On the Significance of Self-Justifying Axiom Systems from the Perspective of Analytic Tableaux

This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into tighter systems, with only a finite number of axioms.) It will explain how self-justification is useful, even when the Incompleteness Theorem limits its reach. Historical Remark about this Draft: All the theorems in this January 2014 manuscript had also appeared in the “Version 1” June 2013 manuscript that was posted earlier in the Cornell archives. The main difference between these two manuscripts is that I essentially spiced up the accompanying narrative, in the January 2014 draft, so as to better explain the motivation for this research endeavor.