Logic, Language and Philosophy: An Introduction to Standard Logic
by Fenrong Liu
CSLI, 2024
eISBN: 978-1-68400-083-8 | Paper: 978-1-68400-082-1
Library of Congress Classification BC71.L58 2024
Dewey Decimal Classification 160
eISBN: 978-1-68400-083-8 | Paper: 978-1-68400-082-1
Library of Congress Classification BC71.L58 2024
Dewey Decimal Classification 160
TOC
TABLE OF CONTENTS
Cover
Copyright
Contents
Preface
1.1 Reasoning and logic
1.2 Arguments and argument schemes
1.3 The anatomy of a logical system
1.4 Logic as a many-splendored thing
2.1 The topic
2.2 The authors
2.3 The texts
2.4 Study and discussion questions
2.5 Further reading
Part I: Proposition Logic
3.1 Introduction
3.2 Formal languages
3.3 Construction trees and induction
3.4 Applying a formal language
4.2 The authors
4.3 The texts
4.5 Further reading
5.2 Truth, truth conditions, truth tables
5.3 Semantics of connectives
5.4 Semantics of complex formulas
5.5 Semantics revisited
6.1 The topic
6.4 Study and discussion questions
6.5 Further reading
7.2 Equivalence
7.3 Tautology, contradiction, contingency
7.4 Validity
7.5 Truth functions and functional completeness
7.6 Conclusion
8.1 The topic
8.2 The author
8.3 The text
8.4 Study and discussion questions
8.5 Further reading
9.1 Validity and derivability
9.2 Natural deduction
9.3 Conjunction
9.4 Implication
9.5 Repetition
9.6 Disjunction
9.7 Negation
9.8 Concluding remarks
10.1 The topic
10.2 The author
10.3 The text
10.4 Study and discussion questions
10.5 Further reading
Part II: Predicate Logic
11.1 Introduction
11.2 Ingredients of a predicate logical language
11.3 Representation
11.4 Syntax: definition
12.1 The topic
12.2 The author
12.3 The text
12.4 Study and discussion questions
12.5 Further reading
13.1 Extending referential semantics
13.2 Ingredients
13.3 Substitutional Interpretation
13.4 Objectual interpretation
13.5 Truth and validity
13.6 Model checking
14.1 The topic
14.2 The author
14.3 The text
14.5 Further reading
15.1 Truth
15.2 Validity
15.3 Proving validity
15.4 Equivalence
15.5 Invalidity
16.1 Why?
16.3 Adding identity
16.4 Examples revisited
16.6 Model checking
17.1 The topic
17.2 The authors
17.3 The texts
17.4 Study and discussion questions
17.5 Further reading
18.1 Introduction
18.2 Some core properties of relations
18.3 Orderings
18.4 Use of orderings
18.6 Concluding remarks
19.1 Recap
19.2 Existential quantifier introduction
19.4 Universal quantifier introduction
19.5 Existential quantifier elimination
19.6 Identity introduction
19.7 Identity elimination
19.8 Concluding remarks
20.1 The topic
20.2 The author
20.3 The text
20.4 Study and discussion questions
20.5 Further reading
21.1 Introduction
21.2 Proofs about proofs
21.3 The soundness theorem
21.4 The completeness theorem
Part III: Beyond Standard Logic
22.1 Why many-valued logics?
22.2 But what about logic?
22.3 Three-valued logics
22.4 Concluding remarks
23.1 The topic
23.2 The author
23.3 The text
23.5 Further reading
24.1 Extensionality
24.2 Why intensional logic?
24.3 Relational semantics
24.4 Modal logics
24.5 Other interpretations of relational semantics
24.6 Proof theory for relational semantics
24.7 Extending the reach: quantified intensional logics
24.8 Further reading
25.1 The topic
25.2 The authors
25.3 The texts
25.4 Study and discussion questions
25.5 Further reading
26.1 Syntax, semantics, pragmatics
26.3 Literal meaning and context
26.4 Pragmatics
26.5 Varieties of contextualism
26.6 Open questions
27.1 The topic
27.2 The author
27.3 The text
27.5 Further reading
A.1 Sets
A.3 Ordered n-tuples
A.4 Relations, functions
Notes
Bibliography
Index
Back Cover
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