[GR91], [Mar89], [MO89], and [Ros73a] have all argued that common nouns label objects similar across many inter-related and correlated properties. In contrast, dimensional adjectives label objects that are alike on only one property. This difference between nouns and adjectives has important conceptual consequences (see especially Markman, 1989). For example, knowing that an object is a bird allows predictions about many different properties of the object but knowing that an object is a member of the category WHITE-THINGS supports only predictions about the object's color.
This difference also has important implications for
similarity-based learning, as illustrated in
Figure 
.
This figure represents the extensions of idealized nouns and
adjectives as regions in a multidimensional space of all possible
objects.
The relevant spaces are hyperspaces of many dimensions, all of those
along which noun and adjective meanings vary,
but for ease of illustration we confine ourselves to three dimensions.
For example, the dimensions shown could represent SIZE,
SMOOTHNESS, and SHININESS.
Each of the outlined regions within the large cube represents a
hypothetical category associated with a single word, and
instances of the category would be points within the region.
As can be seen in the figure, categories organized by many
dimensional similarities (cubes with thick outlines)
are small and compactly shaped relative
to those that are organized by similarity on just one property.
Thus, the idealized noun is uniformly and closely bounded in all
directions.
It is a hypercube or hypersphere.
In contrast, members of
an adjective category are tightly constrained in only one
direction (the relevant dimension) but extend indefinitely in all
others. The idealized dimensional-adjective category thus may be
thought of as a ``hyperslab.'' Further, the volume of idealized noun
categories, compact in all dimensional directions, is relatively
small whereas the volume of adjective categories, extending
indefinitely in all directions but one, is great.
: Typical Noun and Adjective Categories. Only three
dimensions from the
set of dimensions distinguishing the categories are shown.
Noun categories appear in thick
outline, adjective categories in thin outline.
Given ordinary ideas about similarity and generalization,
these differences clearly favor nouns. The within-category
similarity is greater for the nouns than the adjectives in
Figure .
Further for nouns, generalization can be non-selective in all
directions but for adjectives generalization must be selectively
inhibited in one direction. Learning about adjectives but not
nouns thus requires discovering and selectively attending to one
relevant direction in the multi-dimensional space.
