Table of Contents

Introduction 1. Diagrams and Isomorphism 1.1 Two-dimensionality 1.2 Isomorphism thesis 1.2.1 Informality 1.2.2 Accidental isomorphism 1.2.3 Literal preservation 1.2.4 Non-literal preservation 1.3 Conclusion 2. Diagrams and Language 2.1 Heterogeneous representations 2.2 Text and meaning 2.3 Text and efficiency 2.4 Conclusion 3. Diagrams and Rigor 3.1 Proofs and diagrams 3.2 Individuation of proofs 3.3 Diagrams and formalization 3.4 Conclusion 4. Venn Diagrams 4.1 Syntax 4.2 Semantics 4.3 Rules of inference 4.4 Shin's theorem 4.5 Completeness 4.6 Definability 4.7 Appendix: Proofs for chapter 4 5. Venn Diagrams and First-Order Logic 5.1 Syntax 5.2 Semantics 5.3 Rules of inference 5.4 Completeness 5.5 Appendix: diagrams and models 6. Euler Circles 6.1 Syntax 6.2 Semantics 6.3 Euler diagrams and Venn diagrams 6.4 Rules of inference 6.5 Completeness theorem 7. Higraphs 7.1 Syntax 7.2 Semantics 7.3 Rules of inference 7.4 Completeness 8. Peirce Diagrams 8.1 Syntax 8.1.1 Types and tokens 8.1.2 Linear notation 8.2 Semantics 8.3 Rules of inference 8.3.1 Provability and peircean provability 8.4 Soundness 8.5 Completeness Conclusion Bibliography Indexes.