Polarity & Modality As Pre-Metafunctional

Halliday (2008: 180n):

polarity is as it were pre-metafunctional: it develops (and probably evolved) prior to the distinction between ideational and interpersonal meanings. (Rather in the same way that, in the physical world, positively and negatively charged particles seem to be prior to the distinction between matter and information!) It may be that the “energy levels” of  modality (high / median / low) are also of this kind: both modality and polarity are regularly grammaticalised in combination with other features.

Protolanguage, Appraisal & Grammaticalisation

Halliday (2008: 179-80):

In terms of children’s early language development, the interpersonal metafunction provides the prototype of how meanings come to be grammaticalised. The two systems that were first grammaticalised by one small child (Nigel, aged 0;10) were:

polarity: positive / negative 
modality: value: low / high

followed shortly by the two forms of “appreciation” in conjunction with the feature “positive”:

appreciation (positive): impact (“that’s interesting”) / quality (“that tastes nice”)

Note that these were not yet mother tongue; they were protolanguage, realised by sounds and gestures. But they were systemic, or at least proto-systemic; and they provided the model for the linguistic systems of appraisal, where each lexical item realises the intersection of an appraisal feature with polarity and/or modality.

Appraisal: Attitude

Halliday (2008: 179):

This is a grammatical system that is realised by a selection of lexical items. Each such item is uniquely identified as a set of intersecting grammatical features; eg complicated is

appraisal: attitude: appreciation: composition: ( complexity : complex /  polarity: negative …)

as well as other general grammatical features (e.g. as distinct from confusing, which is “effective”, as in it confuses me, complicated is “descriptive”).  Note that I am interpreting the feature "undesirable" (the "snarl" member of the "purr/snarl" opposition) as negative in the environment of the interpersonal.

Lexical Items

Halliday (2008: 174, 180):

Lexical items, by contrast, form open sets; they are particular to certain domains, but open-ended and not so mutually defining: you can add a new lexical item to a set without perturbing the other members, whereas with a closed system if any term is added or taken away all the others move around. In other words, grammar and lexis are different manifestations of the principle of choice in a semiotic system. … 

each [lexical item] is the intersection of a number of component features, and such features can be networked — they are systemic.

Grammar: The Properties Of A Closed System

Halliday (2008: 174):

The notion of grammaticalisation depends on the notion of a closed system. This has the properties:

1. a small fixed set of possibilities, x/y/z…, which are
2. mutually exclusive, x = “not y or z”, and
3. strictly proportional, x : y : z, is constant, with
4. a defined condition of entry, eg nominal group, and
5. generalised to a large domain of application, eg every major clause

The Three Types Of Complementarity

Halliday (2008: 169):

The complementarity of grammar and lexis brings all of reality into focus, from the most general and all-pervasive kinds of phenomena to the most local, transitory and particular. The complementarity of system and text builds up a massive and open-ended meaning potential from countless small occasions of language use. The complementarity of speaking and writing allows for alternating between different semiotic states in resonance with the different contexts in which language functions. All of these complementarities are what lie behind the awesome power of human language.

Writing Creates Semiotic Stability

Halliday (2008: 168):

Thus the complementarity of speaking and writing is not a case of reciprocity. They do different things; not the same thing in different ways. Writing is secondary, derived; because of this it reaches a higher level of abstraction, creating through semantic junction a kind of semiotic stability, both ideational and interpersonal. Ideationally, it raises the commonsense theory of experience on to a more abstract and explanatory plane; so proverbs are replaced by axioms and equations as repositories of human knowledge. Interpersonally, it creates distance, and interaction among strangers: virtual interaction, as well as virtual dialogue brought about by projection. So writing is at one and the same time both more constraining and more enabling than speaking; and the fullest semiotic potential of the human brain, as we have inherited it, requires both.

Spoken Vs Written Language: Interpersonal Differences

Halliday (2008: 168):

Interpersonally, speaking is a two-way semiotic process, an ongoing exchange of meanings among different speakers; and analogously, spoken language is constantly shifting its deictic base, and alternating among the range of different speech functions. Writing is a one-way process (or was, until the coming of e-mail and then texting); and analogously, written language is largely invariant in mood and has a stable deictic base. While itself it is monologic, it can be turned into “virtual dialogue” by projection — which is another instance of semantic junction.

Written Sentence As Semantic Junction

Halliday (2008: 167-8):

So the written language tends to be configurational in its grammar: it displays the classic “constituent structure” on which formal linguistic categories are modelled — again, like writing itself; while the spoken language is organised like speech, with experience modelled as a flow of events where entities — persons and objects — are given value by their rôles as participants in these events. And since writing is, both as it evolved in the species and as it is developed by each individual, subsequent to and derived from speaking, the written sentence is itself a semantic junction — between its original state of being as a “flow of meaning”, in the spoken mode, and its adopted state of being as inscription, or documentation, in the written.

The Semantic Junction Of Ideational Metaphor: Semiotic Analogues

Halliday (2008: 167):

Those nominalised processes and qualities, which are semantic junctions of the core meaning of their original categories, as verb or adjective, with the core meaning of their adopted category as a noun, are the semiotic analogue of a written clause or sentence, which is a flow of meaning that has been frozen into a text; and the verbalised relators, likewise a semantic junction of their original category as conjunction with the core meaning of their adopted category as a verb, are analogous to the punctuation devices that link one written chunk with another.

The Evolution Of The Written Language

Halliday (2008: 167):

So the written language has always tended to make the world look like itself: stable, solid, dense, with recognisable chunks that may get built into substantial and complex structures. This was highly functional at the birth of experimental science, where the world needed to be held still so that it could be observed, measured and reasoned about.

The Evolution Of Written Languages

Halliday (2008: 166):

Written languages evolved to their present state in the “modern” period beginning with the European “renaissance”; but they were already launched along that journey in the ancient written cultures of Greece and Rome, India and China. The science and technology of the ancient world already needed virtual entities to think with, elements like motion and heat and distance and sum and addition which are the supports of the primary phase of our modern education. The more highly theorised learning of the renaissance took this metaphoric strategy one step further, constructing complex syndromes of virtual entities, virtual qualities and classes and virtual processes to achieve the “favourite clause type” of scientific writing — and now of many other kinds of writing besides the scientific.