Martin (2013: 1):
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[1] To be clear, in SFL Theory, axis is not equivalent to axial or system-structure relations. Axis is theorised as a local dimension of language with two orders, paradigmatic and syntagmatic, with system as the dimension of paradigmatic order, and structure as the dimension of syntagmatic order. Halliday & Matthiessen (2014: 32, 20):
The relation between the two orders, and their dimensions, is realisation: the intensive identifying relation that obtains between two levels of symbolic abstraction. That is, structure (Token) realises system (Value).
That is to say, the dimension of axis is logically distinct from the relation that obtains between its two orders and their dimensions.
This fundamental misunderstanding is the basis of Martin's "axial relations" in this publication.
[2] To be clear, in SFL Theory, systems are not motivated by structures. This is the opposite perspective to that taken in SFL Theory. In SFL Theory, priority is given to the view 'from above', system, whereas Martin's notion that structure motivates system gives priority to the view 'from below', structure. Halliday (2003 [1994]: 433-4):
In systemic theory the system takes priority; the most abstract representation at any level is in paradigmatic terms. Syntagmatic organisation is interpreted as the "realisation" of paradigmatic features. This step was taken by Halliday in the early 1960s so that grammatical and phonological representations could be freed from constraints of structure. Once such representations were no longer localised, they could function prosodically wherever appropriate.
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