Meaning in Dialogue: An Interactive Approach to Logic and Reasoning (Studies in Applied Philosophy, Epistemology and Rational Ethics Book 33)

This book argues for a view in which processes of dialogue and interaction are taken to be foundational to reasoning, logic, and meaning. This is both a continuation, and a substantial modification, of an inferentialist approach to logic. As such, the book not only provides a critical introduction to the inferentialist view, but it also provides an argument that this shift in perspective has deep and foundational consequences for how we understand the nature of logic and its relationship with meaning and reasoning. This has been upheld by several technical results, including, for example a novel approach to logical paradox and logical revision, and an account of the internal justification of logical rules. The book shows that inferentialism is greatly strengthened, such that it can answer the most stringent criticisms of the view. This leads to a view of logic that emphasizes the dynamics of reasoning, provides a novel account of the justification and normativity of logical rules, thus leading to a new, attractive approach to the foundations of logic. The book addresses readers interested in philosophy of language, philosophical and mathematical logic, theories of reasoning, and also those who actively engage in current debates involving, for example, logical revision, and the relationship between logic and reasoning, from advanced undergraduates, to professional philosophers, mathematicians, and linguists.0 Acknowledgements 7 Contents 9 1 Introduction: Reasoning in Time and Space 12 1 From Representationalism to Inferentialism 12 2 A Puzzle Involving a Tortoise 14 3 Inferentialist Semantics and Dialogue 18 4 From the Foundation of Rules to the Action of Reasons 22 5 Structure 25 References 29 2 Inferentialism and Its Discontents 31 1 Inferentialism (A Brief Overview) 31 2 Dispositions and Circular Justifications 34 3 Paradoxical Connectives 40 4 Modest Inferentialism and Its Problems 41 5 An Alternative in Harmony? 47 6 Soundness and Completeness 51 References 53 3 Proof and Assertion 56 1 From the Monological to the Dialogical 57 2 The Nature of ``Proofs'' and ``Proving'' 63 2.1 Proofs as Reducible to Formal Derivation 64 2.2 Proofs as Objects, and as Acts 66 2.3 Liberalising Proofs 69 3 The Dynamics of Assertions 71 4 Meanings and ``Use'' 76 5 Balancing Assertions and Denials 80 References 84 4 Dialogue and Refutation 87 1 Dialogues and Games 88 2 Logical Games 90 3 Mathematical Games 96 4 Dialogical Constraints 102 5 Reasoning, Emotion, and Co-operation 106 6 Internalised Dialogues Without Rules 110 References 113 5 Rules in Dialogue 117 1 Dialogue, Interaction, and Coherence 117 1.1 Shared Focus 118 1.2 Symmetry over Agents 122 1.3 Excursus: Duality as Symmetric Reversal 129 1.4 Coherence, Convergence and Resolution 134 2 Interactions and Coherence Conditions 135 3 Local Completeness and the Reconstruction of Logic 142 3.1 Logic and Transcendental Constraints 147 4 Comparison with Other Systems 148 4.1 Refutability Systems 148 4.2 Bi-Intuitionistic Logic 151 4.3 Linear Logic and Ludics 154 4.4 Non-monotonic Logics and Negation as Failure 158 References 161 6 Structuring Interactions 165 1 Proof Objects and More Standard Semantical Approaches 165 1.1 Dualising Types, Algebras, and Forcing 166 1.2 Categorial Collapse 171 1.3 Dualising Topoi 172 1.4 Harnessing ``Collapse'' Between Topoi 179 2 Processes and Types 184 2.1 Testing and Type-Construction 186 2.2 Operations over Processes 188 2.3 Liberalising Coherence 191 References 195 7 Paradox, Paraconsistency and Logical Revision 197 1 A (Standard) Inferentialist Approach to Paradox 197 2 Logical Revisions Down the Rabbit Hole 201 3 From Paradox to Paracoherence 207 4 Paracoherent Interactions 210 4.1 Local Truth and Falsity 212 4.2 Logic and Truth 215 References 216 8 Naturalization, Normativity, and Ethics 219 1 Naturalising Logic 219 1.1 Collapsing the Normative into the Natural 220 2 Norms, Interactions, and Power 225 2.1 Resuscitating Norms: The Universal in the Local 225 2.2 Interactions Prior to Interaction 230 3 A (tentative Conclusion): From Logic to Freedom 232 References 236 Front Matter....Pages i-xi Introduction: Reasoning in Time and Space....Pages 1-19 Inferentialism and Its Discontents....Pages 21-45 Proof and Assertion....Pages 47-77 Dialogue and Refutation....Pages 79-108 Rules in Dialogue....Pages 109-156 Structuring Interactions....Pages 157-188 Paradox, Paraconsistency and Logical Revision....Pages 189-210 Naturalization, Normativity, and Ethics....Pages 211-230