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The Stability Problem

  • Michael Detlefsen
Chapter
Part of the Synthese Library book series (SYLI, volume 182)

Abstract

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.

Keywords

Stability Problem Mathematical Proof Mathematical Practice Derivability Condition Logical Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    The proof given here generally follows that of Smorynski [1977].Google Scholar
  2. 19.
    An example of this is the symmetrical version of the Rosser provability predicate studied in Kreisel and Takeuti [1974] (cf. pp. 15–16, 46–8.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • Michael Detlefsen
    • 1
  1. 1.Department of PhilosophyUniversity of Notre DameUSA

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