To understand fully what is at stake here, we must recognise the fact that linguists employ two main metaphors for thinking about the levels of language. In the longer established metaphor, the more abstract phenomena such as 'meanings' of various types are regarded as 'higher', and the more concrete phenomena, such as the spoken and written forms of language, are thought of as 'lower'. But in the metaphor implied in the use of Hockett's terms "deep structure" and "surface structure" (as later taken over by Chomsky and others) this model is inverted. In this metaphor, the extension of the model of syntax to take account of 'semantics' involves the addition of a 'deep' or 'underlying' representation, this being seen as the 'level' within syntax that is nearest to meaning. In other words, in choosing to give "Some notes on 'deep' grammar" the title he did, Halliday was adopting the terminology of the then dominant theoretical model of language. In contrast, he had presented in "Categories" a diagram in which the relationships are horizontal, in which "context" is on the left, "form" is in the middle" and "substance" is on the right. After Halliday (1966/76), however, he quickly moved to the use of the model of language in which 'context' and 'meaning' are higher than 'form' and in which 'substance' is lower. It seems that he was influenced in this — at least in part — by the way in which the relationships between the strata of language are represented in Lamb's Stratificational Grammar (from which Halliday took the word "realisation" for its use in denoting the relationship between levels). So in Halliday (1977/78:128), for example, we find a model in which 'meaning' is above 'form' and 'phonetics' is below.
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[1] Here Fawcett misleads by contrasting 'meaning' with 'spoken and written forms of language' instead of 'form'. In Fawcett's own model, it is meaning that is the higher level of abstraction, and form that is the "more concrete". Spoken and written forms of language, on the other hand, are language — i.e. all strata — that vary at points along the cline of instantiation, according to the contextual feature of mode.
[2] In terms of present-day SFL theory, Fawcett here confuses the dimension of symbolic abstraction ("more abstract" vs "more concrete"), in this case: stratification, with the dimension of instantiation ("deep" vs "surface"). The "inversion" is not of the stratification hierarchy, but in the representation of the cline of instantiation, where "deep" (potential) is schematised above "surface" (instance).
[3] Here Fawcett tries to make sense of his confusion by locating potential ("deep or underlying") as a higher level of symbolic abstraction within his level of form ("the level within syntax that is nearest to meaning"). In terms of Fawcett's own model (Figure 4), "deep or underlying" at the level of form actually corresponds to his bottom-left module, the intersection of potential and form: realisation rules/statements.
[4] This is misleading because it misrepresents Halliday. Halliday (1966) is concerned with arguing for the system as the underlying form of representation ('deep grammar'). The deep vs surface distinction in this early paper is not the stratification of levels of abstraction.
[5] This is misleading because it implies that Halliday (1966) is a reworking of the stratification hierarchy in Halliday (1961). Trivially, but unsurprisingly, the diagram in Halliday (1961) is laid out in the opposite way to Fawcett's description, as shown below:
[6] This confuses the orientation of diagrams (theoretical expression) with levels of symbolic abstraction (theoretical content).
[7] The theoretical advantage of the term 'realisation' is that it explicitly identifies the relation between strata as an identifying: intensive: symbolic between a lower Token and a higher Value. This is a case of turning the theory back onto itself.
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