Having Said That,

Gödel was legitimately nuts, subject to paranoid delusions, hypochondria, depression, and obsessive-compulsive behavior. Of course, this doesn't affect the validity of the theorems, but it may impact his opinions about them -- about the kind of world they imply. 

When depressed he dwelled on the fact that "all of his contributions" to philosophy "were of a negative kind -- proving that something cannot be done, not what can be done." 

About this he is correct: the theorems tell us only what definitely cannot be the case, not necessarily what is the case. 

They tell us, for example, that "it is impossible to define the concept of truth within a formal system itself," but they do not tell us what truth is. Likewise, they tell us a formal system cannot be both consistent and complete.

Gödel's leap to a Platonic conception of truth is in no way entailed by his own theorems. For example, postmodernists go to the other extreme and say the theorems bar us from knowing any truth at all, enclosing us in language about a reality we can never reach.

Thus, before he was a logician, mathematician, or anything else, Gödel was a seeker of truth, which already implies a worldview -- one in which truth exists and is accessible to man. He would have rejected the alternative a priori. 

Again, he regarded mathematics as not only a search for truth, but for "pre-existing truths that inhabited a reality separate from the human mind." He was likewise "committed to accessing the immaterial world of higher philosophical truths through the power of sheer abstract logical reasoning."

But his forays into *mere* philosophy 

dismayed more than a few of his mathematical colleagues, who did not hide from him their disappointment that he seemed to be squandering his genius on trivialities.

Now, the mind is designed to detect connections between things, but for this reason man can be prone to the over-detection of agency -- thus the sometimes fine line between genius and madness. 

Gödel found "hidden meanings, or mystical significance in things large and small," for example, in "the incorrect listings of movies shown on television." ("One has the impression it is sabotage.")

Ironically, this means that, although he considered himself a seeker after extra-mental truth, he was often very much confined to his own intra-mental projections. Even more ironically, such delusional ideation could crystallize into a kind of rigidly consistent and pseudo-complete system the theorems forbid.

Nevertheless, he argued that the human mind "could not have come about through any mechanistic process," and disagreed "with the entire worldview that 'regards the world as an unordered and therefore meaningless heap of atoms.'" But it seems his paranoia made him vulnerable to finding too much meaning, and in all the wrong places.

On the one hand, a possible interpretation of the theorems is that mathematics -- and by extension, language -- is "a mere game played with symbols according to certain rules." Again, this would be the postmodern view. But this is not how Gödel saw it; rather, he believed

that the human mind can literally see mathematical realities through a kind of perception, no different from the direct sensory perceptions that the empiricists decreed to be the only valid basis of physical laws.

Here again, this latter interpretation is in no way a necessary consequence of the theorems. Moreover, it begins to converge upon someone like Schuon, for whom the necessary truths of existence are indeed directly "perceived" via intellection:

Intellectual intuition comprises essentially a contemplativity which in no way enters into the rational capacity, the latter being logical rather than contemplative.... 

[Rationality] perceives the general and proceeds by logical operations, whilst Intellect perceives the principial -- the metaphysical -- and proceeds by intuition (Schuon). 

Gödel saw no reason "why we should have less confidence in this kind of perception" than in the lower kind, and he's not wrong. Nor was he wrong to wonder

what kind of sense would there be in bringing forth a creature (man), who has such a broad field of possibilities of his own development and of relationships, and then not allow him to achieve 1/1000 of it.

In other words, what kind of irrational -- not to say perverse -- Creator gives infinite potential to a finite being? Gödel thought this was sufficient proof of an afterlife: 

it follows directly that our earthly existence, since it in and of itself has at most a very dubious meaning, can only be a means to an end for another existence.

Again, he had little use for religions but was very much open to Religion, perhaps one that hadn't yet been discovered. He thought that the great majority of philosophers were as guilty as "bad churches" in turning people away from these deeper questions.

"Gödel's public renown continued to grow after his death" in 1978, partly because "The general idea that there are truths that cannot be proved has an irresistible appeal." 

But in his own way he has been misappropriated for as many dubious agendas as quantum physics: "probably more wrong things have been said about his proof than any other mathematical theorem in history."

Interestingly, his ideas seem to inspire two kinds of skeptics, those who recognize "that their knowledge is limited," which "troubles them deeply." The other kind acknowledge "the same thing but find it liberating." Gödel was in the latter camp, believing that

Humans will always be able to recognize some truths through intuition..., that can never be established even by the most advanced computing machine....

In place of limits on human knowledge and certainty, he saw only the irreplaceable uniqueness of the human spirit. 

So, having said all this, where does it leave us?