A Structuralist Theory of Logic

In this 2001 book, Professor Koslow advances a new account of the basic concepts of logic.

Preface; Part I. Background: 1. Introduciton; 2. The program and its roots; 3. Introduction and elimination conditions in a general setting; 4. The Belnap program; Part II. Implication Relations: 5. The theory of implication relations; 6. Implications: variations and emendations; 7. Familiar implication relations: deducibility and logical consequence; 8. Implication relations: direct and derived; 9. Implications from implications; 10. Implication relations and the a priori: a further condition?; Part III. The Logical Operators: 11. Hypotheticals; 12. Negations; 13. Conjunctions; 14. The disjunction operator; 15. The logical operators parameterized; 16. Further features of the operators; 17. The dual of negation: classical and nonclassical implication structures; 18. The distinctness and relative power of the logical operators; 19. Extensionality; 20. Quantification; 21. Identity; 22. Special structures I. logical operators on individuals: mereology reconstituted; 23. Special structures II. interrogatives and implication relations; 24. Completeness; Part IV. The Modal Operators: 25. Introduction; 26. Modality; 27. Modals: existence and nonextensionality; 28. Special modals; 29. The possibility of necessity-style modals; 30. Modals revisited I; 31. Quantification and modality; 32. Modals revisited II; 33. Knowledge, truth, and modality; 34. The comparative strength of modals; 35. Kripke-style systematization of the modals without possible worlds; 36. Model functions, accessibility relations, and theories; 37. Migrant modals; Appendix; Notes; Bibliography; Index.