I of course have no proof, but I sometimes get a feeling that Gödel does have something to do with the limits of rational thought.
To me it seems humans have found a way to cope with Gödel's incompleteness: we accept that some of our axiomatic systems are inconsistent and adapt by simply discounting the value of proofs.
It's difficult to explain, but let me give an example. Among engineers you can often reason along very long logical chains and have your conclusions accepted. Among (some) business people you can't. They seem to refuse the validity of logic itself, being nervous about trusting logical conclusions. I think that's because they know their axiomatic systems are self-inconsistent. :)
By observing business people I have come to the conclusion that the best you can do in an a self-inconsistent axiomatic system is to look for "nuggets of truth" and never wonder too far from them. You can hear people say stuff like "limiting tweets to 140 characters will brings out creativity - people are less afraid to create when they are constrained" and similar. If you accept that as truth then you can wonder a short short distance from it and reason about business opportunities, but you can't combine that nugget with some other nugget and be sure to come to a correct conclusion.
Perhaps it is so, that the likelihood of "proving" an untrue statement in a self-inconsistent system increases with the number of axioms you are basing your proof on. That's perhaps why many people are very skeptical of "proofs" that seam to involve a lot of axioms? :)
Surely a simpler explanation for that is that business people don't usually work with crisp, binary data. Instead they're (implicitly) doing some kind of statistical inference on noisy data.
Propositional logic might be an acceptable approximation to this kind of inference in certain narrow situations, but the approximation breaks down quicker when the chain of inference gets longer.
That could certainly be a simpler (and therefore better) explanation. :) When your "axioms" are fuzzy so to speak, and not real axioms, it's of course dangerous to draw conclusions from several of them (because the risk of one of them being false increases exponentially).
But I still have a feeling there's something there... :) For example, I remember reading here on hacker news about this CS professor who had found a way to predict performance in entry level programing courses: http://www.eis.mdx.ac.uk/research/PhDArea/saeed/. Basically, they just tested their students ability to form a self-consistent model of how programming works. If they could they did well in the course. If they couldn't they did poorly, and it was very difficult to help them.
That experiment leads me to believe that about 50% of the population is in the habit of constructing self-inconsistent systems of hypothesis (provisional axioms you could say). :) If that's true I'm not sure yours is a simpler explanation... ;)
To me it seems humans have found a way to cope with Gödel's incompleteness: we accept that some of our axiomatic systems are inconsistent and adapt by simply discounting the value of proofs.
It's difficult to explain, but let me give an example. Among engineers you can often reason along very long logical chains and have your conclusions accepted. Among (some) business people you can't. They seem to refuse the validity of logic itself, being nervous about trusting logical conclusions. I think that's because they know their axiomatic systems are self-inconsistent. :)
By observing business people I have come to the conclusion that the best you can do in an a self-inconsistent axiomatic system is to look for "nuggets of truth" and never wonder too far from them. You can hear people say stuff like "limiting tweets to 140 characters will brings out creativity - people are less afraid to create when they are constrained" and similar. If you accept that as truth then you can wonder a short short distance from it and reason about business opportunities, but you can't combine that nugget with some other nugget and be sure to come to a correct conclusion.
Perhaps it is so, that the likelihood of "proving" an untrue statement in a self-inconsistent system increases with the number of axioms you are basing your proof on. That's perhaps why many people are very skeptical of "proofs" that seam to involve a lot of axioms? :)