Can enlightenment be achieved through pure reasoning?
Yes, apparently. Jed McKenna did it this way and he dubbed this process “spiritual autolysis”, and it is just as emotional, painful and excruciating as any other process of achieving it. There are no shortcuts, unfortunately.
Basically his process is try to write down one thing that is true beyond all doubt. When you think you did this, ask yourself how you know that it’s true, and if you’re honest with yourself, you’ll throw it out and try again. As with any other method of reaching enlightenment, you gotta have a megalomaniacal level of determination to do it. If you’re truly honest with yourself it will drive you crazy, and you will start sinking into what you might fear is insanity. The key is not to stop. Apparently there’s a point after which you cannot stop. Most people never reach that point.
Look him up. This is his description, I have no experience with it, but I can totally see how it can work. I would have never been able to do it this way, but apparently he did and some of his students, too, at least that’s what he says. I read his books and I have no doubt he’s enlightened himself, or at the very least realized very deeply.
His process is about attaining self-realization. As for the path from self-realization to enlightenment, he doesn’t say much except “And then it takes about 10 years to learn to navigate here”. But self-realization is the most important thing. Everything before that is of little consequence, spiritually speaking.