The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary

The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name.

  
       
         
    STUDIA PHILOSOPHIA - Issue no. 1-2 / 2001  
         
  Article:   FALLACIOUS PRESUPPOSITIONS IN GÖDEL`S INDECIDABILITY THEOREM.

Authors:  I. NARIŢA. 		 
       
         
  Abstract:  One of the famous achievement of contemporary logic was K. Gödel`s argumentation that the axiomatic systems which contain arithmetic, (like the Russell and Whitehead`s system in Principia Mathematica), if they are consistent, then they are also indecidable. This result was interpreted against logicism, as the foundation of mathematics program, which proposes just to embed the arithmetic in a logical system.The decidability is the property of an axiomatic system (S) in which, for every well formed expression in that system (which isn`t an axiom), we may establish if it is a theorem of the system or not, using only the axioms and the derivability rules accepted in S. Gödel`s indecidability theorem shows that in such a system, we may always find a formula about which it`s impossible to decide if it is theorem or not. Of course, the problem appears only in the case of consistent axiomatic systems because, for an inconsistent system, any formula is a theorem.  
         
     
         
         
      Back to previous page