Formal Post-Modern Legal Structures for a Post-Modern Political World
Michael. Heather, Northumbria University, Newcastle upon Tyne, UK, NE1 8ST, email@example.com
B. Nick Rossiter, Informatics, Northumbria University, firstname.lastname@example.org
Politics and Law are not to be confused. In domestic jurisdictions the distinction may be latent and political theories can be disguised as Law but only for a while. Like Soviet and Eastern European legal systems of the last century they fall apart in time unless they are coherent within the real-world. In international jurisdictions it is much harder to disguise reality. The League of Nations failed early on. Fairly recently the disarray among experts in international law on the legitimacy of the second gulf War has been quite an academic embarrassment. The confusion of politics with law is quite patent both amongst those who claim the war was in accordance with international law as much as those who claim otherwise. Although its constitution was founded upon the advice of the jurist Hans Kelsen  the United Nations, it would seem, has the fatal flaw for mistaking politics for law.
The past when international issues could be resolved between governments at the diplomatic level had less of a problem. Now where there is a question of new-supra constitutions like the present proposals of the European Union, now where there is globalisation from the technology of rapid communication both physical and electronic, now where there is a transition from modernity to post-modernity … now the old simple structures no longer hold. New structures soundly founded on theory are needed to replace old ad hoc methods. However, it may need new theories. The League of Nations was founded on the mathematical theory of Leibnitz as interpreted by Christian von Wolff .
The scientific advances of the 20th century have unearthed a number of fundamental formal relationships of a philosophical universal nature which can give great insight to the understanding of legal structures. Those of the first half of the last century like relativity, uncertainty principle, non-locality are at least well-known if not understood in the context of law but those of the last 50 years are not even familiar by name like the existence of limits and co-limits, adjointness, freeness and co-freeness. The 19th century language of mathematics is inadequate to express the dynamic nature of politics and law which can be better expressed in terms of arrows and categories .
The world is composed of a system of interlocking subsystems like society or legal constitutions. It is an adjoint relationship. The freedom of political expression generates the model system on the right which is a configuration of the system on the left. The co-free functor is the underlying law which constructs the resulting structure
F —| G
That is politics is left adjoint to law and law is right adjoint to politics. By the fundamental theorem of adjointness  once a functor F is selected, the co-free functor G is unique. Therefore if the political structure and the legal constitution are not left and right adjoint, the system cannot survive in the real-world. This is because the principle of non-locality will be unsatisfied. Political will in the mind may only exist locally and cannot succeed unless it has a non-local right adjoint, namely a generally applicable legal system.
 Heather, M A, & Rossiter, B N, Law, Logic and Language in Legal Computer Science, Law, Philosophy and Computer Science, 1-2 345-365 (1998).
 Kelsen, Hans. The Law of the United Nations. A Critical Analysis of Its Fundamental Problems. Frederick A. Praeger, New York (1964); reprinted Lawbook Exchange (2000).
 Mac Lane, S, Categories for the Working Mathematician, 2nd ed, Springer-Verlag, New York (1998).
 Wolff, Christian, Freiherr von, Jus gentium methodo scientifica pertractatum (1764); I: facsimile edition of H. Milford; II: translation by Joseph H Drake, Clarendon (1934).