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There are two strategies with regard to the question of how to confront the all-pervasive presence of chance in the structure of the universe. Both are extreme in their ambitions and equal in their zeal. According to the first strategy, chance explains everything; according to the second, chance contradicts explanation and should be eliminated as much as possible in order to make the universe understandable. Both of these strategies, however, are wrong. I suspect that their adherents share a misplaced idea of what chance really means. 

As usual in philosophical matters, the story goes back to the Greeks. Aristotle believed that all responsible knowledge is based on causal explanation. The essence of chance consists in the fact that it breaks down the causal relationship between events. In this sense, chance contradicts explanation and is beyond the domain of rationality. The influence of Aristotle's teaching on our philosophical imagination is still powerful and, from this perspective, the dichotomy of "chance or Intelligent Design" is rendered particularly powerful. The other strategy, however, also owes a lot to Aristotle. If chance explains nothing then chance itself does not require any explanation. If, therefore, we assume that chance is the source of everything, we remove the problem of explanation. 

Aristotle's doctrine on chance was one of his greatest errors. Chance is indeed a little stubborn, but it can be tamed. The history of the calculus of probability can be regarded as a tedious road towards the taming of chance. It was not by chance that the first steps along this road were enforced by human greed. If you aim at winning a large sum in a game of hazard, you must defeat chance. Pascal, when consulted by a gambler, wrote to Fermat, and it is from their exchange of letters that the first mathematical approach to chance and probability was born. The very name probability was the contribution of theology to this process. Jacob Bernoulli, the author of the first fully mathematised treatise on probability entitled Ars conjectandi, was a pious Calvinist but he also knew Catholic theology well, and was aware of the prolonged dispute between Dominicans and Jesuits on moral matters. The problem concerned how to act if there are two sets of rules, contradictory with each other, that are to be applied to a given situation, and both of them have only probable arguments on their behalf. In his Ars conjectandi Bernoulli proved the "first limiting theorem" on probability which, roughly speaking, states that in a sufficiently long series of random trials (e.g. throwing dice) the average of results tends to a certain value (later on called the expectation value). How could chance events be the subject matter of a mathematical theorem? As a Calvinist, Bernoulli believed in predestination: what to us seems to be a random or chance event, for God is fixed once and for all. In this way, Bernoulli's theology helped his mathematics. The London plague death lists and annuity documents collected by Dutch bankers provided ample material on which to test reasonings based on probability. From then on, statistical calculations became an important factor in economic analysis. 

In the first decades of the 20th century, the powerful applications of probability in physics preceded rapid developments in mathematics that have changed probability calculus from a set of useful rules and algorithms into a mature branch of modern mathematics. The process culminated in 1933 when Andrei Kolmogorov expressed the probability theory in the form of an axiomatic system. Thanks to this achievement, probability entered into a network of interactions with other mathematical theories and initiated a chain of rapid progress.

Chance has finally been tamed. It is no longer a gap in causal explanations but a sensitive tool providing explanations where causal mechanisms fail. Chance can now be described as an event, the (a priori) probability of which is less than one (where by convention "one" means "certitude"). There are two sources for an event to have "probability less than one". The first is our own ignorance when, for instance, we guess whether the white or black ball is in the box. The second is when the probabilistic behaviour is intrinsic to a given natural process such as the process of radioactive decay. 

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elixelx
March 24th, 2012
6:03 AM
"Grand design contains both laws and chance"... Wonder of wonders! The Universe and all within it, most especially the Man who is able to witness it...is a paradox! It is mathematically certain and impossible to prove at the same time...Hooray! Here are three paradoxes that come from Jewish Sources, all of which sustain your perception.. "All things are in the hand of G-d (certain) EXCEPT the fear of G-d (Chance)" Talmud. "Everything is known (Certain) and yet Free Will(Chance) is given" Rabbi Akiva "He who believes in Chance (Keri) WILL suffer the Fury of Chance (Be-keri)" Maimonedes

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