A theory of concepts and concept formation introduced in 1973 by the US psychologist Eleanor Rosch (born 1938) to overcome problems inherent in the classical componential theory originally put forward by the Greek philosophers Plato (?427–?347 bc) and Aristotle (384–322 bc). According to the componential theory, concepts can be expressed in terms of their defining properties, which are the necessary and sufficient attributes that items must have to be instances of the concept. But the Austrian-born British philosopher Ludwig (Josef Johann) Wittgenstein (1889–1951) argued in his Philosophical Investigations (1953, paragraph 66) that a concept such as that of a game has no necessary or sufficient attributes, and hence no defining properties, and that instances of games are linked to one another by family resemblance, just as some members of the family may share the same build, others the same eye colour, and others the same gait, without any characteristic being shared in common by all members of the family. According to prototype theory, instances of a natural concept are defined by their resemblance to a prototype (2) that is a best or most typical example of the concept, sharing the maximum number of features (1) or attributes with other instances and a minimum number with instances of other concepts. Thus a prototype consists of characteristic features rather than defining properties, and according to this interpretation concepts have indistinct boundaries and may be represented by fuzzy sets (but see guppy effect). If an item is clearly similar to a prototype, as table is to the prototypical furniture, then it is likely to be perceived as belonging to the concept, whereas if it is somewhat (but not entirely) dissimilar to the prototype, as carpet is to furniture, then it may be unclear whether or not it belongs to the concept. See also basic-level category, schema. Compare componential theory.