… 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.
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[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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