The Stability Problem
Presumably, if the Gödelian is to find a solution to the Stability Problem for a given system T (T being an ideal system whose soundness is in question, and therefore a system whose syntax is to be represented or “arithmetized”) he must locate a set C of conditions on formulae of T (T now being treated also as the system in which the syntax of T is to be represented) such that (1) every formula of T that can reasonably be said to express the consistency of T satisfies the conditions in C, and (2) no formula of T that satisfies C can be proven in T provided that T is consistent. This being so, the Gödelian’s success in dealing with the Stability Problem will evidently depend crucially upon his ability to defend the reasonableness of his choice of C.
KeywordsStability Problem Mathematical Proof Mathematical Practice Derivability Condition Logical Technique
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