(This post is the second installment in an ongoing series on logical fallacies. Check out my first one here.)
Let me tell you about a problem I’m having with my eye right now. For the past few days, I’ve had what appears to be some sort of allergic reaction — swelling and itching around both eyes but primarily my left one. I don’t know for a fact that it is an allergic reaction, but the symptoms seem to fit and it’s not bad enough to get it checked out. Whether or not it is one, I’m treating it like an allergic reaction by taking benadryl. After popping pills for four days, the swelling and itching have gone down almost entirely. So why am I writing about this on my science blog? Because it’s an excuse to talk about a common problem in assigning causation.
Post hoc, ergo propter hoc, or “after this, therefore because of this,” is a logical fallacy that deals with misattribution of causation. Here’s how this works:
1) event A occurs
2) event B occurs
3) event B is believed to be caused by event A
In my particular case, event A was taking antihistamine pills and event B was the swelling and itching around my eyes going down. These two events might be related, or they might not be. The swelling and itching may have gone down on their own even without taking the pills. How long do these things usually last if you don’t treat them?
This does not mean that events are never caused by other events that preceded them. On the contrary, events are ALWAYS caused by other, previous events (the quantum world notwithstanding). This is only a fallacy if you do not have good reason to believe that they are connected. If all you know is that two events happened and one happened first, then you cannot assume they are causally related.
If I knew for sure that my eye problem was an allergic reaction, it would be reasonable to assume that taking the benadryl — which is an experimentally-validated treatment for allergic reactions — was the cause of my eye problems subsiding. As it stands, though, all I can say is that my symptoms subsided over four days and also I was taking some pills. The two might be related but I cannot say with confidence whether or not they were. And what if I had taken something else? What if I had followed some bizarre old wives’ tale about burying a potato under a full moon?* Or used some bogus homeopathic remedy? If my symptoms eventually disappeared, I might conclude that, for example, sleeping with a pinecone under my pillow** had cured my ailment.
Avoiding this fallacy is exactly why scientists use a control group in their experiments. Let’s say you discover a new soil treatment that you believe will make plants grow faster. You plant 100 seedlings and give all of them your soil treatment. After 30 days the average height of the plants is 48cm. What have you learned from this? Absolutely nothing. Because you have nothing to compare your plants to, you can’t say anything about whether the height they reached had anything to do with your treatment. Maybe plants would have grown to 48cm in 30 days anyway.
As a more relatable example, lots of people will take a homeopathic remedy for a minor ailment. When their symptoms subside they will conclude that it was due to the pills they took. “It worked for me,” they will say. But to really know the effectiveness of the treatment, you need to do a study. Take a bunch of people people with the same problem, give half of them the homeopathic remedy, and half of them a placebo. If the people in both groups have the same level of symptoms after the same amount of time, then the treatment does not work. And this is what they have done for homeopathy, and they found that it doesn’t work.
The human mind is a remarkable thing. One of its abilities is to recognize patterns in the world. It is so good at finding patterns that it can find them even when they don’t exist. This is why we are susceptible to the post hoc, ergo propter hoc fallacy and why we develop superstitions if we’re not careful. If a bad thing happens to you for a random reason — let’s say your car got a flat tire, or you got struck by lightening — you may attribute it to the most recent thing that you did that was unusual, or to an event that you had already been primed to believe was the cause of bad luck. The same is true for positive events. As a result, people don’t like to break mirrors, walk under ladders or open umbrellas inside, they carry charms and trinkets for luck, throw salt over their shoulders, and cross their fingers.
* This is part of a fabled cure for warts.
** This is not a cure for anything I’m aware of.
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