The Theory of Logical Types
Monographs in Modern Logic
Routledge – 1971 – 130 pages
This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.
Part One: The Paradoxes 1. Logical Paradoxes 2. Semantic Paradoxes 3. Classification of the Paradoxes 4. Importance of the Paradoxes. Part Two: The Simple Theory of Types 5. Informal Exposition of Simple Type Theory 6. Formalization of the Simple Theory of Types 7. An Alternative Formulation of Simple Type Theory 8. Criticisms of the Simple Theory of Types. Part Three: The Ramified Theory of Types. 9. The Vicious Circle Principle 10. The Hierarchy of Propositions 11. Simple Type Theory as Part of Ramified Type Theory 12. Hierarchies of Orders 13. The Axiom of Reducibility 14. Criticisms of the Axiom of Reducibility 15. Criticisms of the Ramified Theory of Types 16. An Alternative Resolution of the Semantic Paradoxes.