Sorry for the allegorical language if it offended you.
I am not offended
There is a difference between not finding a solution for a problem, and not even understanding what a solution may look like even in the abstract form.
Certainly. And further on that scale, there is "understanding so little of the problem that you're nor even sure there's a problem in the first place".
Progress on the the P vs NP problem has been largely limited to determining what the solution doesn't look like , and few if any people have any idea what it does look like, or if it (a solution) even exists (might be undecidable).
So, this scale goes
Solved problems
Unsolved problems where we have a pretty good idea what the solution looks like
Unsolved problems where we have no idea what the solution looks like : subjective experience is not here
problems we suspect exist, but can't even define properly in the first place : subjective experience is here!
It is also not a good sign when the problem gets to be more of a mystery the more science we discover.
Consciousness and the subjective experience of pain have not gotten more mysterious the more science we discover. At worst, we understand exactly as much now as we did when we started, i.e. nothing (and neurologists would certainly argue we do understand more now).
The concern here is that we have an irrational view that rationalism is a universal tool.
It is. Have a look at Solomonoff induction
The fact that we have unsolved scientific and intellectual problems is not a proof of that.
It's not proof, but it is evidence.
The fact that there seem to be problems that in their very nature seem to be unsolvable by reason is.
What makes you think that these problems are "in their very nature unsolvable by reason" ? Is it because you think they are inherently mysterious ?
I will make a point about the progress of science in this subject and then use that to step towards a more general argument for the innate mystery of consciousness with regards to reason.
Ever since the time of the enlightenment there has been a real movement in the west to view the world as purely mechanical/physical so that a conclusion of reason as a universal tool could be accepted. That meant the elimination from society of not just God but also the soul and other things.
Ironically it was a particular invention of science and reason that made ration...
I encounter many intelligent people (not usually LWers, though) who say that despite our recent scientific advances, human consciousness remains a mystery and currently intractable to science. This is wrong. Empirically distinguishable theories of consciousness have been around for at least 15 years, and the data are beginning to favor some theories over others. For a recent example, see this August 2011 article from Lau & Rosenthal in Trends in Cognitive Sciences, one of my favorite journals. (Review articles, yay!)
Abstract: