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

Abstract

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.

arXiv commentCover page + 33 pages of text. All the theorems in this January 2014 manuscript also had appeared in the earlier "Version 1" June 2013 draft. The main difference between these two drafts is that I substantially spiced up the accompanying narrative, so as to better explain the motivation for this research endeavor