<p>Enumerative inductive methods, which infer universal claims from a finite set of positive instances, are a cornerstone of empirical science and are also implicitly employed to justify belief in unproven mathematical conjectures like Goldbach’s Conjecture. This paper examines the scope and limits of this justificatory strategy. While I defend its use against simple “size-biased” skepticism for first-order mathematical claims, I argue that its application to justify the consistency of foundational axiomatic theories like Peano Arithmetic (PA) or Zermelo-Fraenkel set theory (ZF) is fundamentally problematic. The core of the argument is that evidence for consistency is not merely enumerative but also dimensional, crucially dependent on the length or complexity of the derivations surveyed. Drawing on proof theory, I demonstrate that inconsistencies can reside exclusively in proofs of lengths that transcend human practical and cognitive limits. Therefore, the inductive evidence from the absence of contradictions in all humanly surveyed proofs is probably weak and incomplete. Justified belief in consistency, I conclude, must be grounded not in enumerative induction alone, but in a holistic framework.</p>