Repeating A Bare Assertion That Assumes The Conclusion Of This Monograph

Martin (2013: 73):

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This is misleading, because it is untrue. As the examination of this chapter has demonstrated, Martin has not shown that metafunction and rank are based on axis — nor could he.

As previously explained, Martin misunderstands axis as system/structure relations, as stipulated in realisation statements. In SFL Theory, axis is a local dimension whose two orders are the paradigmatic and syntagmatic (Halliday & Matthiessen 2014: 32), with system and structure as their respective dimensions. Realisation statements are located on the paradigmatic axis, and as the name suggests, the relation between the axes is simply realisation.

Moreover, metafunction and rank are not based on either axis or system/structure relations. On the one hand, the metafunctions are a distinct global dimension from the local dimension of axis (ibid.), and first appeared in Language Structure and Language Function (Halliday 1970). 

On the other hand, the SFL approach to constituency, a rank scale, is a distinct local dimension  from the local dimension of axis (Halliday & Matthiessen 2014: 32), and derives from the method of ranked constituency analysis, rather than immediate constituency analysis, as first set out in Categories of A Theory of Grammar (Halliday 1961), and explained more fully in Introduction to Functional Grammar (Halliday 1985).

The rhetorical significance of Martin's misleading bare assertion (the ipse dixit fallacy) is that it assumes the conclusion (the petitio principii fallacy) of the entire monograph. That is, it is one logical fallacy serving another in an invalid argument for a false conclusion. In dialogue, the repeating of this bare assertion would be an example of the logical fallacy known as the argument from repetition.