The principal kinds of structure so far investigated for grammar are multivariate constituency structures and univariate dependency structures. … Martin then establishes that there are relationships between elements at a discourse level which do not fit these categories developed for grammar. There appear to be at least two kinds of additional relationship, both heralded by the notion of cohesive ties: phoric relationships, where one element is ‘presumed’ by another, and expectant relationships, where two (or more) items are ‘mutually expectant’. The former is illustrated in reference chains such as a robot—the android—it—it—...; the latter in lexical strings such as manoeuvring— crossing—separated—tacking—veered—...[p364]. Both kinds are termed covariate (cf. Lemke, 1985), which distinguishes them as a group from the previously considered grammatical structural relationships. Most of the kinds of discourse structure discussed later in the book draw on covariate structures.
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[1] This is misleading. Of the multivariate structures, only those of the experiential metafunction are said to be based on constituency. Halliday & Matthiessen (2014: 451, 85):
… the relationships among the elements in a multivariate structure can be characterised as segmental from an experiential point of view but as prosodic from an interpersonal point of view and as culminative from a textual one.
[2] This is very misleading. Martin does not establish this, he merely asserts it — without defining what he means by structure. More importantly, the reason why these 'relationships between elements' do not fit the structure types developed for the grammar is that they are not structures. Martin relocates the non-structural resources of the textual metafunction, cohesion, from the grammatical stratum to the semantic stratum, rebrands them, and distributes them across the metafunctions. This results in theoretical inconsistencies in terms of structure, stratification and metafunction; see Inconsistencies In The Notion Of 'Discourse Semantic Structure'.
[3] This theoretical use of 'expectancy' can be found in Barthes (1966/1977: 101-4), but Martin uses it in his model of discourse semantics without acknowledging the source. At the symposium to honour the late Ruqaiya Hasan, Martin falsely accused Hasan of not acknowledging Mitchell as one of her sources (evidence here).
[4] Here Bateman uncritically accepts Martin's misinterpretation of cohesive reference, which confuses the referents with the resource for referring. This confusion leads to problems in distinguishing reference chains (Halliday & Hasan's grammatical reference) from lexical strings (Halliday & Hasan's lexical cohesion). See "One Apparently Unresolved Problem With Hasan's Technique" and The Problem Of Overlapping Lexical Strings And Reference Chains.
[5] Lemke (1988: 159) reinterprets his 'covariate structure' as a structuring principle, rather than a kind of structure:
My own 'covariate structure' (Lemke 1985), which includes Halliday's univariate type, is for the case of homogeneous relations of co-classed units, and should perhaps be called a 'structuring principle' rather than a kind of structure.
Martin includes Lemke (1988) in his list of references (1992: 603).
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