Comment on Open Thread June 2010, Part 3

Mon, 21 Jun 2010 01:50:22 GMT

I wasn't familiar with this description of "world states", but it sounds interesting, yes. I take it that positing "I am a think that things" is the same as asserting K(E). In asserting K(K(E)), I assert that I know that I know that I am a thing that thinks. If this understanding is incorrect, my following logic doesn't apply.

I would argue that K(K(E)) is actually a necessary condition for K(E). Because if I don't know that I know proposition A, then I don't know proposition A.

Edit/Revised: I think all you have to do is realize that "K(K(A)) false" permits "K(A) false". At first I had a little proof but now it seems just redundant so I deleted it.

So I guess I disagree, I think the iterations K(K...) are actually weaker statements, which are necessary for K(A) to be achieved. Consequentially I don't see how you can learn anything beyond K(A).

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