The logical nature of Systemic-Functional Grammar and “grammatical logic”

3.1 The logical metafunction

Halliday (1978) identifies the “logical structure” as one of the four components in the grammatical structure of language, since language has to express certain elementary logical relations, like “and”, “or” and “if”, as well as those created by language itself such as “namely”, “says” and “means” (21). He divides the first of the three metafunctions (“ideational”) into the “experiential” and the “logical”, making a distinction between the “content” function of language and something in the linguistic system that is expressed through recursive structures (1978, 48). He explains that the “logical” component is that which is expressed in the form of “parataxis” and “hypotaxis”, including such relations as coordination, apposition, condition and reported speech. By regarding these relations as constituting the “logic” of natural language, Halliday makes a necessary distinction because logical meanings have “exclusively this linear recursive mode of expression” (1978, 49).

In the first and second editions of IFG (An Introduction to Functional Grammar), Halliday (1985, 1994) takes the “logical metafunction” as a subcomponent since the logical element in the linguistic system is “ideational”. But to further the point that “once it is built into language the logical becomes neutral with respect to the other functions” (1978, 48–49), Halliday, many times in the revised editions, upgrades the “logical” as the first of the four metafunctions (e.g. 2004, 63) and specifically prioritises the “logical meaning”: “A text is organised internally as patterns of logical, experiential, interpersonal and textual meaning” (2014, 43).

3.2 The metalanguage

The logical nature of “linguistic metalanguage” facilitates different levels of academic description and everyday communication (Feng 2005). Malmkjaer (1991, xi) writes, “If there is one thing that sets linguistics apart from other disciplines, it is the fact that its subject matter must be used in the description. … and a metalanguage is, in any case, also a language”. Halliday rightly makes the theory of grammar as “taking language as its metalanguage” (2002, 366). Apart from language expressing logical relations (e.g. namely, means), which are “metalingual” in the sense of “glossing” (Jakobson 1960), Halliday has developed a lot of terms in the sense of “language constructing language” (Taylor 2003), such as the four most basic categories (i.e. unit, structure, class and system) that are “of the highest order of abstraction”, each being specifically related to and logically derivable from the others, “without any relation of precedence or logical priority” (Halliday 2002, 41).

Hjelmslev (1961, 119–120) found that there is “a semiotic whose expression plane is a semiotic” in addition to “a semiotic whose content plane is a semiotic”, and “linguistics itself must be” such a semiotic that treats of a semiotic. In other words, linguistics has to be metasemiotics. Following the modern logician’s dichotomy of the object language and metalanguage, Halliday (1978, 3–4) makes a “valid and important distinction” between the object and the instrument: for the linguist, language is object, and for others, language is “an instrument” (i.e. a means of illuminating questions about something else), making clear distinctions between phenomenon and metaphenomenon, description and metadescription, etc. For instance, on his observation that both words and things may “participate in the process”, Halliday distinguishes between “what is perceived or felt or thought of” and “a phenomenon that has already been filtered through the medium of language”. He explains that a metaphenomenon is a “representation at the semantic level” and a metaphenomenon is a “representation at the lexicogrammatical, or syntactic, level” (2002, 184–5).

Firth (1968, 169) pointed out that “Every scientific discipline must necessarily develop a special language adapted to its nature and that development represents an essential part of scientific work”. Unlike some scholars that see metalanguage as “technical” terms (Robins 1997, 34) or the linguist’s “jargon” (Wales 1989, 294), Halliday sees technical terms (e.g. register, grammatics, semiosis) as “not necessarily jargon”, but “an essential part of constitution of scientific knowledge” (2014, 5). Halliday (2002, 296) is fully aware of the problem of interpreting a symptom and labelling its interpretation, which is “common to all sciences”, and uses “a higher status code” to symbolise “a higher order of abstraction”. He observes that in metalinguistic matters, linguistics presents a special case, but is not just another science, thus insisting that “where other sciences need two terms”, linguistics needs three: one for the phenomenon and two for the metaphenomenon (i.e. grammatical and semantic). It is this logical and metalinguistic perspective that has scientificalised SF grammar as a linguistic and metalinguistic theory.

3.3 The meta-ness of theory and theory of theories

In developing a “functional account of English grammar”, Halliday focuses on developing a general theory of grammar and a theory of theories of grammars, i.e. grammatics or metagrammar. He says that, while a grammar is “a theory of experience”, a grammatics is “a grammar of grammars, a theory of theories of experience, or a metatheory” (2002, 365).

In the Introduction to IFG, Halliday (1985, i–xvi) notes that he takes English to manifest in the linguistic system “the two very general purposes which underlie all uses of language”. As a result, he has developed a functional grammar of English in particular and a theory of functional grammar of languages in general. In so doing, he takes English (along with examples from some other languages) as both an object and a means of description. In a 1996 article, he puts forward a metagrammatical concept, “grammatics”, simply to “escape from the ambiguity where ‘grammar’ meant both the phenomenon itself … and the study of that phenomenon” (2002, 416).

Although Halliday declares that his approach leans towards the applied, rhetorical, actual and functional rather than the pure, logical, ideal and formal (1985, xxviii), his functional account of grammar is logically woven and formally expounded. By emphasising text analysis as “a mode of action” and a theory of language as “a means of getting things done”, Halliday believes that paradigmatic functional grammars can also be “generative” in the sense of “being expressed in formal terms and used for generating or parsing by computer” (1985, xxix). He says that “talking about grammar” means “doing grammatics” or “using grammar to construct a theory about itself”. Seeing a theory as a semiotic construct, he is confident in using a grammar as a resource for constructing theories just because “a grammar is itself a theory”, and the construction of knowledge is “the transformation of experience into meaning” (2002, 391).

Some remarkable features of Halliday’s theory lie in the logical meta-ness. His linguistic theorisation is not only significant for such concepts as “system”, “function”, “grammar”, but more importantly, for higher logical levels of “system of systems”, “function of functions”, “grammar of grammars”, “theory of theories”. It is from his keen logical insight that Halliday has developed a grammar of a natural language in particular and of natural languages in general, which is a theory and a theory of theories.

4.1 Embodiment of indeterminacy or fuzziness

As a general feature of natural language and therefore a major concern of SF grammar, Halliday noticed “indeterminacy” in the 1950s and resorted to “probability” and “approximativity” in coping with the large number of linguistic facts that cannot be adequately dealt with in terms of polarities. He holds that “probability” is not a “fuzzy” concept; but probability in grammar adds indeterminacy to the definition of a category (2002, 400). Hu (1990, 8) regards Halliday as the first to “analogise the probabilistic principle of informatics to the description of grammatical system”.

While logicians borrow natural language to study the neatness and wholeness of formal systems, Halliday simulates and models on natural language in describing the linguistic system. Unlike traditional truth-conditional semanticists who did not care about fuzzy areas between entities, Halliday deals with indeterminacy in both natural language elements and their linguistic description (Feng 2012b). Unlike logicians and semanticists who only cared about truth or falsity, Halliday focuses on the validity of the values in between (Feng, 2012a). The most “logical” system in SF grammar, modality, has absorbed both traditional and modern logic, making use of the three terms in traditional modal logic (i.e. possibility, probability and certainty) and extended terms in modern modal logic (i.e. can, could, might, may, must). His logical concept of “finite verbal operator” includes “temporal operators” and “modal operators” (Halliday 1985, 75).¹ One of the remarkable features of this system is not only ranges of intermediate choices between polarities, but also a factual discovery that “all modalities are in the positive ranges”, with the explanation that there is no such thing as a “negative modality”; a modality is an assessment of probability and is not subject to negation (Halliday 1970, 333).

The first time Halliday uses the term “fuzziness”, as I can find, is Halliday (1978, 114), as a logical rather than a sociological concept referring to “a departure from an ideal regularity” (rather than an organic property of socio-semiotic systems). For Halliday, the “fuzziness” of language is “in part an expression of the dynamics and the tensions of the social system”. In my article (Feng 2012b), I traced Halliday’s incremental uses of “fuzzy” or “fuzziness” in IFG and found twice in the first edition: “As with those that are projected verbally, so with those that are projected mentally the exact limits are fuzzy” (1985, 237); and “the line between conjunction and paratactic expansion is a fuzzy one” (1985, 318). In the second edition, there are two more times: “The line between a compound noun and a nominal group consisting of a Classifier + Thing can be very fuzzy and shifting” (1994a, 185); “Wanting something to be done means that it is envisaged, or projected, but may or may not happen: its status is that of a metaphenomenon, not a phenomenon. But the line between the two is fuzzy” (1994a, 289). In the third edition, there are six more times: “Word boundaries are somewhat fuzzy” (2004, 7); “both categories, orthographic word and grammatical word, are equally fuzzy” (9); “such (lexical) sets can be typically fuzzy, with doubtful or part-time members” (40); “in a grammatical perspective, as rather large and fuzzy closed systems or, in a lexical perspective, as somewhat determinate and limited open sets” (45); “the process types are fuzzy categories” (172); and “systemic terms are not Aristotelian categories” but “fuzzy categories” representing “fuzzy sets” rather than “crisp” ones (172). In the fourth edition, there are altogether 11 times, with a revised wording “such (lexical) sets are typically fuzzy” (2014, 61) against “can be” (2004, 40) and in addition: “English needs to be interpreted and described as an assemblage of varieties … with fuzzy boundaries” (2014, 73).

It is obvious that Halliday uses the term “fuzzy” as “indeterminate” in the first two editions of IFG. Terms such as “part-time members”, “fuzzy categories”, “fuzzy sets” and “fuzzy boundaries” appear only in the revised editions of IFG and the only work on fuzziness in References is Matthiessen’s 1995 article “Fuzziness Construed in Language”. Somehow, Halliday’s own 1995 articles “On Language in Relation to Fuzzy Logic” and “Intelligent Computing” and “Fuzzy Grammatics: A Systemic Functional Approach to Fuzziness in Natural Language” are not listed.

4.2 Rejection of fuzzy logic

Preferring the term “indeterminate” to “fuzzy”, an essential feature of language that the grammatics “should accommodate” (2002, 409), Halliday obviously keeps off fuzzy logic; and when he has to use the term “fuzzy” in a logical and computational sense, he only mentions it being borrowed “from its origins in Zadeh’s ‘fuzzy logic’” (399) and “deriving ultimately from” it (416). For Halliday, formal logic is “the designed offspring of grammatical logic, just as the written sentence is the designed offspring of the clause complex of speech” (2005, 176). He explains that mathematics and grammar both are semiotic systems but constitute different and complementary kinds of logic: the logic of numbers and the logic of wordings and meanings – linguistic logic. Just as mathematics enables us to “manage the complexity of numbers”, grammatics enables us to “manage the complexity of language” (250–1).

Holding that SF linguistics is “fuzzy grammatics” (2005, 227), Halliday does not care for fuzzy logic in the way of using natural language as the computational metalanguage. In spite of the highly logical nature of SF grammar, Halliday virtually cites no work of logic.² In the third and fourth editions of IFG (Halliday 2004, 2014), the only entry in the References is Ellis’s Language, Mind and Logic (1993), a book that he had reviewed in 1995. In this review, Halliday writes, “Formal logic is irrelevant to the understanding of language: not because of the limitations of language but because of the limitations of conventional logic” (2003, 236). For Halliday, formal logic and mathematics can be seen as the result of “tidying up the indeterminacies of natural language grammars” (2002, 399). Since indeterminacy is an inherent and necessary feature of a grammar, to be accounted for, construing it is a matter of “managing the complexity”. Although “computing with meanings” can depend on “reasoning and inferencing with fuzzy sets and fuzzy matching processes”, he insists that natural language “requires a grammatics” (416–7).

In his incremental explicitness in using the term “fuzzy/fuzziness”, Halliday never refers to the generative semanticist Lakoff’s (1973) important study of fuzziness in reference to Zadeh’s fuzzy logic, in spite of his commonness with him in using such terms as “prototype” (none in the first edition, but four times in all other editions of IFG), “fuzzy sets” and “fuzzy categories” in the revised editions of IFG and other articles. Lakoff points out that natural language concepts have vague boundaries and fuzzy edges and that, consequently, natural language sentences will very often be “neither true, nor false, nor nonsensical”, but rather “true to a certain extent and false to a certain extent”, “true in certain respects and false in other respects”; hence, any attempt to limit truth conditions for natural language sentences to true, false and “nonsense” will distort the natural language concepts which are not sharply defined but “fuzzily defined boundaries” (1973, 458).

By “hedges”, Lakoff is concerned with the logical semantic systems of degrees of truth between “yes” and “no”; by “modal operators” and “modal adjuncts”, Halliday is concerned with the modalisation system of the degrees of probability and usuality between “yes” and “no” and the modulation system of the degrees of obligation and inclination between “do” and “don’t”. At least in “negotiating information”, Halliday and Lakoff are logically doing the same thing by validating the third type of values in the fuzzy areas between the positive and the negative.

Halliday is well informed and cites many people, including his colleagues and students, but not his Stanford alumnus Lakoff for even once in his own books and articles.³ Lakoff’s paper on fuzziness was written during his residence at the Centre for Advanced Study in the Behavioural Sciences at Stanford University from 1971 to 1972. Halliday was Fellow at the same Centre during a time when Lakoff read the paper at the Eighth Regional Meeting of the Chicago Linguistic Society in 1972 and had it published in the following year. It remains a mystery why Halliday neither cites nor comments on Lakoff’s study on fuzziness.