Summaries
1 Foundational Definitions
2 Intensional Concepts
3 Formation Rules
(Def Sentence)
Informal Notational Conventions
(Def Instance)
4 Sentential Valuation Rules
5 Formulaic and Free Valuation Rules
6 Derivation Rules
7 Tree Rules
Rules for Intuitionistic Sentential Trees
Index
