“Probabilistic missiles” (Critical thinking)

It’s been fun spooking ghostbusters and searching for proof that Loch Ness Monster hunters exist. But I’m taking a respite from those pursuits to focus a few posts on encouraging critical thinking.

There are probably at least 100 types of logical fallacies, so I will focus on specific types in different posts as a way of organizing them. Fallacies fall into two main categories: Formal and informal. A formal fallacy is wrong because of a flaw in the argument’s logical structure.

Let’s say one is making a deductive argument, which is one based on a series of premises that reach a conclusion. It is possible for each premise to be correct and still arrive at an incorrect conclusion. For example:

1. My children are happy when I take them to Toys R Us.
2. My children are happy.
3. Therefore, I took them to Toys R Us.

Although the conclusion may be true, it could be false.

Seldom would such an elementary example be presented, but we can learn to detect it in more subtle forms. A politician might say his opponent believes in high taxes and government involvement in most aspects of life. Then he would add this is how it is done in communist countries, and let audience members infer that the opponent is a communist sympathizer.

Going back to the toys argument, here it is in valid form:

1. If I take my children to Toys R Us, they will be happy.
2. I took my children to Toys R Us.
3. Therefore, my children are happy. (By the way, does anyone know how to make a backwards R in computer type? It would be useful when referencing this store or Korn).

It is also possible for a conclusion to be false despite being supported by correct premises:

1. If Bill Clinton was British prime minister, he would be a head of state.
2. Bill Clinton was a head of state.
3. Therefore, Bill Clinton was British prime minister.

Again, it would be rare that such an obviously wrong example would be foisted. (That’s my past tense verb for the day, foisted). But a trained ear can spot a less glaring instance. Creationist Ray Comfort points to order in the universe as proof of God, without bothering to demonstrate that a god is the only way order could be attained. This is the formal, propositional fallacy of Affirming the Consequent, which will be handled more in-depth during a subsequent post. The focus this time is probabilistic fallacies. These occur when a listener wrongly takes something for granted because they deduce that it would probably be the case.

We’ll start with the Base Rate Fallacy. Here, if given both general and specific information, a person tends to focus on the latter. Let’s say all we know about George is that he wears black, has multiple piercings and tattoos, and listens to Deicide. Is he more likely to be a Christian or a Satanist?

Most people would underestimate the probability of him being a Christian, and overestimate the probability of him being a Satanist. Doing so requires downplaying in this instance the Base Rate of being a Christian. There are about 500 times more Christians in the world than Satanists. While it is more likely that George is a Satanist than someone who favors blue, is without piercings and ink, and listens to Count Basie, the probability of George being a Christian is more likely than his being a Satanist. It is important to understand that there are only two possibilities being offered, meaning he could be an atheist, agnostic, apatheist, Druid, or Pagan without being a Satanist.

We also see the Base Rate Fallacy when a person decides for safety reasons to travel by road or rail instead of air. An airplane is the safest method of travel, but since surviving an airplane crash is a far more remote possibility than making it through a bus or train wreck, persons fall prey to the fallacy.

The Conjunction Fallacy assumes that specific conditions are more probable than a single, general one. The most well-known example was offered by psychologists Daniel Kahneman and Amos Tversky, who presented the Linda Problem. In it, Linda is a 31-year-old, single, intelligent, philosophy major who has been active in liberal causes. Based on this information, which is more probable: That Linda is a bank teller; or, that Linda is a bank teller who is active in the feminist movement?

Most would guess the second choice. But the probability of two events occurring in conjunction is always less than or equal to the probability of just one occurring. Even though there is a tiny chance that Linda is a bank teller, and a good chance she is active in feminism, the chance that Linda is a bank teller feminist is less than her being just a teller.

Next, we have the Hot Hand Fallacy, and its opposite, the Gambler’s Fallacy. In the former, persons think that a run of events is likely to continue, whether it be a basketball player’s shots, consumer trends, or the stock market. By contrast, in the Gambler’s Fallacy a person thinks a trend is likely to end. Both ideas are wrong since random events cannot be predicted with certainty.

The Hot Hand Fallacy causes fans to think a basketball player is likely to hit or miss based on his performance in the previous few minutes. However, each shot is a separate occurrence, so the chance of a player making it is the same whether or not he sank the previous one. A study of four years’ worth of NBA field goal attempts bore this out.

Meanwhile, the Gambler’s Fallacy is the false belief that random numbers in a small sample will balance the way they do in large quantities. The best known example was at Monte Carlo in 1913, when the roulette ball landed on black 26 straight times. The casino made millions of francs off gamblers who figured red was surely coming up next. The chance of 26 straight black spins was one in 67,108,863. However, those were the odds of all red-black combinations that could occur in 26 spins.

When tossing a quarter, a run of five heads has just a one in 32 chance of occurring. But that’s before any tosses are made. After four straight heads, the chance of the next one coming up George Washington is one in two. This is reasonably common knowledge, but is harder to detect when the ideas become more abstract.

The chance of any one person dying from a tightrope fall is very small. If a person did perish in such a manner, it would be the Gambler’s Fallacy for his brother to conclude, “I can tightrope walk with virtual impunity since the chance of two persons in the same family dying this way is infinitesimally small.” No one would reach such a ludicrous conclusion, but persons can employ logic just as faulty when dealing with more complex issues.

Finally, we will consider the multiple comparisons fallacy. Usually, this is the result of politicians, columnists, or advertisers using selective reporting to bolster a claim, rather than the result of a lack of logical thinking on the listener.

Suppose 100 studies are done on the impact of wearing black slacks to contracting Alzheimer’s. Ninety-four of the studies show no impact. Three studies indicate wearers are twice as likely to have the disease, while the other three show they are half as likely. As a result, a clothing advertisement makes the boast, “Studies show black slack wearers less susceptible to Alzheimer’s.”

I’m wearing black slacks right now and don’t have Alzheimer’s, which sadly is the best transitional, closing sentence I can come up with.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s