Every system, every belief, every idea has some one or more points with which it becomes self-contradictory or contradictory in principle. My favorite example has always been the police. These are people who, er, serve and protect the citizens of our country. Idealistically, in reality they enforce laws that the people of that country have ideally put in place by choice to service their ideals of a free and democratic country (can you tell I lived in the states for awhile?). There are a variety of allowed means to this end from ticketing to shooting, and of course, as large a variety of less than allowed means that are also put to this end. Anyhow, since a society needs some manner to ensure that the laws of the land are nothing more than words, some form of policing is required. (My dyslexia took hold here, I swear!) Let me try that one again.
Since a society needs some manner to ensure that the laws of the land are more than just words, some form of policing is required. Grant me that much. Since a policing system is staffed by gasp people, and since the police police people, it comes as no surprise that the police need policing too. And here is where it gets sticky. Since the police may themselves not follow the laws of the land while they are policing the land, some form of policing is required to catch this.
Here we see a need for meta-police. The need arises since the alternative would be to have the police police themselves directly, and if this were so easy, we could as easily have had the entire populace police itself in the first place. Once we granted the need for a police force (oh for the day when it is called a police request instead), we are committed to the belief that people don't, for whatever reasons, police themselves successfully. And if people can't, then police can't either. Hence the need for meta-police.
The godel point of the policing system happens here. For as the police are merely people with special jobs, so are the meta-police. And although the meta-police might in large part be effective about policing the police, they must be similarly ineffective at policing themselves. And the regress goes on indefinitely, although we may try to make it a circle if we want by letting the people police the meta-police. giggle
To be clearer, the policing of the police is the godel point of the policing system, of the need for police in the first place. We called this the godel point in reference to the mathematician Kurt Godel, who back some 50 years or so tried to prove many things including that basic arithmetic was a complete mathematical system and at the same time that all of the statements within that system are true. Well it turned out that although there are many systems which are both complete and consistent, basic arithmetic was not. In other words, there are statements which one can deduce in arithmetic which are self-contradictory. In particular, the statement "This sentence is false." was deducible in a numeric equivalent in arithmentic. Neat, eh.
Peter and I played with this notion for awhile, and we noted the following neat thing. Every system has a hole in it like this. Just as the police can't be expected to police themselves, the lawyers can't be expected to judge themselves, and the politicians cannot be held reliably to govern their own behaviour. The Americans tried to solve this problem of accountability in making the government accountable to the people - drawing a circle in place of a regress politically.