Gödel and the School Board

In the early decades of the Twentieth Century there was an interest in creating  a purely formal system  for mathematics consisting of symbolic objects and propositional entities  created by concatenations of symbols according to the rules of the system without much reference to what the objects or entities  actually were or meant and which was complete in the sense that  every such  entity allowed by the rules of the system  would be decidable as valid or not according to the rules of the system. (Why people worried about doing this is interesting in itself, but that is a story for another day.) In 1930 Kurt Gödel  proved that such a complete formal system was impossible, basically by showing that any such system tripped over an elaborate version of the liar paradox.

Bureaucrats, school administrators, and officials typically have a somewhat analogous set of interests and desires. Many of them yearn in a heartfelt way for a set of rules complete and comprehensive enough to dictate their actions and rulings in every case without any need for applying intelligence, common sense, general principles, or considerations of context. Indeed this reverence for and reliance upon rules and the accompanying reluctance to consider context and actual meaning are often seen as the hallmarks of the bureaucratic mentality.

These is also a relevant  analogue of Gödel’s theorem, not a proof,  but an observation: it is impossible to construct a set of formal rules governing human behavior which will answer every question under their purview in a just and appropriate way without applying thought and considerations of context to individual situations.

A general understanding and acceptance of this limitation and its implications probably would spoil the lunches of public servants everywhere and induce devastating clinical depression in human resources directors and school superintendents from coast to coast - neither a particularly bad thing.  However it should also be a warning to those libertarians who yearn for a somewhat similarly comprehensive set of rules for a free society. It reminds them that there will always be unusual cases and special situations.

As a simple example consider a free  society with laws and rules respecting property rights. Suppose that person A buys rural land completely surrounding the land owned and occupied by person B. It is fairly easy to come up with laws based on principles of individual rights saying that in such a situation A must grant B some sort of easement to come and go to and from his property, and B while using the easement must  respect A’s general right to control his own property.  Such rules, however, may not get things anywhere near to an actual solution, particularly if there are unusual conditions about the properties or if A  and/or B is a jackass.  It then would be necessary to arrive at an ad hoc solution based on general principles of fairness and reasonableness and the details of the particular situation.  A reasonably written law would anticipate such situations and allow for their resolution in this manner rather than striving for prescriptive completeness. A reasonably thought out legal and political theory would do the same. This incompleteness is not a problem for libertarian theory. It is really only a reminder that most of the time you can’t get away without thinking and paying attention to the facts and details.