Augustin Cournot is famous for the principle that an event of small probability singled out in advance will not happen. Yet Dick Cheney is famous for his “1% doctrine”: “if there’s a 1% chance that Pakistani scientists are helping Al Qaeda build or develop a nuclear weapon, we have to treat it as a certainty in terms of our response.” According to the US Nuclear Regulatory Commission, the probability of a severe reactor accident in one year is between roughly 1 in a million and 1 in a 100,000.
Much of my philosophical research has concerned the extremely improbable: events that we typically disregard because their probabilities are so low. And yet many such events should be important to philosophers, some of them should be important to scientists, and some of them should be important to all of us. I will survey more examples of improbable events in engineering, science, and daily life. I will discuss some of the mileage that philosophers have got out of such events in motivating philosophical positions. I will then put them to philosophical work of my own. I will appeal to them to question some probabilistic orthodoxy, and to argue that most counterfactuals (statements about what would happen if things were different in particular ways) are false. I will conclude with three practical cases important in everyday life, in which even the improbable needs to be taken seriously because of the high stakes involved: ‘Pascal’s Wager’, Pascal’s argument for the rationality of belief in God; a new argument for vegetarianism; and responding to the prospect of global warming.

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