Gödel's Theorem

Re:Gödel's Theorem by smallnamespace on Thursday January 31, 2019 @01:09AM (#19042777)

> sometimes you just don't know enough, but with more information or context you could prove it is true

Yes, but that larger system itself contains statements that are true but unprovable in itself, and so on in an infinite regression.

And before one hand-waves it away as a mere 'hole' that we can safely ignore, Chaitin extended Godel's work to show that there are in fact an infinitude of 'relevant' mathematical statements that are unprovable within any formal system S:

https://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin'...

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Re:Gödel's Theorem by heavenlyblue on Thursday January 31, 2019 @12:49PM (#19046850)

Then if you're discussing the topic in the context of "whether our current mathematics is useless in the context of Godel's theorem" - then we can easily define progress in mathematics as "how many contradictions we had found today" and thus continue living with an objective till the heat death of the universe.

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