The definitional problem
While the classical theory holds that categories have definitional structure, in practice it is remarkably difficult to identify a precise set of conditions that are necessary and sufficient to define a category. This requires the identification of all those features that are shared by all members of a category (necessary features) and that together are sufficient to define that category (no more features are required). The following famous passage from the philosopher Wittgenstein’s discussion of the category GAME illustrates the difficulty inherent in this approach:
Consider for example the proceedings that we call ‘games’. I mean board-games, card-games, ball-games, Olympic games and so on. What is common to them all? – Don’t say: ‘There must be something common, or they would not be called “games”’– but look and see whether there is anything common to all.– For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don’t think, but look! – For example at board-games, with their multifarious relation ships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost.– Are they all ‘amusing’? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball-games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups in the same way; we see how similarities crop up and disappear. (Wittgenstein 1958: 66)
This passage reveals that there is no single set of conditions that is shared by every member of the category GAME. While some games are characterised by AMUSEMENT, like tiddlywinks, others are characterised by LUCK, like dice games, still others by SKILL or by COMPETITION, like chess. In other words, it appears to be impossible to identify a definitional structure that neatly defines this category. To present a simpler example, consider the category CAT. We might define this category as follows: ‘is a mammal’; ‘has four legs’; ‘is furry’; ‘has a long tail’; ‘has pointy ears’. What happens if your cat gets into a fight and loses an ear? Or gets ill and loses its fur? Does it then stop being a member of the category CAT? The definitional approach therefore suffers not only from the problem that the definitions are often impossible to identify in the first place, but also from the problem that definitions are, in reality, subject to exceptions. A three-legged one-eared hairless cat is still a cat. It seems, then, that a category need not have a set of conditions shared by all members in order to ‘count’ as a meaningful cate gory in the human mind. It is important to emphasise here that we are not dealing with scientific categories, but with the everyday process of categorisation that takes place in the human mind on the basis of perceptual features. While a biologist could explain why a three-legged one-eared hairless cat still ‘counts’ as a member of that species from a scientific perspective, what cognitive psychologists and linguists want to explain is how the human mind goes about making these kinds of everyday judgements in the absence of scientific knowledge.
