It seems to me that transitivity and ideation (lexical relations) are complementary resources for realising register. They make different kinds of generalisations about experience that both need to be captured in text analysis to interpret what it’s saying. Ideational metaphor is a particular type that makes this complementarity obvious. What’s more, neither transitivity nor ideation define lexical items, just relations between them. Recognising the relations depends on intuitive recognition of the lexical items that instantiate them.
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[1] By 'ideation', Rose means the experiential discourse semantic system in Martin (1992); see the many critiques here. By 'register' Rose means the misconstrual of context as register in Martin (1992); see the many critiques here.
[2] As the critiques on Discourse Semantic Theory demonstrate, Martin's experiential discourse semantic system of ideation is a confusion of lexical cohesion (textual metafunction), lexis as most delicate grammar (delicacy) and logical relations between elements of clause structure (mostly misapplied). As the critiques also demonstrate, Martin's model also misconstrues some ideational semantics as field.
On his model, Martin (1992: 325) writes:
The level of discourse semantics is the least differentiated as far as ideational meaning is concerned. This is mainly due to the fact that the description developed here has focussed on relationships between experiential meanings, rather than the experiential meanings themselves.
A critique of this can be found at The Avoidance Of Experiential Semantics In Discourse Analysis.
[3] Martin (1992) misunderstands and misrecognises grammatical metaphor, interpreting it largely in terms of the transcategorisation of elements through nominalisation. Evidence here. Moreover, the discourse semantic systems of ideation (experiential) and conjunction (logical) don't provide the means of determining congruent realisations from metaphorical realisations of the semantics in the grammar. The system of conjunction is a confusion of textual (non-structural cohesion) and logical (structural) deployments of expansion relations, and largely misinterprets the expansion categories. Evidence here.
[4] In SFL theory, lexical items are the synthetic output of the most delicate grammar. That is, they are the output of increasingly more delicate subcategorisations of grammatical systems, such as process type and the rest. A phonological analogue of this is the phoneme /p/ being the synthetic output of features from the systems of phonation, place, manner: [voiceless], [bilabial], [stop].
[5] This misunderstanding arises from the confusion in Martin's (1992) experiential discourse system of ideation between lexical cohesive relations (hyponymy etc.) and lexis as most delicate grammar, both subsumed there under 'lexical relations'.
[6] This misunderstands the architecture of SFL theory. Defining is an identifying relation. Identifying relations obtain between different levels of abstraction, such between strata or between system and structure. On the other hand, the dimension of delicacy is structured by the attributive relation: i.e. class membership; more delicate features are members (carriers) of less delicate classes (attributes). Lexical items are the output of attributive relations, and the question of identifying (defining) relations is irrelevant.
[5] This misunderstanding arises from the confusion in Martin's (1992) experiential discourse system of ideation between lexical cohesive relations (hyponymy etc.) and lexis as most delicate grammar, both subsumed there under 'lexical relations'.
[6] This misunderstands the architecture of SFL theory. Defining is an identifying relation. Identifying relations obtain between different levels of abstraction, such between strata or between system and structure. On the other hand, the dimension of delicacy is structured by the attributive relation: i.e. class membership; more delicate features are members (carriers) of less delicate classes (attributes). Lexical items are the output of attributive relations, and the question of identifying (defining) relations is irrelevant.
[7] The claim here is that recognising the relations between lexical items depends on intuitive recognition of the lexical items that "instantiate" the relations between lexical items.
Again, this misunderstanding arises from the confusion in Martin's (1992) experiential discourse system of ideation between lexical cohesive relations and lexis as most delicate grammar. The relations of lexical cohesion — such as hyponymy, meronymy, synonymy and repetition — are mistaken for systemic relations between lexical items as the output of the most delicate grammatical systems.
Note, also, the illogicality of the claim that lexical items instantiate the relations between lexical items.
For Rose's misunderstanding and misuse of the notion of instantiation, see here.
Again, this misunderstanding arises from the confusion in Martin's (1992) experiential discourse system of ideation between lexical cohesive relations and lexis as most delicate grammar. The relations of lexical cohesion — such as hyponymy, meronymy, synonymy and repetition — are mistaken for systemic relations between lexical items as the output of the most delicate grammatical systems.
Note, also, the illogicality of the claim that lexical items instantiate the relations between lexical items.
For Rose's misunderstanding and misuse of the notion of instantiation, see here.