If the Gödelian sentence corresponds to an actual statement about arithmetic that is proven to be true outside of the lower-level formal system, then maybe we can just map any math conjecture to a more complicated version of the Gödelian sentence by reverse engineering the Gödel numbering and proving a theorem to be true without actually proving it. We just state the theorem and then say “and this is unprovable” and then we know it’s true. Math is literally so easy.
Too bad Gödel was a fraud
>>17004511nigga, Gödelian sentences are the trivial casehttps://en.wikipedia.org/wiki/Goodstein's_theorem>This was the third example of a true statement about natural numbers that is unprovable in Peano arithmetic, after the examples provided by Gödel's incompleteness theorem and Gerhard Gentzen's 1943 direct proof of the unprovability of ε0-induction in Peano arithmetic.>The Paris–Harrington theorem gave another example.>>17004557chew on my sphincter
>>17004570>goodstein sequenceoof.https://jamesrmeyer.com/infinite/goodstein>Paris–Harrington theoremdouble oof.>Roughly speaking, Jeff Paris and Leo Harrington (1977) showed that the strengthened finite Ramsey theorem is unprovable in Peano arithmetic by showing in Peano arithmetic that it implies the consistency of Peano arithmetic itself. Assuming Peano arithmetic really is consistent, then by Gödel's second incompleteness theorem, Peano arithmetic cannot prove its own consistency. This shows that Peano arithmetic cannot prove the strengthened finite Ramsey theorem.So it literally just follows from Gödel. Too bad both are wrong.
>>17004584>james r meyerAH, sorry, i though you had a functioning brainhttp://r6.ca/blog/20090218T025048Z.html
>>17004584 >>17005157AND just in case you are a lazy faggot to boothttp://r6.ca/Goedel/FFGITReview.html
