Switch to: Citations

References in:

Never trust an unsound theory

Theoria 88 (5):1053-1056 (2022)

Add references

You must login to add references.
  1. There May Be Many Arithmetical Gödel Sentences.Kaave Lajevardi & Saeed Salehi - 2021 - Philosophia Mathematica 29 (2):278–287.
    We argue that, under the usual assumptions for sufficiently strong arithmetical theories that are subject to Gödel’s First Incompleteness Theorem, one cannot, without impropriety, talk about *the* Gödel sentence of the theory. The reason is that, without violating the requirements of Gödel’s theorem, there could be a true sentence and a false one each of which is provably equivalent to its own unprovability in the theory if the theory is unsound.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • On Gödel Sentences and What They Say.Peter Milne - 2007 - Philosophia Mathematica 15 (2):193-226.
    Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  • Solution of a problem of Leon Henkin.M. H. Löb - 1955 - Journal of Symbolic Logic 20 (2):115-118.
  • Aspects of Incompleteness.Per Lindström - 1999 - Studia Logica 63 (3):438-439.
     
    Export citation  
     
    Bookmark   39 citations