 Pursuing this idea leads to principles of harmony and inversion which are different from the the standard ones. As harmony and inversion lie at the heart of proof-theoretic semantics, many of its issues are touched. Taking the topic of intensionality seriously may reshape many fields of proof-theoretic semantics. And since the identity of proofs is a basic topic of categorial proof theory, the latter will need to receive stronger attention in proof-theoretic semantics than is currently the case. 