Title: Axiomatic Semantics Abstract: It is frequently said that Gödel’s discovery of coding formal languages in arithmetic demonstrates that many mathematical theories can reason about their own metatheory. This is undoubtably true if by ‘metatheory’ we have in mind only properties of purely syntactic concepts such as syntax and provability. But what about semantic concepts like truth and logical validity? Or even ones lacking formal definition such as justification and ideal provability? This tutorial will examine the possibilities and limitations for formal representations of these concepts, and the connection between the expressive resources of a theory and deductive (i.e., proof-theoretic) strength. Our primary focus will be on formal representations of truth, motivated by the question: how close can a formal theory come to recognising its own correctness?