Timothy Taylor at Edge:
Polythetic entitation is a way of understanding fuzzy-edged groups of things, the products of human technology. It is easiest to understand by contrast with a biological entity, such the sub-phylum vertebrata. If you want to know whether the cat asleep on your chair is a vertebrate, you check whether it has a backbone. If it does, it is. This is an example of monothetic classification, where a particular attribute—the backbone—is sufficient grounds for making the call and (and this is important) at the same time, a necessary attribute.
Compare that situation with wanting to know whether the piece of furniture the cat is asleep on is actually a chair. That may sound crazy, as you know it is a chair. But you do not know it in the same way as you know that the cat is a vertebrate because—as it turns out—there is no single attribute that is at once sufficient and necessary to define your piece of furniture as a chair. It seems natural to dispute this. Does a chair have four legs, or three, or some other support? Refine the target to four-legged chairs and we find there are four-legged tables—which are not chairs—so possessing four legs could never be a sufficiently exclusive characteristic to define the object in front of you as a chair. There has to be a place to sit on a chair, but a sofa has to have that too, as does a stool.