At some point big numbers become much more about the consistency strength of formal systems than “large quantities”. I.e., how well can a system fake being inc

At some point big numbers become much more about the consistency strength of formal systems than “large quantities”. I.e., how well can a system fake being inconsistent before that fact it discovered? An inconsistent system faking consistency via BB(3) will be “found out” much quicker than a system faking consistency via BB(6). (What I mean by faking consistency is claiming that all programs that run longer than BB(n) steps for some n never halt.)