Classical categorization
Standard logical approaches to language, like the ones discussed in Chapter 6, are two-valued approaches. This means that they only recognize two truth values, true and false. On this approach, any proposition must either be true or false. There is no room for the proposition to be partly true and partly false, or true in some respects but false in others. The two-valued approach goes hand in hand with the classical view of definition (the one assumed throughout Chapter 2). The classical view was summarized as follows by Frege in his 1903 work Foundations of Arithmetic:
A definition of a concept . . . must be complete; it must unambiguously determine, as regards any object, whether or not it falls under the concept . . . Thus there must not be any object as regards which the definition leaves in doubt whether it falls under the concept; though for us men, with our defective knowledge, the question may not always be decidable. We may express this metaphorically as follows: the concept must have a sharp boundary. (In Aarts et al. 2004: 33)
Another way of describing this view is the idea that definitions are lists of necessary and sufficient conditions for particular meanings. Consider as an example the definition of bird as a feathered, egg-laying, flying vertebrate. This definition involves the four properties feathered, egg-laying, flying and vertebrate, and on the classical view of definition those four properties constitute necessary and sufficient conditions of birdhood:
• The conditions are necessary because something must meet all of them if it is to count as a bird – if something only has some of the four properties, for instance, it does not count as a bird. (This might be the case with bats, which are flying and vertebrate, but which are not feathered or egg-laying.)
• The conditions are sufficient because anything that has all four proper ties counts as a bird: no further conditions need to be met.
The classical view of definition is also a view of the nature of the categories to which the definition applies. To say that the definition of bird consists of the four properties above is, quite clearly, the same thing as saying that the category BIRD is also so constituted. Accordingly, this view is often referred to as the classical view of categorization, or, because of the figure credited with its proposal, the Aristotelian view of categorization. Classical or Aristotelian categories have the following two important characteristics:
• The conditions on their membership can be made explicit by specifying lists of necessary and sufficient conditions.
• As a result, their membership is determinate: whether or not something is a member of the category can easily be checked by seeing whether it fulfils the conditions.
QUESTION Try to develop a list of necessary and sufficient conditions for the following categories: sport, building, planet, book, animal, weapon and bodypart. What problems do you encounter?
