Comments on: Knowing what you don’t know is hard http://www.arsmathematica.net/2006/03/14/knowing-what-you-dont-know-is-hard/ Dedicated to the mathematical arts. Fri, 29 May 2015 09:17:44 +0000 hourly 1 https://wordpress.org/?v=4.1.41 By: easwaran http://www.arsmathematica.net/2006/03/14/knowing-what-you-dont-know-is-hard/#comment-505 Wed, 15 Mar 2006 05:28:41 +0000 http://www.arsmathematica.net/archives/2006/03/14/knowing-what-you-dont-know-is-hard/#comment-505 The problem with Rumsfeld is that he believes in positive introspection – the rule that Kp implies KKp. He lists known knowns, known unknowns, and unknown unknowns, but not unknown knowns. There are some things that one knows in such a way that one doesn’t even realize that one knows them (automatic presuppositions that are in fact true, for instance).

Also, note that satisfiability for even simple propositional logic is NP-complete. When you add a modality it in general gets harder (PSPACE-complete in the case of S4, it seems), but adding negative introspection gets you back down to NP, so it really is a useful simplifying assumption, even though it’s clearly false. (Of course, if you believe something like what I said above, then even S4 is too strong, but it’s at least a better approximation.)

]]> By: antiquark http://www.arsmathematica.net/2006/03/14/knowing-what-you-dont-know-is-hard/#comment-504 Tue, 14 Mar 2006 21:19:25 +0000 http://www.arsmathematica.net/archives/2006/03/14/knowing-what-you-dont-know-is-hard/#comment-504 I wonder if Rumsfeld worries about those unknown truths that are, in fact, unknowable…

http://plato.stanford.edu/entries/fitch-paradox/#1

]]>