Yaegan Doran On The Metafunctions In Mathematical And Chemical Symbolism

Yaegan Doran wrote to Sysfling on 25 August 2023 at 7:09:

… we should be wary of metafunctions being considered a basic theoretical parameter for the description of semiotic resources in general.

A basic argument I put in a paper once was:

‘If we take metafunctionality to be the one of the broadest means by which these traditions [SFL/Social Semiotics] conceptualize the intrinsic functionality of semiotic resources, by simply assuming metafunctions across semiosis, we run the risk of homogenizing descriptions and making everything look like the first resource to be comprehensively described (i.e. English). That is, we risk watering down the specific functionality of each resource.’

Rather, following people working in language description at the time, I tried to tease these issues out for mathematical symbolism in the attached paper (and in more detail in my 2018 book Discourse of Physics), by attempting to ‘derive’ metafunctionality from axis (following Martin’s 2013 book on axis). Maths, I figured (with years of excellent help from many), would prove a useful point of contrast to language by virtue of regular common-sense comparisons that considered it to ‘be’ language/a language. But despite its comparability to language, I could find no evidence in the internal systemic/structural organisation of mathematical symbolism for an interpersonal component, and it was really pushing it to interpret an experiential component. But I tried to suggest that there was a major component comparable to the logical in language and a smaller independent one comparable to the textual. Nonetheless, I do think it much closer to language in this regard than most other resources, and so if even it struggles to fill out the full metafunctional complement, we should not assume it across the board (though metafunction is of course still a useful way in for analysis/application that is less concerned with descriptive/theoretical development – which I also tried to emphasise in the attached paper).

Along similar lines, Yu Zhigang followed this up by looking at the range of symbolism used in chemistry and concluded similarly – that the logical dominated, that there was little evidence for an interpersonal, that there was an even smaller textual component than maths, but there was in fact something comparable to an experiential. But he went a little further, and noted that some structuring principles that we often associate with interpersonal meaning in language – i.e. prosodic structure – occurred in various chemical symbolisms, but seemed to have become ‘ideationalised’ in that they were used to realise meaning related to field, not tenor.

Blogger Comments:

[1] To be clear, this is not just an argument against the metafunctional dimension of the theory, but against any dimension of the theory, and so against the theory itself, since in this view, using a theory that was devised for English, SFL, runs 'the risk of homogenising descriptions and making everything look like the first resource to be comprehensively described'. The same argument could be made against generalising Newton's theory of gravitation from falling apples to orbiting heavenly bodies, since it runs 'the risk of homogenising descriptions and making everything look like the first resource to be comprehensively described'. 

[2] To be clear, the metafunctions cannot be derived from axis, even if axis is properly understood. This is not least because they are independent dimensions, with different scopes, and organised according to different principles. Halliday & Matthiessen (2014: 20, 32):

That is, the local distinction between the paradigmatic and syntagmatic orders of axis entails nothing about the global distinctions between construing experience as meaning, enacting intersubjective relations as meaning, and creating text from the two.

For some of the theoretical misunderstandings of axis in Martin (2013), see the review here.

[3] To be clear, from the perspective of SFL Theory, mathematics is a contextual semiotic that is realised in language (e.g. algebraic equations) and a pictorial semiotic (e.g. geometric diagrams). The proof that equations, for example, are language is that, unlike non-language, they can be read aloud. This is because what is projected by saying, locutions, constitutes the lexicogrammatical stratum, and language is the only semiotic system with a stratified content plane. This is why bi-stratal systems, like pictorial semiotics, cannot be read aloud.

[4] To be clear, this is the logical fallacy known as the Argument from ignorance:

Argument from ignorance (from Latin: argumentum ad ignorantiam), also known as appeal to ignorance (in which ignorance represents "a lack of contrary evidence"), is a fallacy in informal logic. It asserts that a proposition is true because it has not yet been proven false or a proposition is false because it has not yet been proven true. This represents a type of false dichotomy in that it excludes the possibility that there may have been an insufficient investigation to prove that the proposition is either true or false.

Here Doran has misconstrued absence of evidence as evidence of absence. The evidence for the interpersonal metafunction in mathematical symbolism is manifold. For example, mathematical symbolism is language, so it enacts interpersonal meaning. As language, the equation E = mc² is a proposition realised by a declarative clause that can argued as valid or not whether it is expressed this way or as energy equals mass times the speed of light squared. If there were no interpersonal meaning in mathematical symbolism, then mathematicians would not be able to argue for or against their validity.

[5] To be clear, mathematical symbolism is deployed in many sciences precisely because it construes experience as meaning. As language, a mathematical equation is a figure of being realised by an intensive identifying relational clause, and the solving of an equation is the iterated elaboration of the clause until one or more unknown Tokens is decoded by reference to a Value.

[6] To be clear, the logical metafunction is concerned with the logico-semantic relations of expansion and projection, so it requires experiential meanings to relate logically to one another. Every equation is an intensive identifying clause that construes an elaborating logical relation between a Token and a Value, and the solving of an equation entails a clause complex in which all clauses are logically related through elaboration. The logical relation of extension, for example, is manifested in processes of addition and subtraction.

[7] To be clear, none of the metafunctions is independent of the others. Halliday & Matthiessen (1999: 532-3):

These three "metafunctions" are interdependent; no one could be developed except in the context of the other two. When we talk of the clause as a mapping of these three dimensions of meaning into a single complex grammatical structure, we seem to imply that each somehow "exists" independently; but they do not. There are — or could be — semiotics that are monofunctional in this way; but only very partial ones, dedicated to specific tasks. A general, all-purpose semiotic system could not evolve except in the interplay of action and reflection, a mode of understanding and a mode of doing — with itself included within its operational domain. Such a semiotic system is called a language.

More specifically, the textual metafunction requires the other metafunctions, since its function is to operationalise them. Halliday & Matthiessen (1999: 7-8, 398):

The textual metafunction is an enabling one; it is concerned with organising ideational and interpersonal meaning as discourse — as meaning that is contextualised and shared. … 

The function of the textual metafunction is thus an enabling one with respect to the rest; it takes over the semiotic resources brought into being by the other two metafunctions and as it were operationalises them…

Every mathematical equation is organised in terms of Theme and information; see [4] above.

[8] To be clear, given the explanatory power of the metafunctions, it would be more prudent to assume that they are a dimension of a semiotic system until it is proved otherwise. As explained above in [4], Doran mistook his inability to identify the metafunctions in mathematical symbolism for evidence that they are not a dimension of its systems. 

[9] To be clear, Yu Zhigang is Doran's collaborator, rather than a scholar working independently of Doran. More importantly, what is said above about mathematical symbolism also applies to chemical symbolism. For example:

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See also Yaegan Doran Failing To Recognise The Interpersonal Metafunction In Mathematics.

David Rose Misunderstanding The Ontogenetic Move From Protolanguage To Language

David Rose wrote to Sysfling on 24 August 2023 at 23:10:

The syntagms of infant protolanguage can’t handle multiple functions. The ontogenetic breakthrough comes with coupling of interpersonal with ideational functions. That’s what the syntagms of language have evolved to enable. The infant recapitulates that phylogenesis through interaction with caregivers.

Blogger Comments:

[1] This misrepresents protolanguage. To be clear, infant protolanguage does not have syntagms, since syntagms are sequences of classes of lexicogrammatical form, and protolanguage has no lexicogrammar, and so no lexicogrammatical form (e.g. words), an so no classes of lexicogrammatical form to sequence in syntagms.

[2] This is misleading because it is untrue. The ontogenetic move from protolanguage to language does not include the coupling of interpersonal and ideational functions in syntagms provided by protolanguage. This is not only because protolanguage does not provide syntagms, but also because all the metafunctions emerge together. Halliday & Matthiessen (1999: 532-3):

These three "metafunctions" are interdependent; no one could be developed except in the context of the other two. When we talk of the clause as a mapping of these three dimensions of meaning into a single complex grammatical structure, we seem to imply that each somehow "exists" independently; but they do not.

[3] On the one hand, this misunderstands evolution. Properties don't evolve in order to function advantageously in some context (Cause: purpose); they are selected because they function advantageously in some context (Cause: reason).

On the other hand, Rose is taking the opposite perspective on semogenesis from the SFL perspective, viewing it 'from below' in terms of form (syntagm) instead of 'from above' in terms of system and function.

[4] Importantly, ontogenesis does not recapitulate phylogenesis; see Recapitulation Theory. For example, a child learning Modern English does not recapitulate the moves from Old English to Middle English to Modern English. Instead, an ontogenetic trajectory that emerged at an earlier time in phylogenesis is maintained at later times in phylogenesis.

David Rose Misunderstanding Axial Relations

David Rose wrote to Sysfling on 24 August at 13:07:

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??

Blogger Comments:

[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.

David Rose On There Being No Such Things As Systems Or Structures

David Rose replied to Kieran McGillicuddy on Sysfling on 24 August 2023 at 4:36:

You’re quite right... there are actually no such things as systems or structures — they are merely generalisations from accumulated instances in the flow of discourse.

Blogger Comments:

[1] To be clear, in this context, systems and structures are abstract things that serve as participants in clauses in the field of linguistic theory.

[2] To be clear, systems and structures are abstractions in the metalanguages that theorise languages.

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Postscript: McGillicuddy promptly denied that he held the view ascribed to him by Rose.

David Rose Misunderstanding Axial Relations And Connotative Semiotics

David Rose wrote to Sysfling on 24 August 2023 at 00:01:

Axis is the systemic in systemic functional. In this theory, the coupling of generalisation with abstraction in the axial relation is the basis of semiosis. It is not merely a formalism of the theory, rather the formalism mirrors the semiotic relation. There can be no structures outside of systems, and no systems without structures. This includes systems at each rank, stratum and metafunction, of denotative semiotics like language and image, and connotative semiotics like register and genre.

There are plenty of other theories out there, but axis is what sets this one apart. SFS has been influenced by many theories in lx and other disciplines. It proceeds by examining the objects of these theories through the lens of axis, with procedures designed by Halliday in the 1960s for phonology and grammar, and applied since to these and other strata and modalities.

Blogger Comments:

[1] This is misleading, because it is untrue. Axis is a dimension with two orders: paradigmatic and syntagmatic. The 'systemic' in 'systemic functional' is the paradigmatic order of axis only.

[2] This is misleading, because it is untrue. The axial relation is the (realisation) relation between the paradigmatic axis and the syntagmatic axis. It is not a "coupling of generalisation with abstraction".

[3] This is misleading, because it is untrue. Structures are, by definition, "outside of systems" since the two are of different orders: structures are syntagmatic (chains), whereas systems are paradigmatic (choices).

[4] This is misleading, because it is untrue. Hjelmslev's connotative semiotic is a semiotic that has a denotative semiotic as its expression plane. What Rose refers to as a connotative semiotic is only the content plane of the connotative semiotic. However, register and genre (text type) are varieties of a denotative semiotic: language. In terms of a connotative semiotic, register and genre are on its expression plane (language) not its content plane (context).

[5] This is misleading, because it is untrue. There was no Systemic Functional theory in the 1960s. Halliday's theory at that time was Scale-&-Category Grammar, which had no system networks and no metafunctions.

David Rose Misunderstanding The Dimensions Of SFL Theory Through Biological Analogies

David Rose replied to John Bateman on Sysfling on 23 August 2023 at 21:02:

It’s a missing piece of other theories John, but central to SFS. 

It originates and is reproduced in interaction, the original replicating nucleus of semiosis, analogous with the original proteins of life... always replicating in/as a community. 

As those proteins make life possible, axis makes culture possible. 

Its ideational and textual functions are much later developments, like the eukaryotic cell... ranks the first multicellular organisms, strata the first complex ones (the proteins of which we still share with all other organisms).

Blogger Comments:

[1] To be clear, it is nucleic acids, not proteins, that replicate in biological systems. But even with this correction, the analogy is invalid, since if anything replicates in semiosis, it is in the semiotic system, not the interactions of meaners.

[2] To be clear, proteins make life possible in the sense that they are the expressions (Tokens) of genes (Values). Axis, on the other hand, in SFL Theory, is a local dimension with two orders: paradigmatic and syntagmatic. Culture, by contrast, is the contextual semiotic realised by language and other social semiotic systems. Thus, it is not axis that makes culture possible but social semiosis.

[3] To be clear, this misunderstands the metafunctions as independent of one another. Halliday & Matthiessen (1999: 532-3):

These three "metafunctions" are interdependent; no one could be developed except in the context of the other two. When we talk of the clause as a mapping of these three dimensions of meaning into a single complex grammatical structure, we seem to imply that each somehow "exists" independently; but they do not.

[4] To be clear, the eukaryotic cell was a phenotypic innovation in biological evolution, whereas the metafunctions were in language from the start as types of meaning that might be said to have "phenotypic effects".

[5] To be clear, multicellular organisms arose from the aggregation of eukaryotic cells, but ranks did not arise from the aggregation of the ideational and textual metafunctions. Rank is one way of modelling formal constituency.

[6] To be clear, complex multicellular organisms evolved from simpler multicellular organisms, but strata did not evolve from rank. Strata are different levels of symbolic abstraction, different perspectives on the one phenomenon, and are a dimension of all semiotic systems from the start, though only language has a stratified content plane.

David Rose Misunderstanding Axis And Realisation (Inter Alia)

David Rose replied to Brad Smith on Sysfling on 23 August 2023 at 15:47 and 16:26:

I used realisation below as the interstratal relation. Axis is the feature/structure relation in systems (which is also confusingly called realisation). Both are abstraction (token/value) relations. Axis is a one-to-one relation between a feature (value) and a structure (token). It also implies the generalisation of a system, because it is a contrast between structures that realises a contrast between features (not individual structures).

It is that coupling of generalisation with abstraction that lies at the heart of semiosis, and hence of SFS theory.

Interstratal relations are not one-to-one. Hence tone choices can be coupled with various mood choices to realise variations in appraisal, //4 don’t you know//. …

Oh sorry Brad, how rude of me.

I meant to say, //5 don't you/know//

Blogger Comments:

[1] Here again Rose misunderstands axis. Axis is a local dimension with two orders: paradigmatic and syntagmatic, whereas system is the dimension of the paradigmatic order of axis. Systems include realisation statements attached to features which specify structural realisations, but that is not 'axis'.

[2] To be clear, realisation is the relation between different levels of symbolic abstraction, and so it applies wherever that relation obtains: between system and structure, between strata, between function and form. It does not obtain between a feature and a structure, since a feature is not realised by a structure. Instead, a system (of a clause) is realised by a structure (of a clause). Importantly, a structure is not a functional element, but the relationships between such elements. Halliday & Matthiessen (2014: 451): 

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

[3] To be clear this argument rests on an invalid premiss:

Premiss: Axis is a contrast between structures that realises a contrast between features

Conclusion: Axis implies a generalisation of a system

The premiss is invalid because this is not what axis is (see [1]). Moreover, a contrast in features is not realised by a contrast in structure. For example, the contrast between the POLARITY features positive and negative is not realised by a contrast in structure, since both are realised by the element Finite in the same structural configuration, e.g. Subject^Finite^Predicator.

[4] To be clear, Halliday & Matthiessen (1999: 618) write:

The developmental dynamic of "generalisation — abstractness — metaphor" provides the semiotic energy for the grammar, enabling it to serve as the powerhouse for construing experience in the form of scientific knowledge.

But this bears no relation to Rose's use of the terms generalisation and abstraction. For example (op. cit.: 615):

This principle of generalisation — that is, naming general classes rather than specific individuals — is what makes it possible to construct an ideation base. …

General terms are not necessarily abstract; a bird is no more abstract than a pigeon. But some words have referents that are purely abstract — words like cost and clue and habit and tend and strange; they are construing some aspect of our experience, but there is no concrete thing or process with which they can be identified.

[5] This is misleading. To be clear, in the absence of grammatical metaphor, semantics and lexicogrammar are in agreement (congruent):

• a statement (semantics) is realised by a declarative clause (lexicogrammar);
• a question (semantics) is realised by an interrogative clause (lexicogrammar);
• a command (semantics) is realised by an imperative clause (lexicogrammar);
• an elaborating sequence (semantics) is realised by an elaborating clause complex (lexicogrammar);
• a relational figure (semantics) is realised by a relational clause (lexicogrammar);
• an element (semantics) is realised by a group or phrase (lexicogrammar).

[6] This is potentially misleading. The phonological system of TONE realises the grammatical system of KEY.  Halliday & Matthiessen (2014: 168):

The tones are not, however, simply additional markers attached to the realisation of mood. They realise distinct grammatical systems of their own, which are associated with the mood categories. The general name for systems that are realised by tone is KEY. The term KEY covers a number of systems …

(1) declarative clauses

unmarked statement: tone 1

reserved statement: tone 4

insistent statement: tone 5

tentative statement: tone 3

protesting statement: tone 2

(2) WH- interrogative clauses

unmarked WH- question: tone 1

tentative question: tone 2

echo question: tone 2 with tonic on WH- element

(3) yes/no interrogative clauses

unmarked yes/no question: tone 2

peremptory question: tone 1

(4) imperative clauses

command: tone 1 (unmarked in positive)

invitation: tone 3 (unmarked in negative)

request (marked polarity): tone 13, with tonic on do/don’t

plea: tone 4

[7] Note that tones 4 and 5 are not used with yes/no interrogative clauses. Since Rose's question is peremptory, it would be realised by tone 1 if spoken. 

David Rose Confusing Axis With System

David Rose wrote to Sysfling on 23 August 2023 at 13:55:

Can I suggest when reading the various philosophers of language cited in this thread, to remember the one missing puzzle piece that lies at the heart of systemic functional semiotics... axis.

Blogger Comments:

To be clear, here Rose confuses axis with system. Axis is a local dimension with two orders: paradigmatic and syntagmatic. Halliday & Matthiessen (2014: 32):

System, on the other hand, is the dimension of the paradigmatic order of axis only. Halliday & Matthiessen (2014: 20):

David Rose Misrepresenting SFL As Rejecting "Form/Meaning Dualisms"

David Rose replied to John Bateman on Sysfling on 21 August 2023 at 10:27am:

… It also gives some context to SFL’s insistence on bidirectionality of realisation, and lexis as delicate grammar, as well as its rejection of form/meaning dualisms.

Blogger Comments:

To be clear, 'dualism' means the division of something conceptually into two opposed or contrasted aspects, or the state of being so divided. Clearly, SFL does not reject the conceptual division of form and meaning as opposed or contrasted aspects, not least because it models grammatical form as a rank scale. 

SFL models grammatical form in terms of its function in realising meaning. The form-meaning relation ("dualism") is a Token-Value relation. This way of modelling is made possible by the 'natural' relation between form and meaning. Halliday (1985: xvii, xviii):

The relation between the meaning and the wording is not, however, an arbitrary one: the form of the grammar relates naturally to the meanings that are being encoded. A functional grammar is designed to bring this out; it is a study of wording, but one that interprets the wording by reference to what it means. …

What this means is that both the general kinds of grammatical pattern that have evolved in language, and the specific manifestations of each kind, bear a natural relation to the meanings they have evolved to express. … the distinction into word classes of verb and noun reflects the analysis of experience into goings-on, expressed as verbs, and participants in the goings-on, expressed as nouns; and so on.

Lise Fontaine On The Distinction Between Complement And Adjunct

Lise Fontaine wrote to Sysfling on 16 August 2023 at 10:59:

Ed is making a very important point here and one that is often overlooked. I think linguistics generally has seen a lot of damage from imposed boundaries around ideas. Even a distinction between Complement and Adjunct is not always clear, especially as concerns spatial reference. There is great benefit in being open-minded about accounts and not being afraid to be wrong sometimes.

Blogger Comments:

[1] This is misleading. The distinction between Complement and Adjunct is clear on theoretical criteria. Difficulty only arises when the theory is not understood.  Halliday & Matthiessen (2014: 153, 154, 155):

A Complement is an element within the Residue that has the potential of being Subject but is not; … Any nominal group not functioning as Subject will be a Complement (with the exception of certain circumstantial Adjuncts of Extent realised by nominal groups without the preposition for, e.g. 180 miles in he sailed 180 miles north on the Company’s armed schooner); and this includes nominal groups of one type which could not function as Subject as they stand, namely those with adjective as Head …

An Adjunct is an element that has not got the potential of being Subject; … (As noted above, certain circumstantial Adjuncts of Extent may be realised by nominal groups without the preposition for; contrast he had walked for miles with he had walked four miles.)

Fontaine's difficulty arises from taking the Formalist view 'from below' (forms: nominal group vs prepositional phrase) instead of the Functionalist view 'from above' (functions: Complement vs Adjunct). That is, the view 'from below' decodes forms by reference to functions, whereas the view 'from above' encodes functions by reference to forms. In other words, the view 'from below' begins with expressions and asks what they mean, whereas the view 'from above' begins with meanings and asks how they are expressed.

[2] To be clear, here Fontaine again engages in her promotion of the culture of anti-intellectualism (see here), reframing it as open-mindedness. Being afraid of being wrong is vitally important for producing high quality work, whether in academic publications or school exams. Ethically, not being afraid of being wrong is a licence to tell lies.

David Rose Misrepresenting Cohesion (Halliday & Hasan) As Discourse Semantics (Martin)

David Rose replied to Robyn Fawcett (again posing as Dmytro Poremskyi) on Sysfling on 15 Aug 2023, at 20:10:

Check out Halliday & Hasan (1976) Cohesion in English for detailed discussion of substitution and ellipsis... very different explanation — as discourse semantic resources rather than grammatical constraints.

Blogger Comments:

This is misleading, because it is not true. Halliday & Hasan (1976) was concerned with lexicogrammatical cohesion, not discourse semantics. Martin (1992) took Halliday & Hasan (1976) as his source and rebranded their lexicogrammatical cohesion as his own discourse semantics. Here Rose is participating in that deception.