CONTENTS

Part I:

Introduction: What is logic the study of ?
-What is logic?
-The legend of Platonic Isles and Beth-trees
-The Beth-games
-The Aristotelian Mansion: Judgements, propositions and arguments, possible situations and counter-example sets
-The Fregean Palace
1 A (semantic) analysis of arguments
-Valid arguments, argument forms, and logical forms
-Truth-values of sentences and the semantic entailment relation
-Sentence functors and compound sentences
-Truth(-value) tables for sentence functors and truth-functors
-Some common truth functors and the standard truth-tables
-Truth-functional language and truth-functional logic
2 Toward propositional logic
-Sequents: formalization of ordinary arguments into argument forms
-Imperfection of natural language
-Toward a logical system -to characterize sequents in a logical system
-A formal language LK suitable for propositional logic
3 Semantics for the propositional language LK
-What is semantics?
-Basic assumptions of the semantics for LK
-Structures, truth-tables for truth-functors, and truth values of formulae in structures
-Semantic entailment relations, semantic sequents, tautology and inconsistency
-Counterexamples
-Testing the correctness of semantic sequents
-Symbolization of ordinary arguments in natural language as LK -sequents
4 Basic properties of semantic entailment relation in LK
-Some general properties of entailment relation in LK
-Substitution instances and substitution scheme
-(Logical) equivalence of formulae and some semantic theorems
-Truth-functions, the truth-functional completeness, expressive adequacy
-Disjunctive and conjunctive normal form
-Interpolation theorem, the compactness and decidability of LK
5 The (classical) propositional calculus (CPC): formal systems for propositional logic
-Elements of a formal system: axioms, rules of inference, derivations and theorems
-(Syntactic) inconsistency, soundness and completeness
-A (Hilbert-Frege style) axiomatic system (HPC) for propositional logic
-A system of formal tableaux for propositional logic
-Constructing counterexamples

6 Beyond propositional logic
-Limitations of propositional logic
-The subject-predicate distinction
-Some grammar, phrase-classes, phrase-markers
-Context-sensitive and context-free grammars
7 Preliminary to first-order languages - logical subjects, variables, predicates and quantifiers
-Designators, grammatical subjects and logical subjects; variables, predicates
-Quantificatoin of predicates and quantifiers
-First-order language
8 Preliminary to semantics for a first-order language
-Satisfaction, relations, identity, functions
-Structures of first order language
9 A first-order language LQ suitable for predicate logic and its semantics
-Elements of first-order languages
-A first-order language LQ suitable for predicate logic
-The standard semantics for the language LQ: structures and interpretations
-LQ -sequents, semantical entailments and validity
-Interpretations of LQ -sentences in ordinary discourse and counterexamples.
10 The (classical) predicate calculus (CQC): formal systems for predicate logic:
-A (Hilbert-Frege style) axiomatic system (HQC=) for predicate logic
-An LQ -tableaux system (a system of formal tableaux for predicate logic)
-Counterexamples and interpretation in ordinary discourse
-A system of formal tableaux for predicate logic which accepts the empty domain
11 Symbolization of ordinary arguments as LQ -sequents
-Simple ordinary sentences, compound predicates, predicative adjectives, quantificational phrases and numeral adjectives
-Descriptions
Appendix A: Traditional (Aristotlean) logic and some traditional topics
-Syllogism, definitions, fallacy, inductive logic vs. deductive logic
Appendix B: The development of modern logic - a historical survey from 1879 to the 1970s
-The background
-The landmark: 1879 - the publication of Gottlob Frege's Begriffsschrift
-The establishment of elementary logic
-The development of formal logic: set theory, model theory, Godel's incompleteness theorems (recursion theory/computability), proof theory
-The rise and development of non-classical logic
-The impact of modern logic on contemporary philosophy
Appendix C: The movement of Anglo-American philosophy in the 20th century -- a historical survey from 1879 to the 1970s