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Comment by saulrh | Hacker News Reader

Sensationalist title. A better one would be "Unreviewed proof claims that Peano arithmetic is inconsistent". This is self-published, hasn't been looked at by anybody else, and contradicts a very well-accepted and thoroughly examined argument for consistency from way back in 1936.

1: http://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof

[edit: as the commenters point out, I'm no mathematician, and I'm working off Wikipedia. Go with what they say.]

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No, it does not contradict Gentzen's proof.

Gentzen's proof proves that one set of axioms we think is consistent proves that another set of axioms we think is consistent is indeed consistent. However both sets of axioms could be inconsistent. We don't think that is so, but it could be.

Gentzen's proof relies on transfinite induction up to epsilon_0, which is not a principle liable to be accepted by someone with Nelson's foundational views. A good primer on these can be found in his book Predicative Arithmetic.

http://www.math.princeton.edu/~nelson/books/pa.pdf

For this kind of stuff there should be a way to flag a submission as 'sensationalist title' or 'likely false'. I just don't have the time to read all the comments for all submission just to find out if the submission is true or not.

Then don't read them; the community will figure out over the next few months whether Nelson's proved what he's claimed. The Peano axioms have stood for 120 years, it's probably not imperative that you find out whether they've been shown to be inconsistent right this minute.

> Then don't read them

I think that's his point: it's difficult to differentiate things that are likely wrong/false and things that have been verified by the community. Flags could help that.

I prefer simply relying on the comments, personally. In the comments you can see who's knowledgeable about the topic and often they'll explain what's wrong with the article. Votes and flagging can't do that.

Flags are a binary mechanism just like voting, and as such are vulnerable to precisely the same epistemic problems. As you say, comments offer a way of demonstrating expertise, not merely asserting it.

For this reason someone interested in a disputed topic such as this will either have to read the comments, in the hope of discovering the main lines of argument and improving the likelihood that the picture they form is correct, or suspend their judgement until such a time as better evidence (in this case, peer review of the claimed proof) is available.

Even so, I don't think most people would mind a disincentive for posts with titles that drastically overstate their content

What a stinking horrible idea.

How do you think scientific authority works, by the way? Why would you trust any given person with powers of "flagging" to flag something correctly? How would such people even be evaluated? Don't you think think the process of peer review is complicated for a reason?

If you want knowledge served up on a silver platter, you are going to starve to death.

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