Gödel and the U.S. Constitution

Kurt Gödel was one of the greatest, some would say the greatest logician who ever lived. His best known (but often misinterpreted) works are his Incompleteness Theorems.

When Kurt Gödel was applying for U.S. citizenship, he studied the Constitution prior to his citizenship hearing. He apparently discovered a logical flaw in the U.S. Constitution that allowed for the possibility of a dictatorship to be installed. He was so disturbed by this that he insisted on trying to draw the judge's attention to it. But the judge waved aside his concerns, and his companions Albert Einstein and Oskar Morgenstern persuaded him to pipe down and not make an issue of it. Gödel's application was granted.

www.telecomtally.com...

linguafranca.mirror.theinfo.org...

Gödel had a number of psychological problems and it has been suggested by some that he was simply suffering a bout of paranoia. Intrigued by this story I scoured the 'net to find out more but nobody seems to know what Gödel had seen in the Constitution that worried him so much.

Do any members of ATS have any thoughts or information on this?

Some have speculated that Gödel was concerned about Article V which allows for the constitution to be amended. But this seems too obvious - amendments that would allow a dictatorship to be installed would first have to be passed and this seems an unlikely prospect. Besides which this isn't a 'logical inconsistency' within the system of the constitution as it stood at the time of reading, which is what Gödel claimed he had found.

Ah well. Looking like nobody has anything on this, then?

I guess it will have to remain an unsolved mystery....

Now I'm a mathematics amateur, so take this with a grain of salt and feel free to correct me where I stray....

Godel was brilliant...truly...but don't you think there was a lot of smoke and mirrors in his Incompletness Theory. (Creating a symbolic mirror to mathematics and leading the two structures into Epimenides paradox...)

If he noted a "hole" in the constitution, the way he discovered a "hole" in mathematics...then I'm not sure I'm too concerned.

Does that make sense?

Well, this is where a lot of people get a bit over-excited about Gödel's theorems.

You see, attractive though the 'hole' analogy is, he didn't really discover a 'hole' in Mathematics. He simply demonstrated the limitations of consistent first-order systems of logic, which is a subset of Mathematical systems as a whole. He proved that such systems could not be fully axiomatised - i.e. that there would always be true propositions that could be constructed within the system, that an 'external' observer could see the truth of, but which could not be proven true within the system.

The important thing to note is that Gödel's theorem only applies to these specific types of system. A lot of people have said things like 'this proves that the laws of physics are all wrong' or similar such ideas. But the laws (more correctly 'well-established theorems') of physics as they are don't claim to be a complete, consistent formal system in first-order logic. There are many philosophical issues surrounding this, for instance if the 'laws' of physics and all the theorems that could be proved from them formed a complete system (in the mathematical sense of completeness) would this satisfy Popper's criterion of falsifiability? Mathematicians still argue about the relative merits of first vs second-order logic and whether the 'laws' of physics might ever be successfully couched in the vocabulary of either kind of logic.

I find that the best way of looking at the 'laws' of physics is to think of them as 'useful a-good-deal-more-than-half-truths that you ignore at your peril', rather than statements of truth.

I may have digressed a bit here!

No, I don't imagine that Gödel's misgivings about the constitution are too much to worry about. For his logical inconsistency to actually be used to install a dictatorship, people would have to be able to understand it. If it's so convoluted as to be beyond the capability of members of the judiciary or other governing bodies to understand then any attempt to enforce it will be met by incredulity and uncooperativeness. And probably the same even if they can understand it!

Still, it's intriguing.

I'll add that I'm not a mathematics 'major', though I studied it as a subsidiary subject as part of my Physics degree.

All great minds have psychological problems... comes with the territory of having excess brain power - A depression disorder, anxiety suffering me.

what a great mind I have.

Just kidding.

Seriously, I'll have to do some more reading on this before I post a serious comment.