As I said last week, there are good ways to use words, and there are bad ways to use words. There are also some wrong ways to use words. This week is all about how to tell the difference between good, bad, and wrong. But before we can get to that, I need to explain the fallacy of equivocation.
Here’s a “proof” that 4 is not divisible by 2. See if you can spot the error.
Premise 1: The number 4 is a prime example of an integer.
Premise 2: A prime integer is an integer which is only divisible by 1 and itself
Conclusion: 4 is only divisible by 1 and itself, and therefore 2 does not divide 4.
Now obviously this proof is faulty, because we all know that 2 does divide 4, and yet the premises are perfectly believable. The error lies in the way the proof uses the word “prime.” It appears twice, once in each premise. Each time the word appears, it has a noticeably different definition. In Premise 1, the word prime is used to mean “good” or “characteristic.” In Premise 2, the word prime is used in its mathematical context, to mean “only divisible by 1 and itself.”
The proof is faulty because the conclusion acts as if the word prime means the same thing in Premise 1 as it does in Premise 2. This is called a fallacy of equivocation. It occurs where two distinct concepts are treated as the same simply because the word used to refer to them is the same. The difference between good definitions and bad definitions is that good definitions pre-emptively dissuade equivocation fallacies while bad definitions invite them.
The key is in connotations. Words all have common uses, and through this common usage we develop an intuition that links various concepts to that word. The links can become quite strong, especially for emotionally charged or exceptionally common words, but it is important to keep in mind that these connotations are a result of how we tend to use the words and are not a property of the words themselves.
It’s tough to completely free yourself of connotations. So when you need to express a group of concepts, pick a word whose connotations match the concept cluster as closely as possible. That way your audience won’t have to work as hard to make the substitution. It will also help you. With less difficulty come fewer errors, so by choosing a word with the right connotations you will be less likely to slip in a stray equivocation fallacy.
Of course, it’s technically viable to choose a definition that goes against connotation. It’s not a wrong definition in the sense that it’s somehow invalid. In a vacuum, such definitions are just as acceptable as others. The only problems arise because our intuitions lead us astray when dealing with such definitions.
Ideally our definitions would align completely with the words’ connotations. But, alas, such an ideal is unattainable. Different people tend to have slightly different connotations, and sometimes we just need to express something that doesn’t quite match any group of connotations. So we need to recognize that sometimes people will use a word in a way that doesn’t quite match our connotations, and we should accept this, so long as the definition does not cause undue confusion. When this happens, we should refrain from being douchebags. We should refrain from attempting to refute their conclusion based solely on their decision to use an unusual off-beat definition, and instead address the actual problems (if any) with the argument. And moreover, when you come up with an off-beat definition, don’t be a douchebag by trying to sneak in all the connotations that don’t actually have anything to do with the definition you’ve made.
Here’s an example:
Theist: Good is that which complies with God’s nature, and God wants you to believe in him. Thus you should believe in God.
Now, it is tempting to respond by saying “but that’s not what good is.” Yet such a response doesn’t precisely highlight what is actually wrong with the argument. The problem is that the conclusion does not follow from the premises. What “but that’s not what good is” is trying to express (but not doing a very good job of it) is that this argument makes a fallacy of equivocation. Even if we do allow the word good to literally mean “that which complies with God’s nature,” the theist has done absolutely nothing to demonstrate that this definition of good has anything to do with what you should and should not do. The theist has used the word “good” in order to sneak in all its connotations about what’s best, without actually doing the legwork of demonstrating these connotations. It’s a fallacy of equivocation. This fallacy is disguised by the theist’s poor definition, (and thus both easier to make and harder to catch) but the definition itself is not what makes the argument fail.
And what about the wrong ways to define words? Well, there are probably some syntactical rules you have to follow. I mean, “alsdkhflsh” doesn’t produce a sentence, much less an actual definition. But aside from these syntactical rules, there is (at least) one other way to make a wrong definition. And by a wrong definition, I mean a definition that doesn’t work regardless of the connotations involved. A bad definition is one that breaks connotations, while a wrong definition is one that breaks reality.
Consider the just-made-up number Illixillion. Illixillion is defined to be the existing largest prime number. What’s wrong with such a definition? The same thing that’s (presumably) went wrong with your attempts to define a tasty snack into existence. Definitions only determine how we reference reality. However much you try, you just can’t use them to change reality itself. Fortunately, it’s very easy to avoid such shenanigans. All you really need to do is stay away from using existence in your definitions.
If we didn’t know that there was no largest prime number, then it might be useful to refer to the concept. Perhaps we wish to express concern that we will run out of keys for RSA. Whatever the reason, suppose it is useful to reference the concept “largest prime number,” so we want to retain the ability to link these concepts while resolving the issues that arise with the current definition of illixillion. Existence is the only other concept left in the definition, so the obvious thing is to nix it. If we define illixillion to be the largest prime number, rather than the largest existing prime number, then we can avoid the mess by simply saying that Illixillion doesn’t exist.
In this sense, existence serves as a safety net, allowing us to group our concepts in whatever ways we find useful without having to worry about making unworkable definitions. As long as we keep existence out of our definitions, we can always just say “well, turns out illixillion just doesn’t exist” and avoid any problems that might have arisen.
So the next time you present a definition, don’t be a douchebag. Stick as close as you can to our connotations, and don’t try to define things into existence.
And, of course, stay tuned next week for Word Play Part III: Philosophistry.