Which Consistency Statement? Made-Canonicity and the Intensionality of Gödel's Second Incompleteness Theorem

Abstract

Gödel’s second incompleteness theorem is sensitive to how axioms are presented: extensionallyequivalent axiomatizations yield consistency statements of different proof-theoretic status. Theformal separation of canonical from deviant cases is established; what is missing is a criterionthat explains why the separation falls where it does. This essay proposes one — made-canonicity — grounded in an asymmetry between what has been produced and the producingthat exceeds it, articulated through Nishida Kitarō’s “from the made to the making.” Thecriterion automatically yields the Hilbert–Bernays–Löb derivability conditions asconsequences, classifies five self-referential patterns, and interprets the strict potentialist’smodal operator.