-An Introduction to Non-Classical Logic:From If to Is- by Graham Priest
This revised and considerably expanded edition of An Introduction to Non-Classical Logic brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics.
Part I, on propositional logic, is the old Introduction, but contains much new material.
Part II is entirely novel, and covers quantification and identity for all the logics in Part I.
The material is unified by the underlying theme of world semantics.
Contents
Preface to the First Edition
Preface to the Second Edition
Mathematical Prolegomenon
0.1 Set-theoreticNotation
0.2 Proof by Induction
0.3 Equivalence Relations and Equivalence Classes
Part I Propositional Logic
1 Classical Logic and the Material Conditional
1.1 Introduction
1.2 The Syntax of the Object Language
1.3 SemanticV alidity
1.4 Tableaux
1.5 Counter-models
1.6 Conditionals
1.7 The Material Conditional
1.8 Subjunctive and Counterfactual Conditionals
1.9 More Counter-examples
1.10 Arguments for ?
1.11 ?Proofs of Theorems
1.12 History
1.13 Further Reading
1.14 Problems
2 BasicModal Logic
2.1 Introduction
2.2 Necessity and Possibility
2.3 Modal Semantics
2.4 Modal Tableaux
2.5 Possible Worlds: Representation
2.6 Modal Realism
2.7 Modal Actualism
2.8 Meinongianism
2.9 *Proofs of Theorems
2.10 History
2.11 Further Reading
2.12 Problems
Normal Modal Logics
3.1 Introduction
3.2 Semantics for Normal Modal Logics
3.3 Tableaux for Normal Modal Logics
3.4 Infinite Tableaux
3.5 S5
3.6 Which System Represents Necessity?
3.6a The Tense Logic Kt
3.6b Extensions of Kt
3.7 *Proofs of Theorems
3.8 History
3.9 Further Reading
3.10 Problems
Non-normal Modal Logics; Strict Conditionals
4.1 Introduction
4.2 Non-normal Worlds
4.3 Tableaux for Non-normal Modal Logics
4.4 The Properties of Non-normal Logics
4.4a S0.5
4.5 Strict Conditionals
4.6 The Paradoxes of Strict Implication
4.7 ... and their Problems
4.8 The Explosion of Contradictions
4.9 Lewis' Argument for Explosion
4.10 *Proofs of Theorems
4.11 History
4.12 Further Reading
4.13 Problems
5 Conditional Logics
5.1 Introduction
5.2 Some More ProblematicInferenc es
5.3 Conditional Semantics
5.4 Tableaux for C
5.5 Extensions of C
5.6 Similarity Spheres
5.7 C1 and C2
5.8 Further Philosophical Reflections
5.9 *Proofs of Theorems
5.10 History
5.11 Further Reading
5.12 Problems
6 Intuitionist Logic
6.1 Introduction
6.2 Intuitionism: The Rationale
6.3 Possible-world Semantics for Intuitionism
6.4 Tableaux for Intuitionist Logic
6.5 The Foundations of Intuitionism
6.6 The Intuitionist Conditional
6.7 *Proofs of Theorems
6.8 History
6.9 Further Reading
6.10 Problems
7 Many-valued Logics
7.1 Introduction
7.2 Many-valued Logic: The General Structure
7.3 The 3-valued Logics of Kleene and Lukasiewicz
7.4 LP and RM3
7.5 Many-valued Logics and Conditionals
7.6 Truth-value Gluts: Inconsistent Laws
7.7 Truth-value Gluts: Paradoxes of Self-reference
7.8 Truth-value Gaps: Denotation Failure
7.9 Truth-value Gaps: Future Contingents
7.10 Supervaluations, Modality and Many-valued Logic
7.11 *Proofs of Theorems
7.12 History
7.13 Further Reading
7.14 Problems
First Degree Entailment
8.1 Introduction
8.2 The Semantics of FDE
8.3 Tableaux for FDE
8.4 FDE and Many-valued Logics
8.4a Relational Semantics and Tableaux for L3 and RM3
8.5 The Routley Star
8.6 Paraconsistency and the Disjunctive Syllogism
8.7 *Proofs of Theorems
8.8 History
8.9 Further Reading
8.10 Problems
Logics with Gaps, Gluts and Worlds
9.1 Introduction
9.2 Adding >
9.3 Tableaux for K4
9.4 Non-normal Worlds Again
9.5 Tableaux for N4
9.6 Star Again
9.7 Impossible Worlds and Relevant Logic
9.7a Logics of Constructible Negation
9.8 *Proofs of Theorems
9.9 History
9.10 Further Reading
9.11 Problems
10 Relevant Logics
10.1 Introduction
10.2 The Logic B
10.3 Tableaux for B
10.4 Extensions of B
10.4a Content Inclusion
10.5 The System R
10.6 The Ternary Relation
10.7 Ceteris Paribus Enthymemes
10.8 *Proofs of Theorems
10.9 History
10.10 Further Reading
10.11 Problems
11 Fuzzy Logics
11.1 Introduction
11.2 Sorites Paradoxes
11.3 . . . and Responses to Them
11.4 The Continuum-valued Logic L
11.5 Axioms for L?
11.6 Conditionals in L
11.7 Fuzzy Relevant Logic
11.7a *Appendix: t-norm Logics
11.8 History
11.9 Further Reading
11.10 Problems
11a Appendix: Many-valued Modal Logics
11a.1 Introduction
11a.2 General Structure
11a.3 Illustration: Modal Lukasiewicz Logic
11a.4 Modal FDE
11a.5 Tableaux
11a.6 Variations
11a.7 Future Contingents Revisited
11a.8 A Glimpse Beyond
11a.9 *Proofs of Theorems
Postscript: An Historical Perspective on Conditionals
Part II Quantification and Identity
12 Classical First-order Logic
12.1 Introduction
12.2 Syntax
12.3 Semantics
12.4 Tableaux
12.5 Identity
12.6 Some Philosophical Issues
12.7 Some Final Technical Comments
12.8 *Proofs of Theorems 1
12.9 *Proofs of Theorems 2
12.10 *Proofs of Theorems 3
12.11 History
12.12 Further Reading
12.13 Problems
13 Free Logics
13.1 Introduction
13.2 Syntax and Semantics
13.3 Tableaux
13.4 Free Logics: Positive, Negative and Neutral
13.5 Quantification and Existence
13.6 Identity in Free Logic
13.7 *Proofs of Theorems
13.8 History
13.9 Further Reading
13.10 Problems
14 Constant Domain Modal Logics
14.1 Introduction
14.2 Constant Domain K
14.3 Tableaux for CK
14.4 Other Normal Modal Logics
14.5 Modality De Re and De Dicto
14.6 Tense Logic
14.7 *Proofs of Theorems
14.8 History
14.9 Further Reading
14.10 Problems
15 Variable Domain Modal Logics
15.1 Introduction
15.2 Prolegomenon
15.3 Variable Domain K and its Normal Extensions
15.4 Tableaux for VK and its Normal Extensions
15.5 Variable Domain Tense Logic
15.6 Extensions
15.7 Existence Across Worlds
15.8 Existence and Wide-Scope Quantifiers
15.9 *Proofs of Theorems
15.10 History
15.11 Further Reading
15.12 Problems
16 Necessary Identity in Modal Logic
16.1 Introduction
16.2 Necessary Identity
16.3 The Negativity Constraint
16.4 Rigid and Non-rigid Designators
16.5 Names and Descriptions
16.6 *Proofs of Theorems 1
16.7 *Proofs of Theorems 2
16.8 History
16.9 Further Reading
16.10 Problems
17 Contingent Identity in Modal Logic
17.1 Introduction
17.2 Contingent Identity
17.3 SI Again, and the Nature of Avatars
17.4 *Proofs of Theorems
17.5 History
17.6 Further Reading
17.7 Problems
18 Non-normal Modal Logics
18.1 Introduction
18.2 Non-normal Modal Logics and Matrices
18.3 Constant Domain Quantified L
18.4 Tableaux for Constant Domain L
18.5 Ringing the Changes
18.6 Identity
18.7 *Proofs of Theorems
18.8 History
18.9 Further Reading
18.10 Problems
19 Conditional Logics
19.1 Introduction
19.2 Constant and Variable Domain C
19.3 Extensions
19.4 Identity
19.5 Some Philosophical Issues
19.6 *Proofs of Theorems
19.7 History
19.8 Further Reading
19.9 Problems
20 Intuitionist Logic
20.1 Introduction
20.2 Existence and Construction
20.3 Quantified Intuitionist Logic
20.4 Tableaux for Intuitionist Logic1
20.5 Tableaux for Intuitionist Logic2
20.6 Mental Constructions
20.7 Necessary Identity
20.8 Intuitionist Identity
20.9 *Proofs of Theorems 1
20.10 *Proofs of Theorems 2
20.11 History
20.12 Further Reading
20.13 Problems
21 Many-valued Logics
21.1 Introduction
21.2 Quantified Many-valued Logics
21.3 ? and ?
21.4 Some 3-valued Logics
21.5 Their Free Versions
21.6 Existence and Quantification
21.7 Neutral Free Logics
21.8 Identity
21.9 Non-classical Identity
21.10 Supervaluations and Subvaluations
21.11 *Proofs of Theorems
21.12 History
21.13 Further Reading
21.14 Problems
22 First Degree Entailment
22.1 Introduction
22.2 Relational and Many-valued Semantics
22.3 Tableaux
22.4 Free Logics with Relational Semantics
22.5 Semantics with the Routley ?
22.6 Identity
22.7 *Proofs of Theorems 1
22.8 *Proofs of Theorems 2
22.9 *Proofs of Theorems 3
22.10 History
22.11 Further Reading
22.12 Problems
23 Logics with Gaps, Gluts and Worlds
23.1 Introduction
23.2 Matrix Semantics Again
23.3 N4
23.4 N?
23.5 K4 and K?
23.6 Relevant Identity
23.7 Relevant Predication
23.8 Logics with Constructible Negation
23.9 Identity for Logics with Constructible Negation
23.10 *Proofs of Theorems 1
23.11 *Proofs of Theorems 2
23.12 *Proofs of Theorems 3
23.13 History
23.14 Further Reading
23.15 Problems
24 Relevant Logics
24.1 Introduction
24.2 Quantified B
24.3 Extensions of B
24.4 Restricted Quantification
24.5 Semantics vs Proof Theory
24.6 Identity
24.7 Properties of Identity
24.8 *Proofs of Theorems 1
24.9 *Proofs of Theorems 2
24.10 History
24.11 Further Reading
24.12 Problems
25 Fuzzy Logics
25.1 Introduction
25.2 Quantified Lukasiewicz Logic
25.3 Validity in L?
25.4 Deductions
25.5 The Sorites Again
25.6 Fuzzy Identity
25.7 Vague Objects
25.8 *Appendix: Quantification and Identity in
t-norm Logics
25.9 History
25.10 Further Reading
25.11 Problems
Postscript: A Methodological Coda
References
Index of Names
Index of Subjects
with TOC BookMarkLinks
& 097;bout: Graham Priest is Boyce Gibson Professor of Philosophy, University of Melbourne and Arche Professorial Fellow, Departments of Philosophy, University of St Andrews. His most recent publications include Towards Non-Being (2005) and Doubt Truth to be a Liar (2006).
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