Rather than a ‘semantic system of modality’, Martin & Matthiessen 1991 explain such motifs as topologies, or ‘fractal principles’ that recur across ranks and strata. They are generalisations of types of meanings that complement the typological generalisations of systems. Crucially they are not more abstract than the systems they generalise across. So does postulating a ‘semantic system of modality’ above the grammatical systems of modality, confuse abstraction with generalisation?
In any case these ‘semantic systems’ were not proposed in IFG1/2 but have been added to IFG3/4.
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[1] This is misleading, because it is untrue. Martin & Matthiessen (1991) are concerned with the semantic system of modality and the diverse ways it is realised in lexicogrammar. Martin & Matthiessen (1991: 376):
With MODALISATION, POLARITY in propositions is used to bound the semantic space under consideration, with degree of usuality and probabilily defining parameters between 'it is' (yes) and 'it isn't' (no). Similarly, obligation and inclination are used as parameters grading the semantic space in proposals between 'do' and 'don't'.
[2] This is misleading. Martin & Matthiessen (1991) don't explain 'such motifs' as topologies. The paper contrasts two perspectives in modelling: the typological and topological.
[3] This is misleading. The one instance of the word 'fractal' (p376) refers only to the system of EXPANSION.
[4] This is misleading, because it is untrue. With regard to expansion, Martin & Matthiessen (1991: 375) write:
All we can do at present is posit a generalised system that we 'abstract' from the specific grammatical environments in which it is manifested.
To be clear, logically, for there to be congruent and metaphorical grammatical realisations of MODALITY, MODALITY must be a more abstract system at the level of semantics that is realised in lexicogrammar, since congruent vs metaphorical relations obtain between strata.
[5] No. The confusion here is entirely Rose's. See [4].
[6] This is still misleading, because it is still untrue. Halliday (1994: 356):
The reason this area of the semantic system is so highly elaborated metaphorically is to be found in the nature of modality itself … Modality refers to the area of meaning that lies between yes and no – the intermediate ground between positive and negative polarity.
