Excellent questions! In order to be rigorous, a mathematical abstraction needs to be characterized up to a unique isomorphism. However, ZFC does not meet th

Excellent questions! In order to be rigorous, a mathematical abstraction needs to be characterized up to a unique isomorphism. However, ZFC does not meet the requirement, because ZFC does not characterize sets up to a unique isomorphism. However, there is a theory that characterizes Ordinals up to a unique isomorphism that as explained in the following article: "Theory Ordinals can Replace ZFC in Computer Science" https://papers.ssrn.com/abstract=3457802 https://papers.ssrn.com/abstract=3457802 Orders can be used to block many different contradictions based on attempted recursive definitions (beyond just The Liar) as explained the following article: "Epistemology Cyberattacks" https://papers.ssrn.com/abstract=3603021 https://papers.ssrn.com/abstract=3603021 The Gödel number of a proposition does not work in foundations because it does not represent the order of the proposition and because there are uncountable propositions in foundations. Criteria for foundations are proposed in the following article: "Information Security Requires Strongly-Typed Actors and Theories" https://papers.ssrn.com/abstract=3418003 https://papers.ssrn.com/abstract=3418003