Relations, categories and constructs

In relatively coarse terms, linguistic structure is defined in terms of paradigmatic relations, i.e. relations of similarity which define classes of linguistic objects, and syntagmatic relations, i.e. relations which join the parts of complex linguistic objects, constructs.

Paradigmatic and syntagmatic relations are often described in introductory linguistics textbooks as `horizontal' and `vertical' dimensions of language structure. This is a misleading metaphor based on conventions of writing European languages (i.e. `horizontally' along lines of a page); for Chinese students, the metaphor should no doubt be reversed. More helpful is the characterisation of paradigmatic relations as relations of substitutability: whatever objects can be substituted for each other within a complex object without changing the type of complex object are in a paradigmatic relation to each other.

The most general, and as experience shows, the most easily understood definitions are those given above. In more detail:

Paradigmatic relation:

A relation of pairwise similarity between linguistic objects, at a level of linguistic analysis (word, sentence, text structure), and based on any the four basic properties of linguistic objects as signs:

INTERPRETIVE DIMENSION : MEANING - SIGN - SURFACE | PARTS

The similarities which define paradigmatic relations may consequently be based on SURFACE form, on MEANING, on similarity of PARTS, or on similarity of distribution in CONTEXT. However, in many introductory textbooks paradigmatic relations are restricted to similarities which define substitutability in CONTEXT.

Similarities may be more or less general or specific; objects which share many properties are more similar, and more highly specified, than those which share few properties. A similarity hierarchy of increasing or decreasing specificity is a taxonomy, which may be expressed in terms of inclusion of sets, elementhood in sets, implications. In `knowledge bases' developed in Artificial Intelligence, these implication relations are often calles `ISA' relations (e.g. cow ISA ruminant, `A cow is a ruminant').

Syntagmatic relation:

A relation linking parts of a complex linguistic object into a construct, a more complex object. A syntagmatic relation may hold between parts and the whole, or between parts and other parts. The CONSTRUCTIVE DIMENSION of a sign is specified in terms of syntagmatic relations: either the syntagmatic relations into which an object enters with its CONTEXT in defining larger units, or the syntagmatic relations in terms of which it is constituted by its own PARTS.

Interpretive relation:] A relation linking a sign at a given level of linguistic analysis to a representation of its SURFACE form in acoustic or visual terms and to a representation of the MEANING in terms of the situation of use. For complex objects such as sentences, interpretations are compositional:

1. The SURFACE form (whether PHON, phonetic representation, or ORTH, orthographic representation) of a complex linguistic object is a function of the SURFACE form of its parts. For example, the pronunciation of a sentence is a function of the pronunciation of its parts concatenated with each other in time, and the spelling of a sentence is a function of the spellings of its parts, concatenated with each other in space.
2. The MEANING of a complex linguistic object is a function of the MEANING of its parts. For example, the meaning of a sentence is a function of the meanings of its parts.

In general terms, for x = y z, where is some compositional operator (one could read: `syntagmatic relation'):

PROPERTY(x) = f(PROPERTY(y), PROPERTY(z))

This principle is called the principle of compositionality or Frege's Principle.