Misunderstanding Redundancy And Structure

Martin (2013: 40):

Technically speaking, as noted above, a sequence of classes redounding with one another is referred to as a syntagm. Redounding functions are referred to as structures. … By 'redound' we mean that the classes of functions are redundant with respect to one another — in other words they are mutually expectant (given one class or function the co-appearance of another is not random). This is simply a more technical way to say that the classes form a syntagm or that the functions form a structure and so make a meaning beyond the sum of their parts.

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[1] This misunderstands the notion of redundancy. To be clear, 'redundancy' refers to the skewing of probabilities away from equiprobability. Halliday (2003 [1987]: 122):

In an ideal system, one having two states that are equiprobable, there is no redundancy. Once we depart from equiprobability, redundancy sets in. In all open systems the probabilities are skewed, so that the system carries redundancy.

In SFL Theory, 'redundancy' is used to refer to realisation relations between strata. Halliday (2002 [1992]: 356):

Consider a minimal semiotic system, such as a protolanguage – a system that is made up of simple signs. This is based on the principle of redundancy. When we say that contents p, q, r are “realised” respectively by expressions a, b, c, what this means is that there is a redundancy relation between them: given meaning p, we can predict sound or gesture a, and given sound or gesture a we can predict meaning p. This relationship is symmetrical; “redounds with” is equivalent both to “realises” and to “is realised by”.

with these probabilities variably skewed along the cline of instantiation. Halliday (2002 [1992]: 359):

The [language] system is permeable because each instance redounds with the context of situation, and so perturbs the system in interaction with the environment.

Halliday (2003 [1997]: 260):

If we consider register variation first: viewing from the "instance" end, we can recognise a text type as a collection of similar instances. But when we shift perspective and see it as systemic variation, each of these text types appears as a register, a kind of subsystem which redounds with the properties of the context in terms of field, tenor and mode.

Martin, however, misunderstands the skewed probabilities of redundancy as just any mutual expectancy, and applies this to the sequencing of items on the syntagmatic axis.

[2] As demonstrated above, redundancy is not a more technical way of saying that syntagms and structures "make a meaning beyond the sum of their parts". The crucial point that Martin omits is that, just as a system is the relationships among its features, a structure is the relationships among its functions. Halliday & Matthiessen (2014: 451):

Note that, although it is the functions that are labelled, the structure actually consists of the relationships among them.