In past columns, I’ve talked a lot about logical fallacies, and I know what you’ve been thinking: “Ben, this talk about logic is all fine and dandy, but the real world is messy, and we have to make decisions based on limited information. Who’s to say what’s reasonable and what’s not?”
It’s true that we have to make judgments under uncertainty. We have to make the best decisions we can using our minds as they are now — y’know, as opposed to using something else. Every piece of knowledge you have about the real world is uncertain to some extent, having been filtered through your senses and your mind. This is not the same as saying there’s no such thing as objective truth. The problem isn’t that the real world is messy; your mind is messy, and so is everyone else’s.
In spite of this uncertainty, we don’t constantly wander around in a confused stupor. How is this possible? Gee, if only there were some mathematical way of quantifying certainty — some kind of “probability theory,” if you will.
A probability is a number that expresses the degree of belief that something is true, between 0 (0 per cent) and 1 (100 per cent). Due to a widespread fear of mathematics, people tend to cower in fear upon hearing the word “probability.”
This is a shame, because without some way of quantifying certainty, we have a limited vocabulary in which to talk about what we believe. We’re either totally certain X will happen, totally certain X won’t happen, or totally uncertain either way. But probability theory is robust; it allows us to work without total certainty. It’s just a matter of figuring out a number that pinpoints how certain you are.
Just as importantly, it gives us a set of rules to identify good or bad reasoning. I’d like to give a famous example borrowed from Daniel Kahneman and Amos Tversky. Imagine a 31 year-old woman named Linda. As a university student, she majored in philosophy and was concerned with issues of social justice. Which of the following statements is more probable?: (A) Linda is a bank teller. (B) Linda is a bank teller who is active in the feminist movement.
Answer: “A” is more likely, because it is less specific than “B.” However, the majority of people who answer this question think that “B” is more likely, because it fits their stereotype based on Linda’s description. This is known as the conjunction fallacy, and is something to watch out for in opinions-based journalism.
Here’s another example for you. Which of the following statements is more probable?: (A) The United States will be the victim of a nuclear attack in the next 10 years, or (B) Iran will attack the United States with a nuclear weapon in the next 10 years. Intuitively, your average pundit might act as though “B” is the answer, ignoring the fact that “A” must be likelier. I encourage you to stare at this paragraph as long as it takes you to understand why it’s exactly like the Linda example.
This is just a taste of the wonderful world of probability, as it would be impossible to give a complete course on the subject in one article. Probabilistic reasoning takes a lot of practice, but it’s worth becoming accustomed to. Instead of asking yourself, “am I certain of this, or not?” ask yourself, “how certain am I?”
