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Ken2 comments on No One Knows What Science Doesn't Know - Less Wrong

38 Post author: Eliezer_Yudkowsky 25 October 2007 11:47PM

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Comment author: Ken2 26 October 2007 04:41:37AM 0 points [-]

Eliezer,

"[L]ogical ignorance is still ignorance; if this were not so, I would know a proof of the Riemann Hypothesis." I understand what you mean by logical ignorance is still ignorance; as for the second part of your statement, I don't think that's necessarily true.

For example, if the RH were true you would need n statements in a particular order. Meaning that you have stated assumptions, then you proceed to S1->S2->...->Sn (where Si is the ith logical statement) and Sn is the conclusion of the proof. What you are saying is that you know all n statements, but not the order and you're trying to figure that out or possibly could if you thought about it. BUT, you may not know all n statements, which is what the second part of your statement claims. Your statement, also, assumes the RH is true, which is what the fuss is all about. No one really knows if it's true.

What I was trying to say is that you may know all n statements, even their order and have come up with them to solve some other problem. But you may never have heard of the RH, so don't know that you can solve it. I understand that this is still a form logical ignorance, but the second part of your statement (that you know a proof of the RH) doesn't follow from the first part.