Do you believe that people waste too much time arguing over definitions?
I do too. But I also have a second problem: I’ve read some philosophy. And so, when I’m frustrated with pointless arguments over definitions, my frustration becomes compounded by the fact that nobody understands the thing that they’re arguing about, and the only way to solve the problem is by spending even more time arguing over useless stuff.
Case in point, in all the time you’ve ever spent arguing over definitions, have you ever once glanced at the relevant articles in either Wikipedia or the Stanford Encyclopedia of Philosophy? I’m guessing not, because I never thought to do such a thing myself for a long time.
So now that I’ve made everyone feel guilty, let’s talk about one of the things you’d learn from some basic research: intensional vs extensional definitions.
An intensional definition provides some rules about what a word refers to. These rules are called the intension of the word (not to be confused with “intention”). For example, the US president is the head of our executive branch.
An extensional definition provides the set of objects that the word refers to. This set is called the extension of the word. For example, we can extensionally define the current US President as Donald Trump.
Now consider the following statement: “The current US President could have been Hillary Clinton.” Clearly what is meant is that Hillary Clinton could have fallen under the intension of the current US president. But suppose we substituted the extension of the current US president: “Donald Trump could have been Hillary Clinton.” By ignoring the difference between extension and intension, we get nonsense.
Some philosophers argue that a way to deal with the extension/intension distinction is to use the language of possible worlds. The extension of a word is the set of things that the word applies to in the actual world. The intension of a word is the set of things that the word could apply to in all possible worlds. However, I do not think this is entirely satisfactory. Consider, for instance, the following intensional definitions of a triangle:
1. A triangle is a polygon with three sides.
2. A triangle is a polygon with three corners.
Since every polygon with three sides also has three corners, both of these kinds of triangles have the same extension in all possible worlds. Nonetheless, it would be incorrect to say that the two definitions are the same. One way to think about it is that the intension describes an algorithm to determine whether an object is a triangle or not. The two definitions of a triangle correspond to two distinct algorithms, and these algorithms happen to always output the same conclusion, but that does not mean that the algorithms were one and the same.
Question: Is the extensional or intensional definition more important?
We often like to believe that the intensional definition is the important one. The intension definition is, after all, what you find in dictionaries. It’s the definition that you try to provide whenever someone asks for a definition.
But there are many reasons to believe that the extensional definition is also important. For example, though I provided two intensional definitions of triangles, most people hardly care which is the “correct” definition. Both definitions specify the correct extension, and that’s pretty much all that matters.
Or consider the definition of “religion”. When a discussion group is asked to define religion, people will think about it and come to different conclusions. But even amidst disagreement, there are at least a few points of agreement. We mostly agree that the extension of religion includes Christianity, Judaism, Islam, Buddhism, and Hinduism; it excludes baseball, vegetarianism, and university. And should someone happen to disagree on any of these aspects of the extension, then that might cause us to object to their preferred definition.
What this suggests is that the extension of religion is actually more fundamental than the intension. Or at least, some aspects of the extension are fundamental. We don’t necessarily agree on whether, say, the Sunday Assembly is in the extension of religion. Of course, definitions don’t need to be complete and unambiguous, but it’s often nice to be able to classify new things that are brought to our attention. So usually, the approach is to come up with a reasonable intensional definition, such that it matches most or all of our preconceptions about the extension. If the intensional definition doesn’t exactly match the extensional definition, we can choose to either modify the intension, modify the extension, or else be satisfied with multiple definitions.
Why is the extension so fundamental? As I’ve pointed out before, all words must ultimately be defined by pointing to examples. Defining by pointing is called an ostensive definition, and it’s basically a variety of extensional definition.
Extensional definitions also appear to be a fundamental aspect of our psychology. I am especially fond of pointing out the existence of prototype theory. The idea is that we think of most concepts by imagining one or more prototypical examples, and then we classify new examples by judging their similarity to the prototypical examples. In other words, for many words, we start with an idea of its extension, and classify new objects according to their similarity to the extension.
Of course, different words behave differently. I avoid claiming that all words operate according to prototype theory. I’m fairly sure, for instance, that our understanding of the US president is based on an intensional definition rather than an extensional one, if only because we don’t like to think about the current extension.
Go forth, and argue about definitions in a more enlightened way. Or don’t, if you prefer.