Linguistics Encyclopedia.pdf

Categorial grammar
The term categorial grammar was coined by Bar-Hillel (see Bar-Hillel, 1970, p. 372) to
refer to a method of grammatical analysis initially developed by the Polish logicians
Leśniewski and Ajdukiewicz (see Leśniewski, 1929; Ajdukiewicz, 1935; English
translation in McCall, 1967, pp. 207–31) on the basis on Husserl’s (1900/1913–21) ‘pure
grammar’, a universal, rationalist (see RATIONALIST LINGUISTICS) grammar
specifying the laws governing the combination of meaningful elements of languages.
According to Husserl, a sentence’s meaningfulness depends on the possibility of
seeing the sentence as an instance of the sentence form This S is p, where S is a meaning
category standing for a’nominal matter’ and p is a meaning category standing for an
‘adjectival matter’. The pure grammar has to do three things: (1) it must assign meaning
categories to linguistic expressions on the basis of substitutability; (2) it must specify
which combinations of meaning categories are possible; and (3) it must state the laws that
govern the combination of meaning categories.
This outline system was formalized by Ajdukiewicz (1935), who postulates two basic
categories, ‘sentence’ (s) and ‘name’ (n), and the notion of functor for derived
categories. A functor is an incomplete sign which needs to be completed by variables.
For instance, in the sentence Caesar conquered Gaul (Frege, 1891), conquered is a
functor which is incomplete until complemented by the arguments, the names Caesar and
Gaul. Together, functor and name(s) yield the value, ‘sentence’ (s). The functor is the
linguistic sign for a function in the mathematical sense, e.g. the function of squaring, ( ) 2 ,
not in the sense in which the term is used in, for instance, functional grammar (see
FUNCTIONAL GRAMMAR). It is not, however, confined to mathematical entities
(Reichl, 1982, p. 46):
The cataloguing rules of a library could also be considered a function.
Here we have as the domain of the function the set of books and as range
the set of sigla; to every book of the library as ‘argument’ the rule assigns
a ‘value’, its shelfmark.
In being built on the mathematical notion of the function, categorial grammars differ
crucially from phrase-structure grammars (Bach, 1988, p. 23): ‘What corresponds in a
categorial system to transformational kinds of rules in other theories are the operations
that compose functions and change categories.’
In natural language, all the arguments for a function (a predicate expression) which
yield a true sentence when combined with it are the linguistic expressions for the
extension of the predicate. So the extension of squints is the class of squinting things.
But when the function squints is applied to the names of individuals in the domain of
discourse, some false sentences will also be generated, namely when a named individual
to which the function is applied does not, in fact, squint. So the extension of squints