Contents -- Preface -- Abbreviations and symbols -- 1 Logic and entailment -- 1.1 What is a logic and why do we need one in the study of language? -- 1.2 The definition of entailment -- 1.2.1 The general concept of entailment -- 1.2.2 The specific concept of logical entailment -- 1.3 The referential independence of logic: no truth-value gaps -- 1.4 Logical form and L-propositions -- 1.5 The Bivalence Principle, sentence types, and utterance tokens -- 1.6 Some problems with the assignment of truth values -- 2 Logic: a new beginning -- 2.1 Entailment, contrariety and contradiction: the natural triangle -- 2.2 Internal negation and duality: the natural square and the Boethian square -- 2.3 Logical operators as predicates -- 2.3.1 Meaning postulates -- 2.3.2 Boolean algebra and the operators of propositional calculus -- 2.3.3 Valuation space modelling: a formal definition -- 2.3.4 Satisfaction conditions of the propositional operators -- 2.3.5 Satisfaction conditions of the quantifiers -- 2.4 Internal negation, the Conversions and De Morgan's laws -- 2.4.1 The internal negation again -- 2.4.2 The Conversions and De Morgan's laws -- 3 Natural set theory and natural logic -- 3.1 Introductory observations -- 3.2 Some set-theoretic principles of natural cognition -- 3.2.1 A résumé of standard set theory -- 3.2.2 The restrictions imposed by NST -- 3.3 Consequences for set-theoretic and (meta)logical relations and functions -- 3.3.1 Consequences for set-theoretic relations and functions -- 3.3.2 Consequences for (meta)logical relations and functions -- 3.4 The basic-natural systems of logic -- 3.4.1 Basic-natural predicate logic: the necessity of a cognitive base -- 3.4.2 Hamilton's predicate logic -- 3.4.3 Basic-natural propositional logic -- 3.5 Neither *nand nor *nall: NST predicts their absence.

3.5.1 The problem and the solution proposed by pragmaticists -- 3.5.2 Preliminary objections -- 3.5.3 The main objection and a stronger solution -- 3.5.4 Parallel lexical gaps in epistemic-modal and causal logic? -- 4 Logical power, Abelard, and empirical success rates -- 4.1 Aristotelian predicate calculus rescued from undue existential import -- 4.2 The notion of logical power -- 4.2.1 The logical power of propositional calculus -- 4.2.2 The logical power of Aristotelian-Boethian predicate calculus -- 4.2.3 The logical power of standard modern predicate calculus -- 4.2.4 The logical power of Aristotelian-Abelardian predicate calculus -- 4.3 Distributive quantifiers -- 4.4 Predicate logics and intuitions: a scale of empirical success -- 5 Aristotle, the commentators, and Abelard -- 5.1 A recapitulation of ABPC -- 5.2 The not quite Aristotelian roots of ABPC -- 5.2.1 Aristotle's own predicate logic -- 5.2.2 The ancient commentators -- 5.2.3 The Square representation -- 5.2.4 An aside on Horn's and Parsons' proposal as regards the O-corner -- 5.2.5 Logic and mysticism: what made logic popular? -- 5.3 Abelard's remedy -- 6 The functionality of the Square and of BNPC -- 6.1 How to isolate the cases with a null F-class: the purpose of space 4 -- 6.2 Extreme values are uninformative in standard modern predicate calculus -- 6.3 The functionality of excluding extreme values -- 6.4 The functionality of BNPC -- 6.5 Conclusion -- 7 The context-sensitivity of speech and language -- 7.1 What is context-sensitivity? -- 7.2 Discourse domains -- 7.2.1 The commitment domain and further subdomains -- 7.2.2 The Principle of Maximal Unity -- 7.3 Conditions for text coherence -- 7.3.1 Consistency -- 7.3.2 Informativity -- 7.3.3 Subdomain hierarchies: subsidiary subdomains -- 7.4 Open parameters in lexical meaning -- 8 Discourse incrementation.

8.1 The incrementation procedure -- 8.1.1 Singular entity addresses and address closure -- 8.1.2 Plurality and quantification -- 8.1.3 Subordinate subdomains -- 8.2 Instructions -- 8.2.1 Conjunction -- 8.2.2 Negation -- 8.2.3 Disjunction -- 8.2.4 Conditionals -- 9 Primary and donkey anaphora -- 9.1 Introduction -- 9.2 Reference by anaphora -- 9.3 Primary anaphora: bound variable or external anaphor? -- 9.4 Donkey sentences -- 9.4.1 The problem -- 9.4.2 The history of the problem -- 9.5 The reference-fixing algorithm -- 9.6 The solution -- 9.6.1 Donkey anaphora under disjunction -- 9.6.2 Donkey anaphora in conditionals -- 9.6.3 Donkey anaphora under universal quantification -- 10 Presupposition and presuppositional logic -- 10.1 Presupposition as an anchoring device -- 10.1.1 Some early history -- 10.1.2 The Russell tradition -- 10.1.3 The Frege-Strawson tradition -- 10.2 The origin and classification of presuppositions -- 10.3 Operational criteria for the detection of presuppositions -- 10.4 Some data that were overlooked -- 10.5 Presupposition projection -- 10.5.1 What is presupposition projection? -- 10.5.2 Projection from lexical subdomains -- 10.5.3 Projection from instructional subdomains -- 10.5.4 Summary of the projection mechanism -- 10.6 The presuppositional logic of the propositional operators -- 10.7 The presuppositional logic of quantification -- 10.7.1 The presuppositional version of the Square and of SMPC -- 10.7.2 The presuppositional version of BNPC -- 10.7.3 The victorious Square -- 10.8 The attempt at equating anaphora with presupposition -- 11 Topic-comment modulation -- 11.1 What is topic-comment modulation? -- 11.1.1 The Aristotelian origin of topic-comment modulation -- 11.1.2 The discovery of the problem in the nineteenth century -- 11.1.3 The dynamics of discourse: the question-answer game.

11.2 Phonological, grammatical, and semantic evidence for TCM -- 11.3 The comment-predicate Be[sub(v)] -- 11.4 Only, even, and Neg-Raising -- 11.5 Why TCM is a semantic phenomenon: the SSV test -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.