Probabilities As A Property Of The System

Halliday (1994: xxii):

Registerial Variation

Halliday & Matthiessen (1999: 563):

In addition, the ideation base is polysystemic in another sense: registerial variation. We have seen that such variation can be construed in terms of the probabilistic nature of the linguistic system, as variation in the probabilities associated with terms in systems. Seen in this light, a register is a particular probabilistic setting of the system; and the move from one register to another is a re-setting of these probabilities. What is globally the 'same' ideational semantic system can thus appear as a collection of different systems, as one moves along the cline of instantiation from potential to instance. As we noted above, the effect is quantitative; but it is also qualitative, in the sense that it provides different perspectives on experience within the same system.

The Significance Of Indeterminacy [3]

Halliday & Matthiessen (1999: 557):

But, thirdly, within the overall construction of experience, the diversity of spheres of social action is realised by variation in the line-up of semantic features — that is, by variation in register. The probabilities are reset; and in some cases one or two "critical systems" are strongly affected in this way, such that the local norm skews the system, or perhaps even reverses the skewing set up by the global norm. It is here that we find future taking over as the unmarked primary tense in weather forecasting. As we said above, we define register variation in just these terms, as the ongoing resetting of probabilities in the lexicogrammar, which then functions to construe the ongoing variation at the level of the social process.

The Significance Of Indeterminacy [2]

Halliday & Matthiessen (1999: 557):

Secondly, systems have varying probability profiles, so that (in terms of information theory) they carry differential loads of information: the skewer the probabilities of the terms in a system, the greater the redundancy that it carries — hence the less we need to attend to its unmarked state. For example: it has been found that, in an English clause, positive is about ten times as frequent as negative (Halliday & James, 1993). What this means is that we build in to our sense of a figure the presumption that something is or something happens, rather than that something is not or does not happen; extra work has to be done if a process is being construed as negative. The same applies to future tense, as we saw: extra grammatical energy is required to assign a figure to the future.

The Historical Significance Of Global Probabilities In The Grammar

Halliday & Matthiessen (1999: 555):

The significance of global probabilities in the grammar emerges in various ways, both historical and synchronic. Historical change in language is typically a quantitative process, in which probabilities in systems at every level are gradually nudged in one direction or another, now and again becoming categorical so that some systemic upheaval takes place. Each instantiation of a tense form, say, whenever someone is speaking or writing in English, minutely perturbs the probabilities of the system — because what we call "system" and "instance" are one and the same phenomenon, being observed from different depths in time. 

There are, of course, more catastrophic types of change: languages become creolised, creolised systems in turn become decreolised, or a language ceases to be spoken altogether. At the "instance" end, a single highly-valued instance may exert a disproportionate effect: quotations from the Bible and from Shakespeare are familiar triggers of this "Hamlet factor" in English (in media discourse today almost every change is a sea change, which goes into our folk taxonomy of types of change). 

But such qualitative effects take place against a background of microscopic quantitative pressures, the sort of nanosemiotic processes by which a language is ongoingly restructured as potential out of the innumerable instantial encounters of daily life — the "sheer weight of numbers", as we sometimes call it. 

And in the ontogenetic dimension of history, the growth and development of language in a human child, an analogous dialectic can be observed: highly valued instances of text (rhymes, favourite stories and the like) interact with the quantitative pressures of the talk going on around (the child's access to the global probabilities — note that children do not begin learning the grammar by sorting out functional variation!) to yield a meaning potential that is a reasonable copy of the probabilistic system shared among the community.

Register Variation Defined

Halliday & Matthiessen (1999: 554):

This illustrates one very powerful feature of a probabilistic system of this kind: that it accommodates systematic functional variation. We have discussed the two text types, weather forecasting and recipes, as examples of variation in register: of the way in which the meaning selections in texts tend to vary systematically with their contextual function — their value in the social process. We pointed out that this variation is seldom categorical: except in very closed registers, or "restricted languages", no major options are likely to be totally excluded. What happens is that the probabilities are reset. This may be a relatively minor skewing affecting a large number of semantic features; but one or other system may stand out by being particularly clearly realigned, as happens with tense and with mood, respectively, in our two examples. We can in fact define register variation as the resetting of probabilities in the lexicogrammatical and semantic systems, including those in the ideation base. We observe these probabilities in the form of frequencies in the text;

Systemic vs Registerial Probabilities

Halliday & Matthiessen (1999: 553-4):

What we are saying is that there is a global pattern of probabilities in English, including a probability profile of the tense system whereby the probability of future is (say) 0.1. The register of weather forecasting, however, sets up a local pattern in which the probability of future is (say) 0.5. This changes the meaning of the system of primary tense, because it reverses the marking and hence sets up a new relationship among the different terms. It construes a realm of experience in which the future becomes the familiar dimension of time, the point of reference by which both present and past are defined.

Text Frequencies Manifest System Probabilities

Halliday & Matthiessen (1999: 552-3):

We have sometimes referred to the relative frequency of a particular feature of the grammar. For instance, in our two examples of the meaning base as a resource in language processing, certain patterns characteristically recurred: future tense in the weather forecasts, imperative mood in the recipes. In each case this was a special feature pertaining to the register in question: in weather forecasts, the future tense is especially frequent relative to the other primary tenses.

To say this means that there is a general expectancy in English discourse that, again relative to the other primary tenses, future will occur less frequently than it does here. In other words, there is some global expectation, in the grammar of English, about the relative frequency of the different terms in the primary tense system, past, present and future. Similarly there is some global expectation about the relative frequency of imperative and indicative mood. Frequency in the text is to be interpreted, therefore, as the manifestation of underlying probability in the system.

Local Indeterminacies vs Global Indeterminacy

Halliday & Matthiessen (1999: 552):

Local indeterminacies of all these types are found in all regions of the content plane, either within one stratum or at the interface between one stratum and another (including of course puns, which are formed at the interface of content and expression). Some of them involve very general categories, and hence resonate across wide stretches of semantic space, like the transitive/ergative complementarity. We may call them "local", however, in contrast to one global form of indeterminacy which is a feature of the entire system of language, and probably of any evolved semiotic system, namely its probabilistic character.

The Evolution Of Language Involves Gradual Changes In Probabilities

Halliday & Matthiessen (2014: 73-4):

If we include probabilistic information in the description of the lexicogrammar, we also pave the way for interpreting the system as one that is always in the process of becoming, not one that is in a frozen state of being: the evolution of language involves gradual changes in probabilities, over long periods of time but also over much shorter periods.

The System Of Lexicogrammar Is Probabilistic In Nature

Halliday & Matthiessen (2014: 73):

Variation in lexicogrammar across varieties of English is, of course, not only qualitative but also quantitative; the system of lexicogrammar is probabilistic in nature, and probabilities vary across varieties of English – dialectal, codal and registerial varieties.

Grammatical Systems Are Probabilistic

Halliday & Matthiessen (2014: 52):

It is clear by this time that grammatical systems are probabilistic in nature: that, for example, the system of POLARITY in English has to be modelled not simply as ‘positive/negative’ but as ‘positive/negative with a certain probability attached’ (which has been found to be of the order of 0.9 : 0.1).

A Topological Perspective On Systemic Probability

Halliday & Matthiessen (1999: 68):

The types in the semantic system are instantiated according to probability values; these are manifested as relative frequencies in text. The equivalent in the spatial interpretation of meaning would be curvature or ‘chreodisation’. Chreodisation embodies time and represents the change of systemic probabilities over time.