Mathematics selfproves its own Consistency (contra Gödel et. al.)
Carl Hewitt  International Society for Inconsistency Robustness  [Home Page] 
Notice: Hosted by Richard Waldinger
Date: 20120424 at 16:00
Location: EJ228 (SRI E building) (Directions)

The consistency of mathematics has long been of concern. Using selfreferential propositions, Gödel et. al. proved that if mathematics is consistent, it does not prove its own consistency. Regardless, this paper presents a simple nonconstructive selfproof of consistency:
Of course, the above proof does not show that mathematics is really consistent, i.e., that is impossible to infer an inconsistency using the inference rules because the proof is valid even if mathematics is inconsistent. In fact, selfproving consistency raises that possibility that mathematics could be inconsistent because of contradiction with the result of Gödel et. al. One resolution is not to have selfreferential propositions. This can be achieved by carefully arranging the rules for propositions so that selfreferential propositions cannot be constructed. Fortunately, selfreferential propositions do not seem to have any important practical applications. The above proof of consistency is carried out in Direct Logic [Hewitt 2011] that is a powerful inconsistencyrobust inference system that is its own metasystem. Having such a system is important in computer science because computers must be able to carry out all inferences (including inferences about their own inference processes) without always relying on humans. A tradeoff is that in return for having such a powerful inference system, selfreferential propositions are not allowed. 

Please arrive at least 10 minutes early as you will need to sign in by following instructions by the lobby phone at Building E. SRI is located at 333 Ravenswood Avenue in Menlo Park. Visitors may park in the parking lots off Fourth Street. Detailed directions to SRI, as well as maps, are available from the Visiting AIC web page. There are two entrances to SRI International located on Ravenswood Ave. Please check the Builing E entrance signage.
©2015 SRI International 333 Ravenswood Avenue, Menlo Park, CA 940253493
SRI International is an independent, nonprofit corporation. Privacy policy 