Why it’s easy to be misunderstood when talking about probability

The words we have for probability make it hard to say what we mean Makhbubakhon Ismatova/Getty Images If someone told you that they were “probably” going to have pasta for dinner, but you later found out that they ate pizza, would you feel surprised - or even lied to? More seriously, what does it mean to be told that it is “very likely” that Earth will exceed 1.5°C of warming within the next decade, as the United Nations reported last year ? Translating between the vagaries of language and the specifics of mathematical probability can be tricky, but it turns out it can be more scientific than you might think - even if it took us quite a long time to arrive at a translation. There are two words that most of us can agree on when it comes to probability. If something is “impossible”, its chance of occurring is 0 per cent, while a “certain” event has a 100 per cent chance of coming to pass. In between, it gets murky. Ancient Greeks like Aristotle distinguished between eikos , that which is likely, and pithanon , meaning plausible or persuasive. Already, we are in trouble - in the right rhetorical hands, something that is persuasive doesn’t necessarily have to have a high probability of being true. To make matters worse, eikos and pithanon were sometimes used interchangeably, leading the ancient Roman orator Cicero to translate them both as probabile , the root of our modern word probability . The idea of a measurable, mathematical approach to probability didn’t emerge until much, much later. It was first developed in the mid-17th century during the Enlightenment, by mathematicians who wanted to solve various problems in gambling , such as how to fairly divide the winnings if a game is interrupted. Around the same time, philosophers began asking whether it was possible to quantify different levels of belief. For example, in 1690 , John Locke labelled degrees of probability by their strength on a spectrum, from assurance or “the general consent of all men, in all ages, as far as it can be known”, through confidence in our own experience, to testimony, which is weakened by being repeated second- or third-hand - an important legal principle both today and at the time he was writing. This link between the law and probability remained an important one for philosophers. Writing in the mid-19th century , Jeremy Bentham noted that when it comes to quantifying the strength of evidence provided by a witness, “the language current among the body of the people is, in this particular, most deplorably defective”. He wondered whether words can reflect certainty “in the same way as degrees of probability are expressed by mathematicians”. Bentham suggested asking people to rank the strength of their belief, positive or negative, on a scale from 0 to 10, where 0 corresponded to no degree of persuasion. Ultimately, he concluded the idea has merit, but its subjectivity and variation from person to person would...

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