Aristotelian theory of concepts state that a concept must be defined in terms of certain necessary and sufficient conditions, failing which it is not a concept. However such a notion of concept does not seem to agree with our present understanding. For one, concepts do not seem to have sharp boundaries as implied by Aristotelian theory. Also their domain of applicability is more or less vague.
Thus, with growing dissatisfaction with the classical theory of concepts, an alternative theory was put forth in cognitive psychology. This theory was called Prototype Theory and its main proponent was Eleanor Rosch. The main idea is that of a category of objects some members are judged to be more representative of the category than the others. For Eg. a Robin is more representative of the category Bird than a Penguin. The most representative members of a category are called prototypical members. Thus, now there is no more binary, but a graded membership of classes. Each member does not have equal status as category members.
A conceptual space consists of a number of quality dimensions. Quality dimensions include color, pitch, temperature, weight, and the three spatial dimensions. Time is a one-dimensional structure which we conceive of as being isomorphic to the line of real numbers. Similarly, Weight is one-dimensional with a zero point, isomorphic to the half-line of non-negative numbers. Some quality dimensions have a discrete structure, they divide objects into classes, e.g., the sex of an individual.
The cognitive representation of colors can be described by three dimensions. The first dimension is hue, which is represented by the color circle. The second dimension of color is saturation, which ranges from gray (zero color intensity) to increasingly greater intensities. The third dimension is brightness which varies from white to black. Together, these three dimensions, one with circular structure and two with linear, make up the color space which is a subspace of our perceptual conceptual space.
In more abstract terms, a conceptual space S consists of a class D1, ... Dn of quality dimensions. A point in S is represented by a vector v = (v1,v2,...,vn) with one index for each dimension. Each of the dimensions is endowed with a certain topological structure.
A natural property is a convex region of a conceptual space, i.e. if some objects which are located at v1 and v2 in relation to some quality dimension, are examples of the property P, then any object that is located between v1 and v2 will also be an example of P.
If some object o1 is described by the color term C in a given language and another object o2 is also said to have color C, then any object o3 with a color that lies between the color of o1 and that of o2 will also be described by the color term C.
Thus, we can see how this fits nicely with the Prototype theory. In a convex region one can describe positions as being more or less central. For example, if color properties are identified with convex subsets of the color space, the central points of these regions would be the most prototypical examples
of the color.
Deese conducted a series of experiments on Word Intrusions in free recall of word lists. In the experiment word lists were given to subjects to memorize and then recall. In such experiments often an 'intruder' word used to come up in recall which was not present on the list. It was seen that the most likely intruder was the word which had maximum average association frequency with the words on the word list.
