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 rationalists realize the problem of eliminiating all non-mechanical/physical realities from a human being: the computer. With the development of the computer it became painfully obvious that human beings were fundamentally different from any designed piece of technology. Although they could theoratically design and program a coputer for all kinds of amazing functions, there is no rational model as to how to make that machine 'conscious'. It was through computers that mankind realized in the most clear and blunt way the mystery of consciousness.
So to reassert my point....from the development of computers throughout this past century into the advancment of it to this century, the more we progress the more we understand that consciousness does not seem to be a matter of just complexity and sophistication.
Secondly, our faculty of reason itself does not even work in the same way a computer works. A computer's mechanical structure "signals" a conclusion. The machine moves in a certain way, albeith at the tiniest levels, to signal that something is right or wrong. For us, it is understanding that makes us realize a right or wrong, it is a feeling. Even at the most fundamental level of using reason itself the mystery of consciousness is engaged and operating in a way we do not understand.
With the development of the computer it became painfully obvious that human beings were fundamentally different from any designed piece of technology.
Evidence-based Citation needed. ( From a neurologist or computer scientist. Nothing about how our own massively parallel architecture differs from the Von Neumann architecture.)
The more we understand of the workings of the brain, the more we can mimic it on a computer. ("Ha, but these are simple tasks! Not difficult tasks like consciousness." How convenient of you to have chosen a metric you can'...
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: