A two letter word packing a lot of heat
By Ben Buckley
Photos by Ben Buckley
It always astounds me that, in this day and age, the majority of people — including well-educated members of society — don’t seem to understand what the word “if” means. The concept of implication is a subtle one I hope to clarify in this column.
Suppose I say the following: “If there are unicorns, then you will hear hoofbeats.” What evidence would you need to determine whether or not this statement is true? There are two ways to go about doing this. The first, most obvious way to do it, would be to search the entire universe for unicorns, and where there are unicorns, listen for hoofbeats. If you always hear hoofbeats when unicorns are present, the statement is true. But if, even once, there are unicorns but no hoofbeats, the statement is false.
There is another, less obvious way to verify the statement. The sentence, “if there are unicorns, then you will hear hoofbeats,” means the same as, “if you do not hear hoofbeats, then there are no unicorns” (its contrapositive). Stare at those sentences until you’re convinced that they mean the same thing.
This gives us another way of checking whether the statement is true. Simply search the entire universe for places where you do not hear hoofbeats. If, in every one of those places, there are no unicorns present, the statement is true. But if even one case occurs where the absence of hoofbeats is accompanied by a unicorn, the statement is false.
Here’s where it gets tricky: Assume our statement about unicorns is true. Suppose that you’re in the middle of a field, and you hear hoofbeats. What do you conclude? Intuitively, one’s first instinct might be to conclude that there is a unicorn nearby.
One would be wrong. The hoofbeats could just as easily be coming from a horse, a zebra, a centaur, or a hallucination generated by your own mind. Implication is a one-way street — unicorns imply hoofbeats, but hoofbeats don’t necessarily imply unicorns. An interesting thing is, in any statement insisting, “if A, then B” in which we know that B is always true, the statement is true whatever A is. For example, the statement, “if the moon is made of cheese, then one plus one is two” is technically true.
Unfortunately, this means that you can pair any statement you want with a true statement to make an argument that might convince an unwary listener. For instance, start with the sentence, “if climate change is a hoax, then it will sometimes snow.” This is true as long as snow exists somewhere. But if the speaker concludes that, since snow exists, climate change is a hoax, their conclusion is unjustified.
To make this valid, they would first have to establish the less obvious converse, “if it sometimes snows, then climate change is a hoax.” This would require actual work, so you can understand why people often skip this step. This fallacy is sometimes referred to as “affirming the consequent” and is just one of the many errors people make with the word “if.”
For a simple two-letter word, it can do a lot of damage. Perhaps someday, we will move past this error and be able to think with more clarity. If only, if only.
