Theory of Types

The Theory of Types is a logical framework that prevents certain kinds of paradoxes and errors in formal systems by organizing expressions into different levels or "types." It ensures that statements or objects of a certain type only refer to or interact with those of the same or compatible types. For example, a type might distinguish between individual objects, statements about those objects, or sets of objects. This layered structure helps avoid self-referential paradoxes, like trying to talk about "the set of all sets that do not contain themselves," by preventing certain kinds of inappropriate references across different types.