Adjectives: A Uniform Semantic Approach - University of Windsor

334 N. Abdullah and R.A. Frost
3 Our Approach
Some authors (e.g. Strawson, see [2], and Jespersen, see [15]) argue that common
nouns and adjectives are ontologically different. We believe that representing
common nouns on a par with adjectives is “forcing” a behaviour on adjectives that is
not in their nature. This behaviour manifests itself in the intersection failure of sets
representing adjectives and sets representing common nouns, which leads to the
conclusion that adjectives must be of complex nature.
We argue that it is possible to represent all adjectives as sets, and yet capture their
idiosyncrasies. This can be done by considering sets representing adjectives as having
typed objects as their members. A schema for an adjective-representing set may look
like the following:
Set_name ={member: type1}: type2
(1)
where type1 is a non-property type and type2 a property type
For example, clever pet, clever man, and clever police dog in the sentences John is
a clever man, Fido is a clever pet, and Fido is a clever police dog can be represented
as follows:
Clever={j: human, f: pet, f: policedog}: clever
where j =|| John|| 5 , and || f = Fido||
This representation of the adjective ‘clever’ captures the intuition that although j
and f are members of the set Clever, both are clever in their own way. John is clever
as a man 6 while Fido is clever as a dog. What they have in common is “cleverness”.
This is reflected by ascribing the type “clever” to the set containing them.
This representation of adjectives makes it possible for an object to have more than
one occurrence in adjective-representing sets, as done with “f: pet” and “f: policedog”
in the set Clever.
Common nouns may have the following representation schema:
Set_name ={member: type}: type
(2)
where type is a non-property type
The representation of (2) is different from that of (1) in that the members’ type is
the same as the set’s type. The representation of (2) serves two purposes: 1) it makes
the internal structure of common nouns similar to that of adjectives (i.e. “member:
type” pattern); and, 2) it eliminates the co-extension problem. Regarding the latter
point, if for example, as is the case in the actual world, the set of cordate contains the
same elements as those in the set of renate (see, definition of set equality, below) the
two sets are not equal. Hence, they do not mean the same thing.
3.1 Equality in Typed Sets
Since sets now contain typed elements, set operations must take the type of set
members into consideration. This can easily be accommodated as follows:
5
The symbols “|| ||” represent the interpretation function.
6
The correct type for the intersective reading for ‘clever’ is “T”, as explained in the next
section.