I think this is an important question... 'post-Deictic' is actually functionally defined in IFG p373a second Deictic element in the nominal group, one which adds further to the identification of the subset in questionMore specifically...The post-Deictic identifies a subset of the class of ‘thing’ by referring to its fame or familiarity, its status in the text, or its similarity/dissimilarity to some other designated subset.Examples follow, illustrating these identifying functions. But then...Also found in the post-Deictic position in the nominal group are words expressing the speaker’s attitudeExamples follow that have no identifying function. They actually evaluate the Numerative+Thing...the splendid three Pyramidsthose miserable two miles of asphalt and concrete.a lousy two weeks in New Jerseyan impressive 30 or 60 minutes of high-quality recordings.a disappointing 9,000 copies.With this in mind, here are the preceding examples of ‘non-attitudinal’ post-Deictics. Some are clearly identifying...this same containerthe whole four hoursthe only right wayOthers are evaluating, and less obviously identifying...the necessary first stepthe possible rolethe customary grisly inhabitants of TartarusA typical elution curveEpithets can also have an identifying function...if I say the long train, the specific Deictic the indicates that you can tell, and that the necessary information is contained in the experiential Epithet long. This particular train, in other words, is defined by its length [p376]The functional difference between post-Deictics and Epithets seems fuzzy...The words occurring as post-Deictic are adjectives, and may also occur in the function of Epithet but with a different sense. This different sense is not defined.This seems like a potentially fruitful area for further research.
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At this point, Rose has finally given up disputing CLÉiRIGh's analysis of the aforementioned instances of 'mere' functioning as post-Deictics, and switched to questioning the theoretical status of 'post-Deictic'.
[1] To be clear, as Halliday & Matthiessen (2014: 373) explicitly states: the function of the post-Deictic is to identify the subset of the class of Thing, and this is the case in all the examples they provide and which Rose quotes. Here Rose has misunderstood this use of the word 'identification' to mean Martin's discourse semantic system of IDENTIFICATION, which is itself a misunderstanding of grammatical reference (Halliday & Hasan 1976).
[2] This is misleading, because it is not true. The different sense of an adjective functioning as post-Deictic vs Epithet is explained as the different function of post-Deictic vs Epithet. The function of the post-Deictic was quoted by Rose from Halliday & Matthiessen (2014: 373):
The post-Deictic identifies a subset of the class of ‘thing’ by referring to its fame or familiarity, its status in the text, or its similarity/dissimilarity to some other designated subset.
The function of the Epithet, on the other hand, is clearly distinct from that of the post-Deictic. Halliday & Matthiessen (2014: 376):
The Epithet indicates some quality of the subset, e.g. old, long, blue, fast; since qualities are denoted by adjectives, Epithets are often realised by adjectives. … (i) The quality of the subset may be an objective property of the thing itself, construed as a depiction of the experience of the entity that it represents; or (ii) it may be an expression of the speaker’s subjective attitude towards it … . We refer to these as (i) experiential Epithets and (ii) interpersonal, or attitudinal, Epithets, respectively. … The principal difference is that experiential Epithets are potentially defining, whereas interpersonal ones are not.
[3] To be clear, adequate research has been done — just not by Rose.
