We discuss and develop a semantics for the truth predicate in belief contexts, which is loosely based on some of ideas of Awareness semantics for epistemic logic.
We present a theory of propositional functions based on Russell’s philosophical insights, which lead to the development of the theory of types, and Gödel’s later suggested amendments of those.
We explore some possible answers to the question of how the intuitive, natural language notion of truth is connected to the theoretical notion of truth at play in truth-conditional semantics.