Expanding our terms a little, the axial relation is abbreviated as system/structure, but is actually features/structures in systems. Systemic contrasts are simultaneously between features and the structures that realise them. Structures are more precisely function structures. Their functions are either interpersonal, ideational or textual (at least at higher ranks). They are realised by syntagms (or syntagmatic structures). In a metafunctional semiotic, syntagms must be able to realise multiple functions at once (eg nom gps realising Theme/Subject/Actor). This seems basic to semiotic organisation??
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[1] This is misleading because it is untrue. The axial relation — the relation between the paradigmatic and syntagmatic orders of axis — is realisation. System is the dimension of the paradigmatic order, and structure is the dimension of the syntagmatic order. Halliday & Matthiessen (2014: 20, 32):
[2] This is misleading because it is untrue. On the one hand, there are no structures in systems, since these are each different dimensions of different orders of axis. On the other hand, the axial relation, realisation, does not obtain between features and structures; for example, the clause feature [existential] entails the realisation statement 'insert Existent' (Halliday & Matthiessen 2014: 355), which is the specification of a participant, not of the structure in which the participant figures.
[3] This is misleading, because it is untrue. For example, a systemic contrast between features, such as [positive] vs [negative] POLARITY is not realised by a systemic contrast in (agnate) structures, since both are realised by the same structure, e.g. Subject^Finite^Predicator.
[4] This is misleading because it is untrue. A syntagm is a sequence of classes, whereas a structure is a configuration of functions. (Halliday & Matthiessen 2014: 60):
Such a sequence of classes is called a syntagm (e.g. Halliday, 1966a). However, this tells us very little about how it is organised or what it means. The significance of such a syntagm is that here it is the realisation of a structure: an organic configuration of elements, which we can analyse in functional terms.
