The Theory of Logical Types.

Abstract

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.