How the Greeks Won Debates With Absurdity: Reductio ad Absurdum

Plato and Aristotle (source)

Reductio ad absurdum is Latin for ‘reduction to absurdity’ – a method of reasoning that originates from classical Greek philosophy. Its use is common in debates, philosophy, and in formal mathematics (where it is referred to as proof by contradiction). Consider the examples below:

Example 1: Is intelligence determined by genes or the environment?

Let’s say someone is arguing that intelligence is 100 percent determined by genes. You can counter this with reductio ad absurdum:

If intelligence were only determined by genes, then someone raised without human contact or knowledge could still be a genius.

On the other hand, if someone were to argue that intelligence is 100 percent determined by the environment, upbringing and hard work, you could counter that argument as follows:

If intelligence is 100 percent determined by the environment, show me a professor who contributes to his field, despite having down syndrome (a form of intellectual disability).

Example 2: What is the smallest number ever?

If someone told you that they had discovered the smallest positive number in the world, you could easily disprove their claim as follows:

There can be no ‘smallest positive number’, because whatever that number is, you can divide it by 2 and get a smaller number!

But Watch out for straw man arguments!

Reductio ad absurdum can be an effective way of disproving or proving claims, but use it with caution. You have to be wary of straw man arguments – situations where the contradiction is made out of ignorance and without full appreciation of the specific assertions in a claim.

For instance, a person who believes the world was created would be inaccurate to argue against the theory of evolution as follows:

If evolution were true, we would be seeing monkeys turning into humans all the time.

The above is a straw man argument (and the wrong use of reductio ad absurdum) because it takes an extreme view of evolution and ignores the fact that evolution is a process that spans millions of years!

Burn Your Ships: Options Distract Us from Our Main Objective

Predictably Irrational

“In 210 BC, a Chinese commander named Xiang Yu led his troops across the Yangtze River to attack the army of the Qin (Ch’in) dynasty. Pausing on the banks of the river for the night, his troops awakened in the morning to find, to their horror, that their ships were burning. They hurried to their feet to fight off their attackers, but soon discovered that it was Xiang Yu himself who had set their ships on fire, and that he had also ordered all the cooking pots crushed.

Xiang Yu explained to his troops that without the pots and the ships, they had no other choice but to fight their way to victory or perish. That did not earn Xiang Yu a place on the Chinese army’s list of favorite commanders, but it did have a tremendous focusing effect on his troops: grabbing their lances and bows, they charged ferociously against the enemy and won nine consecutive battles, completely obliterating the main-force units of the Qin dynasty.”

Excerpt from Predictably Irrational by Dan Ariely.

Note: This reminds me of the documentary, Jiro Dreams of Sushi. In the film, a young child (who would go on to become the world’s greatest sushi chef) faces a similar trial:

“I was in my first year of school. My father told me ‘You have no home to come back to. That is why you have to work hard.’ I knew that I was on my own. I did not want to have to sleep at a temple or under a bridge. So, I had to work hard just to survive.”

Confounding

Van Leeuwen Artisan Ice Cream – New York, New York (photo credit: Martin Adolfsson)

In statistics, confounding is when things are mixed up to the point of confusion, such that it is difficult to determine what causes what. Why is this a concept you should care about? Consider the following textbook example, which is similar to some of the headline-grabbing claims you may come across in newspapers or on the internet:

“In New York City, researchers have documented a positive association between ice cream consumption and burglary. On days when New Yorkers eat lots of ice cream, the burglary rate tends to be high. On the other hand, on days when people refrain from ice cream consumption, these rates are much lower.”

Given the above findings, what sort of conclusions would you draw? A lousy newspaper may report the above as follows:

“Study Shows Eating Ice Cream Causes Burglary.”

Another media outlet may spin the same research in a different way:

“Is Burglary Causing Us to Eat More Ice Cream?”

But in both cases, we have to be careful never to jump to any immediate conclusions because it is possible that a confounding variable exists. That is, a third variable may be confounding (mixing up/confusing) the relationship between ice cream sales and burglary.

In the above example the confounding variable happens to be temperature. This is because when it is hot people eat a lot of ice cream. They also spend a lot of time outdoors and this increases the opportunities for burglary.

So while ice cream sales (X) and burglary (Y) appear to move together, this does not mean X causes Y or vice-versa. A third variable, temperature, is the culprit.

Researchers usually make an effort to identify and eliminate the effects of confounding variables but this isn’t always successful. So be sure to maintain a bit of a skepticism whenever you come across studies that claim some factor, X, causes another factor, Y.