A hot dog

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Well, what is a sandwich?

I’m sure you can come up with a reasonable definition, and many people have, but is that definition really what you have in mind when you think of a sandwich? Is that definition the way you first learned to identify a sandwich, or did the definition come later, based on a concept you were already familiar with?

For me personally, I don’t determine if something is a sandwich by checking if it meets a given set of necessary and sufficient conditions. I just check if it’s like a sandwich.

In the philosophy of language, there are two types of definition: intensional and extensional. Intensional definitions are the kind we normally talk about, a concise set of necessary and sufficient conditions that determine whether something is a member of a category. Extensional definitions are given by pointing out specific examples and hoping that you can figure out the connection between the examples.

Intensional definitions are great, because they’re easy to communicate, easy to check and unambiguous. But extensional definitions are what we use for most of the concepts we use daily. What’s the definition of a door, a chair, a car, a cat? You can come up with intensional definitions for those things, but they’ll almost certainly include things that aren’t in the category, exclude things that are, be difficult to apply, or all three.

This is the basic idea behind exemplar theory, which says that we evaluate whether an object belongs to a category by comparing it to known examples of that category. Under this paradigm, you might say that a hot dog is a non-typical member of the sandwich category. Or, depending on your understanding of exemplar sandwiches, maybe you’d say that a hot dog is a somewhat sandwich-like non-sandwich.

But more importantly, what’s the point of the category in the first place? A whale is a mammal, not a fish, and that’s an important distinction to a biologist studying phylogeny. But if you’re a fisherman, maybe all you care about is whether it lives in the ocean, in which case it would make sense to group fish and whales together, both separate from horses. Neither category is wrong, they’re just more or less useful to certain applications.

So, what’s the point of the sandwich category? What are you going to use the answer for?