IMPOSSIBILITIES, POSSIBILITIES AND PROBABILITIES
In my note on these themes in Frontier of May 21-27, 2000 (Amartya Discourses) I argued that modern theorems explicitly, frankly, nonchalantly, amorally sacrifice aspects of essential realities in all contexts, contingencies or circumstances so as to prove irrefutably that some selected aspects are absolutely or approximately or mainly true and must be accepted. In the case of most of them, the acceptance must hold unless and until new evidence requires enlargement of the scope of the theorem. Thus, the theorem 'crows are black' must hold until white crows appear or are discovered or are bred in captivity and kept in cages or released. The theorem is then restated to say 'crows are black or white and of no other colour', to be accepted until by cross-bredding under controlled conditions, crows of other colours are produced.
As I also pointed out in my earlier note, some economists and collective-choice theorists, whether or not they are also interested in politics and sociology, have also suggests that there are some foundational or 'mother theorems' which are more fundamentally true, though it is conceded frankly that what is the foundation and what is the infra-structure and the superstructure (references to all three, however vaguely identified, are in vouge), or indeed whether anything at all can be called the foundation for anything (a pertinent question asked by Marx in the Grundrisse) are all decided arbitrarily and selectively, to prove irrefutably what is to be proved.
Let me add here that Baye's irrefutable theorem about probaility (upheld by the modern Bayesian school) is sometimes more guardedly referred to as a refutable formula. But whether it is a theorem or a formula, it says candidly that to ascribe probability to some event we must first specify a certain level of existing knowledge, based on an average of various structured or unstructured samples of observation of its occurrence.
Let me add also apropos base-supersturcture theorems also mentioned in my earlier note, which overlap partially with 'foundational' theorems, that the structuralist schools of historians and sociologists insist that only structures matter, neither superstructures nor infra-structures do.
These modern theorems about impossibilities, possibilities and probabilities have diverted attention from or side-tracked two notable, increasingly non-ignorable on-going human experiences of the 20th Century in all contexts, contingencies or circumstances globally, as well as separately in various countries and within some countries.
First, there is the almost irresistible, increasingly insistent, sometimes strident clamour, sometimes soft-spoken pleas, for transparency about everything, everywhere. Constantly reinforced by the accelerating revolutions and counter-revolutions in modern computer-information-communication-transport technology and robotonics, it became a reality when front-runners in global, inter-regional and intra-regional conflicts of various kinds began to make drastic about-truns and began to opt for transparency instead of confidentiality and secrecy. As a first step, secrets were leaked on a trial basis, to see what happened. Next, more and more secrets became open secrets. Then opponents and enemies began trading their secrets, at first sporadiclly and informally, then fromally as a routine matter. Till a point was reached when these front-runners concluded that they should out-compete opponents and enemies within and without in playing the transparency card. Among these front-runners are: (1) spies, agents and double-agents of states, international organizations, political parties and factions within and across several political parties, (2)cohesive traditional as well as non-traditional disintegrating families, (3) media persons (4) instruments of state terror and of anti-state terror (the former with 'shoot-to-kill' missions; the latter with 'kill or be killed' as their motto) and 'Do or Die' karenge ya marenge forces and anarchists opposing both kinds of terror; (5) ethno-communities within and across countries, (6) scientists, military commanders, businessmen, trade unions; peasant and caste organisations whether organised or unorganised both consolidated and represented by civic bodies, co-operatives, collectives, and private and public limited partnerships and companies. Among them are also atheists, deists, mystics, secularists, communists, anti-communists, fascists and anti-fascists (and anti-anti-fascists) of dozens and hundreds of kinds, who resemble each other in word and deed and sometimes in thought as well so much that it is hard to take their differences seriously.
Second, not only is diversity the name of the game of every game in all spheres everywhere in the existential universe. It seems that barring a few still unexplained cases, nothing that has evern taken shape seems to become non-existent and become extinct. Moreover, powerful cross-currents of increasing and decreasing diversity in all spheres do not seem to cancel out. Instead, there is a net increase in deversity: some kind of law or non-binding but inexorable tendency towards increasing diversity seems to hold.