A Structuralist Theory of Logic

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

Arnold Koslow (Author)

9780521412674, Cambridge University Press

Hardback, published 27 March 1992

436 pages, 15 b/w illus.
23.6 x 15.8 x 2.7 cm, 0.722 kg

"Koslow's theory permits us to identify logical operators independent of their form in both logical systems and in natural languages. For linguists, his theory opens up the possibility of an entirely new approach to the study of natural-language semantics, one which does not require the postulation of a level of logical form." D. Terence Langendoen, University of Arizona

In this 1992 book, Professor Koslow advances an account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual, are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics.

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.

Subject Areas: Philosophy: logic [HPL]