Let us say you are the sort of thoughtful (or idle) person who occasionally wonders about the meaning of everyday concepts. So there you are, at the fair, laughing at yourself in a concave mirror, when suddenly it hits you. You don’t really know what “concave” means. You just recall vague ideas of concave and convex lenses and mirrors from high school and using the term in general conversation to describe certain shapes. So you decide to figure out a definition.

What do you? How do you make up a definition? Let’s get you into some trouble.

[Read more…]

We think about abstract concepts in terms of prototypical instances. These prototypical instances inform how we construct arguments using these concepts. At a more basic level, they determine how we go about constructing definitions themselves. Prototypes pop up in all sorts of conceptual domains, ranging from “war” to “airplane” to “bird.” So how do prototypes work in our thinking? Let’s start with an apparently simple example — the concept of triangle — that can get tricky really quickly.

[Read more…]