Vague concepts are fuzzy. They lack strict definitions and contain edge cases. One classical example is baldness: we would call a person bald even if they have three hairs on their head, so exactly how many hairs could someone have and still be bald? Another example is a heap of sand: a single grain of sand is not a heap, two grains of sand is not a heap, but if we keep adding sand grain by grain it will eventually become a heap.

Many concepts are vague. In general, concepts are only non-vague when they have technical, legal, scientific, or mathematical definitions (and sometimes even then). Notably, language functions perfectly fine in spite of vagueness. Through context and other mechanisms, language use naturally narrows down ambiguities. There are exceptions in which ambiguity is conspicuous, such as in poetic and comedic usage.

How, though, can vague concepts actually be understood? One answer is defining a concept in terms of a cluster of properties. If an object has enough, but not necessarily all of these properties, then it fits the concept. Some properties may be more important than others. For example, something may be identified as “dog” if it has properties like having four legs, having a tail, having fur, having sharp teeth, and so on. In this way we can understand something like an anthropomorphic cartoon dog as being a dog.

We can apply this to our previous example of a heap of sand. It may have properties like individual grains being indistinguishable, having the shape of a mound, and so on. As grains are added, the collection of sand grains acquires more and more of these properties, becoming gradually more of a heap.