Christians chose the cross as the primary symbol of their religion. Of all messages contained in the Bible, the cross singles out the message of the ultimate non-violence. Jesus was God, according to Christians, and as such, he could have defeated his enemies in the physical and immediate sense. Instead, he chose the terrible and humiliating death on the cross. One cannot invent a more potent symbol than the omnipotent supreme being subjected to the most horrifying death out of his own will.
I will match the above element of the Christian ideology with a particular historical event - the conquest of America by the Spaniards (and, to some extent, the Portuguese). There were many examples of non-Christian behavior of (mostly) Christian groups of people in more recent times but I prefer to talk about events that are in the distant past so that we can think about them in a dispassionate way. The conquest of America was an act of unprovoked aggression. The only major civilizations and states on the continent (Aztecs and Incas) were destroyed. The populations were decimated mainly by disease but also by direct human actions (combat etc.). All the valuables (for example, gold) that could be hauled across the Atlantic were robbed.
The conquest of America was performed by the agents of the Spanish monarchy. Christianity was the ideology of Spain and of the conquistadores. The contrast between the values symbolized by the Christian cross and the reality of the conquest was striking.
I will come back to Christianity later. First, let us have a brief look at the communist ideology. Among different elements of the Marxist philosophy perhaps the most profound one is the claim that the matter controls the spirit and not, as people commonly believe, vice versa. For example, it may seem that a king in his mind decides to start a war and thus greatly affects material world. In the Marxist view of the world, king's decision is the consequence of the material conditions via the winding route of the social structure, religion, etc. A corollary of this fundamental axiom of Marxist philosophy is that social revolutions can and do come only when the material (economic) conditions are ripe for them.
There were a number of communist revolutions but only two of them had a major and lasting impact on the world. These were the Russian and Chinese revolutions. Each of these revolutions occurred in a pre-industrial society, in obvious contrast to the Marxist theoretical predictions. I have to note parenthetically that Marx himself contemplated a revolution in the pre-industrialized Russian society. Contradictions in philosophical writings are not unusual---the temptation to allow for exceptions whenever convenient is simply too strong.
I will now address a few natural questions about the contradictions between the two ideologies and their accompanying historical events. The first question is why people ignored the ideologies. The answer seems to be rather obvious. The leaders wanted to achieve some practical goals and they did not care about the consistency of the goals and methods applied to achieve them with the dominating ideology, or they self-deluded themselves that there was consistency. The rulers had no choice, in a sense. A conquest of a continent or a major social revolution in a large country are huge undertakings. Rank and file participants in those events needed more than just a utilitarian justification for their actions. Everybody wants to be rich but projects on a cosmic scale require cosmic scale ideologies. The Spanish had only one such ideology at hand, and the same can be said about communist revolutionaries. The two ideologies were used to support the struggle not because they provided good rational arguments but because they were the only reasonably well functioning ideologies available to the leaders.
The second question is whether it would have been wise or at least moral for the leaders to tell their subjects or followers that the practical undertakings were inconsistent with the theoretical claims. Should they have told the ordinary people that the tenets of the ideologies would be ignored for some time so that the practical goals could be attained, and only then the world would achieve the cosmic balance including the consistency of the ideology and reality? It seems that very few leaders follow this intellectually (and morally?) honest path. Ideology is treated as a weapon and nobody wants to blunt a weapon at a time of struggle.
Now I am ready to argue that statistical methods are photo negative images of the philosophical theories that supposedly represent them.
First, let me review a few facts. De Finetti and von Mises created philosophical theories to address certain philosophical questions. Their theories turned out to be radical. In particular, both philosophers claimed that individual events did not have probabilities.
Von Mises claimed that individual events do not have probabilities but it is meaningful to apply probability to a sequence of identical observations or experiments (a "collective"). For this theory to be applicable, we must be able to recognize a collective in real life, that is, we have to be able to recognize in some way that the experiments or observations are "identical". It follows from von Mises' theory that it is impossible to compare probabilities of individual events because they exist neither in theory nor in practice.
Frequency statisticians apply hypothesis testing in various contexts. One of them is scientific, in which various researchers test completely different hypotheses about completely different phenomena. The procedure is justified in the following way. Although there is no guarantee that the conclusion of an individual test is correct, the long run frequency of correct conclusions can be made high by appropriate application of mathematical formulas and collection of sufficient amount of data. Statistical tests in the scientific context are not identical so they do not form a "collective". We know that the long run frequency of correct conclusions is high only because we calculate the probability of an error for every test separately. In this way, the theory of hypothesis testing, commonly regarded to be the most frequentist of all statistical methods, is a photo negative image of the philosophical frequency theory of probability created by von Mises.
The contrast between Bayesian statistics and its closest philosophical ally, the subjective theory of probability invented by de Finetti, is at least as large. The starting point of de Finetti's philosophy is the claim that probability does not exist. This claim may appear to be plain lunatic but it can be given an interpretation that sounds quite rational. De Finetti says that none of the algorithms developed to measure probability of a single event is sufficiently reliable from the logical and practical point of view to be accepted as a scientific method. De Finetti claims that the most we can achieve in face of uncertainty is to make our actions "consistent" in an appropriate sense, to avoid losses that are preventable in a specific deterministic sense.
The common interpretation of the Bayesian statistics is that it can deal with randomness in situations where one cannot observe frequencies. In other words, Bayesian approach can be applied to individual events. This is the photo negative version of de Finetti's theory. In his theory, no event has probability. For a Bayesian, every event has a probability.
Are frequency and Bayesian statisticians undereducated? Are they irrational? Don't they know how to apply logic? Can't they see that their practice is the photo negative image of their theory? I think that statisticians behave just like the Spanish monarchs and revolutionary leaders. They are engaged in a mortal struggle with the representatives of the other branch of statistics. To win, they have to be equipped with a good ideology, among other things. Frequency statisticians could not find a better ideology than the frequency theory of probability. Many Bayesians are not quite happy with the subjective theory of probability or with the identification of Bayesian statistics and subjective thinking. But they did not find a different philosophical theory that could support their branch of statistics. The reality of scientific struggle is in some respects the same as that of the armed struggle. Just like Catholic monarchs and communist leaders, statisticians instinctively feel that it is better to claim that their practical actions are consistent with their ideologies despite all the evidence to the contrary than to admit that there is an inconsistency. The winners write history books. In science, the winners will determine the shape of both practice and the dominating scientific theory in the future.
I end with a pessimistic conclusion concerning the progress in the ideological struggle between frequency and Bayesian statistics. I have to confess that I believe that my theory of probability, encapsulated in (L1)-(L5), is the best scientific theory of probability available at this point. But even if I abandon this opinion and imagine that some other theory of probability is better than (L1)-(L5), I see little chance that statisticians will adopt the new theory, no matter how convincing it might be. The first group of statisticians who abandons their current philosophical crutches risks losing the war. Only if one branch of statistics scores a clear victory over the other do I envision openness of mind among the victors sufficient to admit that their scientific practice is the photo negative version of their philosophical theory.
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