For obvious psychopolitical reasons, the following passage from Incompleteness caught my attention:
no validation of our rationality -- of our very sanity -- can be accomplished using our rationality itself.
Thus, there exist millions of people who are completely sane from within their ideological system, but only insane from outside it. We call these lunatics progressives. It's not quite correct to say that they "can't be reasoned with." Rather, they can only be reasoned with -- in the manner described by Chesterton in chapter 2 of Orthodoxy, The Maniac:
The madman is not the man who has lost his reason. The madman is the man who has lost everything except his reason.
Similarly, Goldstein writes that "Paranoia isn't the abandonment of rationality. Rather, it is rationality run amuck, the inventive search for explanations turned relentless." Such a person is "irrationally rational," characterized by "logic run wild."
More cosmic Orthodoxy via Chesterton:
Poetry is sane because it floats easily in an infinite sea; reason seeks to cross the infinite sea, and so make it finite.... The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.
Flipping through this maniacal chapter, there are some additional statements that prefigure Gödel:
the strongest and most unmistakeable mark of madness is this combination between a logical completeness and a spiritual contraction. The lunatic's theory explains a large number of things, but it does not explain them in a large way....
His cosmos may be complete in every rivet and cog-wheel, but still his cosmos is smaller than our world (emphasis mine).
One more important observation:
As long as you have mystery you have health; when you destroy mystery you create morbidity.
The normal man "has always cared more for truth than for consistency. If he saw two truths that seemed to contradict each other, he would take the two truths and the contradiction along with them. His spiritual sight is stereoscopic, like his physical sight: he sees two different pictures at once and yet he sees all the better for that."
Note that this stereoscopy isn't so much horizontal as vertical: it requires the recognition of a hierarchy of levels, both on the terrestrial and celestial planes. To reduce the hierarchy to a single level is to guarantee inconsistency and ultimately absurdity. To appreciate hierarchy is to situate things in their proper place.
Contrast this with the ideologue, the man of system, the progressive lunatic. As Goldstein says, "Anything at all can be deduced within an inconsistent system, since from a contradiction any proposition can be derived."
Thus, it is common for conservatives to point out the daily hypocrisies of the left, but this gets us nowhere, since it is utterly beside the point. You can't be a hypocrite if you have no consistent principles. Rather, they would only be hypocrites if they were to deny their hypocritical expediency in service to power.