Intro -- Preface -- Introduction -- Contents -- Part I Harmony -- 1 Harmony via Reductions and Expansions -- 1.1 Meaning Theory and Harmony -- 1.2 Harmony and Natural Deduction -- 1.3 Harmony, Reductions and Expansions -- 1.4 Some Formal Definitions -- 1.5 Some Formal Results -- 1.6 Canonicity -- 1.7 Normalization, Subformula Property, Canonicity and Harmony -- 1.8 A Quick Comparison with Other Approaches -- 2 Identity of Proofs -- 2.1 Proof-Theoretic Semantics -- 2.2 Proofs as Constructions -- 2.3 Derivations and Proofs -- 2.4 From Reductions and Expansions to Equivalence -- 2.5 Formula Isomorphism -- 2.6 An Intensional Picture -- 2.7 Weak Notions of Reduction and Equivalence -- 2.8 Derivations and Proofs, Again -- 2.9 Validity -- 2.10 Correctness of Rules -- 2.11 The Relative Priority of Correctness and Validity -- 3 Towards an Intensional Notion of Harmony -- 3.1 Disjunction: A Problem for Stability -- 3.2 A ``Quantum-Like'' Implication -- 3.3 Generalizing the Expansions for Disjunction -- 3.4 Harmony: Arbitrary Connectives and Quantifiers -- 3.5 Stability and Permutations -- 3.6 The Meaning of Harmony -- 3.7 Comparison with Jacinto and Read's GE-Stability -- 3.8 Harmony by Interderivability -- 3.9 Yet Another Inversion Principle -- 3.10 Harmony by Interderivability is Not Intensional -- Part II Paradox -- 4 Paradoxes: A Natural Deduction Approach -- 4.1 The Prawitz-Tennant Analysis of Paradoxes -- 4.2 A Simplified Presentation -- 4.3 Which Background Logic? -- 4.4 A Substructural Analysis -- 5 Validity, Sense and Denotation in the Face of Paradoxes -- 5.1 Paradoxes as Non-denoting Derivations -- 5.2 Non-denoting Derivations and (In)validity -- 5.3 The Need of Revising Prawitz's Validity -- 5.4 The Local Correctness of an Inference -- 5.5 Local Correctness Versus Global Validity -- 5.6 rhoρ Versus monospace t o n ktonk.

5.7 Paradox and Partial Functions -- 5.8 Meaning Explanations for Paradoxes -- 5.9 Conservativity -- 6 Two Kinds of Difficulties -- 6.1 From Naive Comprehension to Separation -- 6.2 Ekman's Paradox -- 6.3 A Solution to Ekman's Overgeneration -- 6.4 Von Plato's Solution to Ekman -- 6.5 Another ``Safe Version'' of Russell's Paradox -- 6.6 Ekman on Decomposing Inferences -- 6.7 Implication-as-Link and General Ekman-Reductions -- 6.8 Copy-and-Paste Subproof Compactification -- 6.9 General Introduction Rules and EkmanSubscript gg -- 6.10 Conclusions and Outlook -- Appendix Concluding Remarks -- Appendix A The Calculus of Higher-Level Rules -- A.1 Some Preliminary Remarks -- A.2 Concrete Rules -- A.3 Structural Derivations -- A.4 Rules and monospace upper KK-derivations -- A.5 Derivation of Rules and Derivability -- A.6 Identifications up to Renaming Discharge Indexes -- A.7 Composition of Derivations and Transitivity -- A.8 Identity Derivations and Reflexivity -- A.9 PSH-Inversion and Harmony -- Appendix References -- -- Index.