30.2146, Sum: Matrices in Linguistics

Wed May 22 04:14:11 UTC 2019

LINGUIST List: Vol-30-2146. Wed May 22 2019. ISSN: 1069 - 4875.

Subject: 30.2146, Sum: Matrices in Linguistics

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Date: Wed, 22 May 2019 00:13:14
From: David Denison [david.denison at manchester.ac.uk]
Subject: Matrices in Linguistics

My question (LINGUIST List 30.1801, Sat Apr 27 2019) was prompted by Randolph
Quirk's (1965) use of matrices of pluses, minuses and question marks to
describe and perhaps explain similarities and differences of morphosyntax
between linguistic items. I'm planning some work on the ideas there.
Meanwhile, in case of interest to LINGUIST readers, here's my current
understanding of what came before it. Thanks to Peter Matthews (private
communication before I posted to LINGUIST), Magdalena Zoeppritz, Bruno
Maroneze, Herb Stahlke, Mareike Keller and Dick Hudson for their helpful
responses; further information or correction to this summary would be welcome.

Tabular arrays are a convenient, economical descriptive device. According to
Dick Hudson, 'I don't think you get tables, at least not in printed grammars,
till the nineteenth century because printing technology couldn't cope with
straight vertical lines'. Often a linguistic table is populated with a direct
representation of the item or property concerned, but space will be saved if
item and property define the rows and columns and the table cells are filled
only with '+' and '-' symbols (or equivalently, 'x' vs. blank) to indicate
whether or not a given item has some property, possibly with the option of
'?', etc. Such tables may be called 'matrices', but most linguistic tables
don't count as matrices in the mathematical sense of a rectangular array of
numbers or algebraic symbols potentially subject to addition, subtraction,
multiplication and other transformations. Genuinely algebraic matrices
appeared in the work of Pike in the 1950s, as also now in the recent 'matrix
syntax' of Juan Uriagereka and colleagues (Orús et al. 2019; reference due to
Mareike Keller).

Distinctive features in phonology go back to Trubetzkoy (1939), according to
Magdalena Zoeppritz, and visual inspection of the reprint shows arrays of
phonetic symbols (e.g. 1939: 153) where the rows and columns represent shared
features; I don't see pluses and minuses. I haven't yet had a chance to check
the first edition of Jakobson, Fant & Halle (1952), but the 3rd edition
presents such distinctive feature matrices (1965, 6th printing: 43ff.).
Jakobson & Halle (1956) has distinctive fatures, but no matrices either by
name or in tabular form (to judge from a reprint of the 2nd, rev. edn.). The
term 'distinctive feature matrix' occurs in Halle (1959: 34, etc.), with
pluses, minuses and zeros, and recurs in work of the mid-sixties by Halle and
by Chomsky. One column of (almost always) binary features represents a
segment. That also appears to be the usage in Chomsky & Halle (1968).
Multi-column 'matrices' are used for two distinct purposes: (i) to represent a
lexical item, where the relationship between columns is the linear sequence of
segments, and (ii) for a tabular presentation of (some of) the phonemes found
in a particular language variety, displaying relationships of similarity and
contrast.

In semantics, componential analysis is a structural approach modelled 'on the
phonological methods of the Prague School' (Wikipedia), of whom Trubetzkoy and
Jakobson, among others, were members, and it can use the same kind of display.
Among the few tables in Lyons (1963: 112), one (1963: 180) has '1' and '0' to
indicate presence or absence; in principle that would allow for mathematical
operations on it qua matrix. Goodenough (1956) uses formulas for set
intersection and union but not, apparently, +/- tables. Pace Bruno Maroneze,
+/- tables are not found in Pottier (1964) either, though that work does have
tabular representations of semantic and other properties (e.g. 1964: 115)
among a variety of other kinds of table and figure. Lamb (1964: 74) has one
+/- table.

By 1965, then, such tables or matrices are definitely 'in the air' in several
branches of linguistics, but it's morphosyntax that Quirk was doing, and the
most pertinent forerunner of all is Kenneth Pike. Herb Stahlke pointed me to
Pike (1959), which employs 'multiplication matrices', with combinatorial
properties that are truly mathematical. Even closer (and actually cited by
Quirk 1965: 209 n.9) is Pike (1962), which has matrices of syntactic
properties that -- as a presentational device, at least -- may well have
stimulated Quirk's discussion in the same journal a few years later. In the
same footmote, Quirk also cites Pike's follower Longacre (1964). Longacre's
has x-blank tables (1964: 60, 64, 120), which he calls 'matrices'. This, then,
seems to be the context in which Quirk was writing.

References:

Brend, Ruth M. (ed.). 1972. Kenneth L. Pike, Selected writings: To commemorate
the 60th birthday of Kenneth Lee Pike. (Janua Linguarum, series maior, 55.)
The Hague and Paris: Mouton.
Chomsky, Noam & Morris Halle. 1968. The sound pattern of English. New York:
Harper and Row.
Goodenough, Ward H. 1956. Componential analysis and the study of meaning.
Language 32, 195-216.
Halle, Morris. 1959. The sound pattern of Russian: A linguistic and acoustical
investigation. 
Jakobson, Roman, Gunnar M. Fant & Morris Halle. 1952. Preliminaries to speech
analysis: The distinctive features and their correlates. (Massachusetts
Institute of Technology, Technical Report No. 13). Repr. 3rd edn., 1965.
Jakobson, Roman & Morris Halle. 1956. Fundamentals of language. 2nd, rev. edn,
1971. Berlin and New York: Mouton de Gruyter.
Lamb, Sydney M. 1964. The sememic approach to structural semantics. American
Anthropologist 66.3 (special issue on Transcultural Studies in Cognition),
57-78.
Longacre, Robert E. 1964. Grammar discovery procedures: A field manual. (Janua
Linguarum, series minor, 33.) The Hague: Mouton.
Lyons, John. 1963. Structural semantics: An analysis of part of the vocabulary
of Plato. (Publications of the Philological Society, 20.) Oxford: Basil
Blackwell for the Society.
Orús, Román, Roger Martin & Juan Uriagereka. 2019. Mathematical foundations of
matrix syntax. arXiv 1710.00372v2. (https://arxiv.org/abs/1710.00372).
Pike, Kenneth L. 1959. Language as particle, wave, and field. Texas Quarterly
2.2, 37-54. Repr. Brend (1972: 129ff.).
Pike, Kenneth L. 1962. Dimensions of grammatical constructions. Language
38.3.1, 221-44. Repr. Brend (1972: 160ff.).
Pottier, Bernard. 1964 Vers une sémantique moderne. Travaux de Linguistique et
de Littérature publiés par le Centre de Philologie et de Littératures Romanes
de l'Université de Strasbourg 2, 107-137.
Quirk, Randolph. 1965. Descriptive statement and serial relationship. Language
41.2, 205-17.
Trubetzkoy, N. S. 1939. Grundzüge der Phonologie. (Travaux du Cercle
Linguisticque de Prague, 7.) Prague.
(https://pure.mpg.de/rest/items/item_2399346_2/component/file_2399345/content)
.

Linguistic Field(s): Discipline of Linguistics
                     General Linguistics
                     Morphology
                     Syntax

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