SFL Is A Dimensional — Not Modular — Theory

Halliday & Webster (2009: 231):

In SFL language is described, or “modelled”, in terms of several dimensions, or parameters, which taken together define the “architecture” of language. These are 

• (i) the hierarchy of strata (context, semantics, lexicogrammar, phonology, phonetics; related by realisation); 
• (ii) the hierarchy of rank (e.g. clause, phrase/group, word, morpheme; related by composition); 
• (iii) the cline of instantiation (system to instance); 
• (iv) the cline of delicacy (least delicate to most delicate, or grossest to finest); 
• (v) the opposition of axis (paradigmatic and syntagmatic); 
• (vi) the organisation by metafunction (ideational (experiential, logical), interpersonal, textual).

The mistaken notion that SFL is a theory of "interacting modules" can be sourced to Martin (1992).

(1) Martin (1992: 390);

Each of the presentations of linguistic text forming resources considered above adopted a modular perspective. As far as English Text is concerned this has two main dimensions: stratification and, within strata, metafunction.

See critique here.

(2) Martin (1992: 391):

Within discourse semantics, the ways in which systems co-operate in the process of making text is much less well understood. … A more explicit account of this co-operation is clearly an urgent research goal; English Text has been concerned not so much with addressing this goal as with making it addressable by proposing four relatively independent discourse modules to beg the question [sic] … . The point is that integrating meanings deriving from different metafunctions is not a task that can be left to lexicogrammar alone.

See critique here.

(3) Martin (1992: 392):

The modularity imposed by stratification is also an important issue. Discourse systems generate structures which in principle cut across grammatical and phonological ones.

See critique here.

(4) Martin (1992: 488):

In this chapter a brief sketch of some of the ways in which discourse semantics interacts with lexicogrammar and phonology has been presented. The problem addressed is a fundamental concern of modular models of semiosis — namely, once modules are distinguished, how do they interface? What is the nature of the conversation among components?

See critique here.

(5) Martin (1992: 490-1):

Grammatical metaphor then is the meta-process behind a text. It co-ordinates the synoptic systems and dynamic processes that give rise to text. It is the technology that let's [sic] the modules harmonise. It is their medium, their catalyst, the groove of their symbiosis, their facilitator, their mediator. It is the re/source of texture.

See critique here.