John Bateman On The Interpersonal Metafunction In Mathematics

John Bateman wrote to sysfling on 24 February 2017 at 10:10 in reply to the query 'To what degree is TENOR important in mathematical discourse?':

one of the well known kinds of proofs for more advanced mathematics is 'proof by intimidation': sounds pretty interpersonal to me! :-) 

And as soon as you move down to educational contexts, you'll want to be hitting your tenor variables right. Since all metafunctions in less-grammaticised semiotic modes are in any case discourse interpretations, I'm sure you'll be able to find something... 

I'd be with Yaegan though in doubting that the technical resources employed in mathematics have any inherent interpersonal organisation, although certain variations,

'x(1-y)' compared to 'x times (1 - y)'

may move in that direction. But is that what you meant?

Blogger Comments:

[1] The use of the word 'down' here — from genre to tenor — indicates that Bateman is using Martin's (1992) model* in which genre and register are misconstrued as context strata instead of functional varieties of language (a point on the cline of instantiation).  For some of the many theoretical misunderstandings on which Martin's model is based, see the arguments here.

[2] The use of the word 'discourse' here — instead of 'semantics' or 'meaning' — indicates that Bateman is using Martin's (1992) model* of discourse semantics.  For some of the many theoretical misunderstandings on which Martin's model is based, see the arguments here.

[3] The typical mathematical equation is a proposition realised by a declarative clause, and structured as Subject^Finite/Predicator^Complement, whether realised in the graphology peculiar to the field of mathematics or in the unspecialised graphology (or phonology) of an individual language.  A sample structural analysis can be viewed here.  Proposals realised by imperative clauses are also used, and take the form exemplified by let x =3.

[4] The variation here is textual (mode), not interpersonal (tenor).

∞

* Postscript: A critical examination of Bateman's review of Martin (1992) will be the subject of a new blog: Thoughts That Didn't Occur.  At first glance, it appears that Bateman has failed to notice any of the 2000+ theoretical inconsistencies in Martin's work (identified here).

Yaegan Doran Failing To Recognise The Interpersonal Metafunction In Mathematics

After Ruslana Westerlund wrote to Sysfling on 24 February 2017 at 7:52:

Hi all, I am curious about the usefulness of the Interpersonal metafunction in mathematics or science Or To what degree is TENOR important in mathematical discourse? If you know of anyone who has written on that, I would love any pointers or references.

Yaegan Doran replied to Sysfling on 24 Feb 2017 at 9:22:

Two places that discuss this are:

1) Kay O'Halloran's (2005) Mathematical Discourse: Language, symbolism and visual images. London: Continuum. 

- In this book, O'Halloran argues that the interpersonal metafunction in mathematics is greatly constrained in comparison to language, using this to explain certain patterns of mathematics in text. 

2) My PhD Thesis (soon to be in book form!) - Doran (2016) Knowledge in Physics through Mathematics, Image and Language. PhD Thesis, Department of Linguistics, The University of Sydney. 

- I go one step further than O'Halloran and argue that if we don't assume metafunctions occur for all semiotic resources, but rather seek to derive them from patterns in the system, there appears to be no evidence to recognise a distinct interpersonal metafunction - mathematical text patterns can be explained using purely ideational and textual systems.

Blogger Comments:

[1] To be clear, the metafunctions are an integral feature of SFL Theory, and the theory that Doran applied to mathematics was SFL Theory.

[2] Trivially, in theoretical terms, this is nonsensical. In SFL Theory, there are no "patterns in the system". The system represents the potential as an array of interrelated choices; patterns occur in the instantiation of the system.

[3] To be clear, if there were no interpersonal meaning in mathematics, mathematicians would not be able to argue about the validity of equations. Every equation of the type a + b = c is a proposition in terms of SPEECH FUNCTION, and a declarative clause in terms of MOOD; and every equation of the type let x = y is a proposal in terms of SPEECH FUNCTION, and an imperative clause in terms of MOOD. And this is true whether equations are realised phonologically, graphologically or in the formalisms peculiar to mathematics. If it were not true, then, on hearing a mathematical equation, an addressee would need to ask if it corresponded to the graphological expression or the mathematical formalism in order to ascertain whether or not the speaker was enacting interpersonal meaning.

Moreover, as the above suggests, the semiotic system that realises the cultural field of mathematics is language itself, or more specifically, registers (sub-potentials) of language. Language is the only semiotic system that can be read aloud — verbally projected as wordings — because language is the only semiotic system that has a stratum of wording (lexicogrammar).

For example:

E	=		mc2
Theme	Rheme
Given			New
Identified Token	Process: intensive		Identifier Value
Subject	Finite	Predicator	Complement
Mood		Residue

That is, the wording of every mathematical equation realises

• a quantum of information
• a figure of identity, and
• a proposition (or proposal).