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Apr 25, 2019

What did it mean for something to be 'probable' in mediaeval Latinate Europe? Chances are (no pun intended), anyone living after Thomas Aquinas would have understood the term as having to do with opinions that are warranted by authority. Empirical likelihood by counting numbers mattered less than whether something was plausible and capable of being proven, especially if supported by the authority of a biblical passage or the words of a bishop. If anything, probabilities measured not so much the instability and contingency of the natural world but rather the extent of human ignorance—of course God's creation was perfect, it is our fallible minds that are too weak to comprehend it. This belief persisted for a long time even after probability became mathematised from the 17th century onward.

But if any opinion that was plausible in the realm of morality was to be considered probable, the creeds of non-Christians might also be valid. The Society of Jesus, who propounded a doctrine of 'probabilism' in the early seventeenth century, were following Aristotle's teachings in the Nicomachean Ethics that seeking absolute certainty in the moral realm was futile. It was Blaise Pascal, a first-rate mathematician but also an extremely devout Catholic, who fiercely repudiated this view in the Lettres Provinciales. Pascal saw this Jesuit probabilistic doctrine as dangerously lax and a threat to the church. He accused the Jesuits of allowing Asiatic converts to Christianity in India and China to continue practising their idolatrous customs under this doctrine.

Running parallel to this theological-moral arc of debate over probabilism was a growing mathematical discourse of the probability of chance, especially games and gambling. This was, of course, a popular theme for both the mathematically-minded literati and for aristocrats who enjoyed gambling as a pastime. Cardano is one of the best-known early theorists in this vein, and by the latter half of the seventeenth century mathematical problems of chance was a core preoccupation for the greatest minds of the age, from Huygens to Jakob Bernoulli.

What interests me about this narrative of the development of probability as a field of knowledge is its implications for contemporary understandings of the human mind and its limits. As I mentioned, even in the age that mathematical probability as a systematic enterprise was blossoming, people saw it as a tool to make up for the restrictions to knowledge due to human ignorance. It took a long time for statistics to merge with this new probability. But here and there some kernels can be found, and the question is how to put together the story without allowing modern expectations to anachronistically anticipate each of the steps in the process of this convergence.