[FOM] 18 Word Proof of the Godel, Rosser and Smullyan Incompleteness Theorems

Panu Raatikainen panu.raatikainen at helsinki.fi
Wed Jul 21 09:32:23 EDT 2010

"Charlie V" <axiomsandrules at yahoo.com>:

> But you can get three concrete undecidable sentences utilizing a lot  
> less proof by noting more of my post, viz,
> "When any one of these sets, P, is expressible or representable, the sentence
> that expresses or represents, respectively, 'This is in P.' is undecidable."
> This requires only the Recursion Theorem and includes:
> 1. Since unprovability is expressible: The sentence that expresses  
> "This is not provable." is undecidable.
> 2. Since refutability is expressible: The sentence that expresses "This is
> refutable." is undecidable.
> 3. Since refutability is representable: The sentence that represents "This is
> refutable." is undecidable.

Very well. But this was not what was said in your first posting, which  
(and only which) I was commenting.

>> This I would happily call equivalent with Gödel's first incompleteness
> theorem.
> And what would you call it if you get three undecidable sentences?

Three different theorems... Why should they have a common name?

Cheers, Panu

Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy, History, Culture and Art Studies
P.O. Box 24  (Unioninkatu 38 A)
FIN-00014 University of Helsinki

E-mail: panu.raatikainen at helsinki.fi

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