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).