4 ms·
Gödel's theorem: If you print only true statements, you can not print all true statements. Proof: "I do not print this statement"
by rjprins 17y ago
Gödel's theorem:
If you print only true statements, you can not print all true statements. Proof:
"I do not print this statement"
- maurycy 17y agoNot quite; this is a liar's paradox. the Gödel's sentence deals with "provability", not "truth". (see Tarski's undefinability theorem if you wonder why it matters)
- anatoly 17y agoThis is a version of the Liar paradox, not Goedel's theorem.
- dejb 17y agoThey are pretty close to a 1:1 mapping http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Relation_to_the_liar_paradox http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t... 'The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.'
- anatoly 17y agoThis is only approximately true. What really is a straightforward formalized version of the liar paradox is Tarski's undefinability theorem, which is what's demonstrated in the blogpost. Goedel's incompleteness sentence is more like inspired by the liar sentence rather than being its formalization; and the proof of Goedel's incompleteness is much more challenging than the simple true->false->true bounce of the liar paradox.
- joe_the_user 17y agoDude, there's no formal version "the liar's paradox". Back to base camp...