Formal Semantics: The Model Theoretic Approach To Meaning

Halliday & Matthiessen (1999: 422):

The model theoretic approach to meaning is a transcendent one: meanings are located in the world outside of language. This is seen as a strength by the proponents of the model theoretic approach. Dowty et al (1981) criticise various other theories of meaning for ignoring the "inherent aboutness of language", its relationship to the real world:

Any theory which ignores this central property, it is argued, cannot be an adequate theory of natural language. Examples would be theories which, in effect, give the meaning of a sentence by translating it into another language, such as a system of semantic markers or some son of formal logic, where this language is not further interpreted by specifying its connection to the world. The approach of Katz and his coworkers seems to be of this sort (Katz and Fodor, 1963; Katz & Postal, 1964), as is that of Jackendoff (1972) and of the framework of Generative Semantics (Lakoff, 1972; McCawley, 1973; Postal, 1970).

Formal Semantics: Meaning As Extensional And Intensional

Halliday & Matthiessen (1999: 422):

In modelling meaning, formal semantics models it as both extensional and intensional: extensional meaning is cast in terms of sets of entities in a model of some world, and intensional meaning is the relation between a linguistic expression and its extension in any possible world. Formal semantics has thus been concerned with how semantic representations can be related to some extra-linguistic world model. Dowty et al (1981: 5) emphasise the relationship between language and the world in their introductory characterisation of truth conditional semantics:

"... truth conditional semantics, in contrast to other approaches mentioned [including Katz & Fodor, Jackendoff, and generative semantics, MAKH & CM], is based squarely on the assumption that the proper business of semantics is to specify how language connects with the world — in other words, to explicate the inherent "aboutness" of language."

This is, of course, an ideational orientation: the focus here is on representational meaning only. One central method has been to build models of the world in set theoretic terms, and to relate these to linguistic expressions — the model theoretic approach.

The Semantic Focus Of The Logico-Philosophical vs Rhetorical-Ethnographic Orientations

Halliday & Matthiessen (1999: 417-8):

…we can note that the two orientations differ in what kind of semantic organisation they focus on. 

In the logico-philosophical orientation scholars have focussed on syntagmatic organisation: they have been concerned with semantic structure — including principles relating to structure such as those of compositionality and semantic decomposition. For example, in their analysis of the senses of "words", they have tended to analyse these as being composed of semantic components, semantic markers, semantic primitives or the like (following Katz & Fodor, 1963, in the generative tradition). 

In the rhetorical-ethnographic orientation scholars have focussed on both paradigmatic and syntagmatic organisation, often foregrounding the paradigmatic: they have been concerned with the semantic system, with the meaning potential — including principles of taxonomy and the metafunctional simultaneity of systems. For example, scholars in "ethnoscience" have studied folk taxonomies of animals, plants, diseases and the like; and systemic-functional scholars have tried to map out semantic systems such as those of speech function and conjunction. Another example is our own work on the ideation base presented here.