¹ Presidential Address delivered at the meeting of the Linguistic Society of America in Chicago, 28 December 1961.

² Hierarchical structuring of Amuzgo grammar, IJAL 23.143–4 (1957).

³ Hierarchical structure of Isthmus Zapotec = Language dissertation No. 56, (Baltimore, 1960).

⁴ See the reproduction of a part of the Zapotec clause chart in (42) below. For Pickett's phrase chart, see her page 35.

⁵ Of the Jivaro family. Her paper will appear in 1962 in Peruvian studies I, Linguistic series of the Summer Institute of Linguistics. Materials cited here are based on that article, where specific illustrative sentences may be found.

⁶ In Lorrie Anderson and Mary Ruth Wise, Contrastive features of Candoshi clause classes, in Peruvian studies I.

⁷ Matrix based on Structural summary of Záparo, in Ecuadorian studies I, Linguistic series of the Summer Institute of Linguistics, to appear in 1962.

⁸ Of the Pano language family of Peru. Based on data from Eugene E. Loos, Capanahua narration structure, to appear in Texas studies in literature and languages.

⁹ See Olive A. Shell, Cashibo II: Grammemic analysis of transitive and intransitive verb patterns, IJAL 23.179–218 (1957).

¹⁰ I take the use of the term ‘multiplication’ from John G. Kemeny, J. Laurie Snell, and Gerald L. Thompson, Introduction to finite mathematics 198 (Englewood Cliffs, N. J., 1957). (A row or column in a matrix may be called a vector; a vector by itself is a special case of a matrix.) When, however, one total matrix is to be multiplied by another, their stipulations as to the relation between the number of rows and columns of their matrices are not at the moment useful to our linguistic dimensional analysis. Their treatment of partitions (77–111) and cross-partitions of sets and subsets is closer to the remainder of our approach here.

¹¹ See my Language in relation to a unified theory of the structure of human behavior, 3.§11.6 (Glendale [now Santa Ana], Calif., 1960).

Transformation of construction types, therefore, is developed in tagmemic field theory as a phenomenon of matrix multiplication—appearing first of all as a characteristic of the relationship between subsystems in a field, rather than primarily as a set of rules. Passage from kernel matrix to derived matrices and to productive application of the field notation in speech is mediated by tagmemic (plus lexemic and phonological) formulas.

¹² Hart 143–4.

¹³ Pickett 77–80.

¹⁴ Viola Waterhouse, The grammatical structure of Oaxaca Chontal §1.2 (University of Michigan dissertation, 1958), to appear as a supplement of IJAL.

¹⁵ For some illustrative data, see Eunice V. Pike, Mazatec, Huautla de Jiménez Dialect, to appear in a volume of studies on Middle American Languages, to be edited by Norman McQuown. Her dimensional analysis reached me through correspondence.

¹⁶ See my Language for congruent systems with topological distortion or systemic modification: 2.13, 20b–21a, 23a, 48a (1955); 3.75–6 (1960).

¹⁷ The term comes from Kemeny et al. 54; see also 79. For us, a linguistically well-defined unit is emically structured.

¹⁸ Through the formula U = F M D; unit has feature mode, manifestation mode, and distribution mode. This high degree of generality applied to the definition of all linguistic units is characteristic of tagmemic theory, which avoids centering its attention on the well-formedness of any one selected unit of any one hierarchy—say the unit named sentence—or giving it analytical, presentational, and theoretical priority.

¹⁹ String constituent analysis, Lg. 36.75 (1960). Careful work on contrastive constructions on the sentence level is done by Waterhouse (1958), who for Oaxacan Chontal gives detailed indications of structural contrasts as she passes from the discussion of one type to the next. But it is not until Longacre's work that the relevance of a minimal essential difference comes into view.

²⁰ After the first pair was placed at the top, however, all the others could arbitrarily be assigned as subdivisions of the first vertical pair. Elegance of results and the innate structure of a particular language—not the matrix approach as such—influence judgment as to further arrangement of the dimensions.

²¹ Note, therefore, its analogy to displays of contrastive features—a type exploited effectively by Roman Jakobson, Gunnar M. Fant, and Morris Halle, Preliminaries to speech analysis (Technical Report No. 13, second printing, Acoustic Laboratory, Massachusetts Institute of Technology, 1952). If grammatical dimensions turn out to be few in number, as these authors consider the phonological ones to be few, the implications for grammar will be very great. I personally believe that the similarity of the types we have used for illustration, above, are not only due to their geographical source, or to the English etic bias of the authors, but in part reflect some phases of such a limitation.

²² Harwood Hess, for Otomí, has in preparation extensive test displays of this kind.

We should also be able to prepare Unit-Times-Unit matrices to parallel Component-Times-Component and Unit-Times-Component matrices. Perhaps this would help us define some types of matrix multiplication in which pairs of distinctive matrices serve as the dimensions, and complicated or compound constructions are placed in the cells.

²³ Abbreviated from Pickett 56.

²⁴ Based on Ray Elliott, Ixil (Mayan) clause structure, Mayan studies I, Linguistic series of the Summer Institute of Linguistics 5.127–54 (1961). This particular arrangement is suggested to me by George Hart.

²⁵ Suggested to me by Ilse Lehiste.

²⁶ In my Language 3.20–22. Part I §7 gives extensive discussion of contrast, variation, and distribution of tagmemes (under the earlier label ‘grameme‘); revised, tabulated treatment of tagmeme variants is found at 3.18–19.

²⁷ For etic concord symbolized in Zapotec, see Pickett 43. For Cashibo concord across clauses, with a dependent clause marked for the expected occurrence of a same or of a different subject in the next clause, see Shell 203–5. The anticipatory marking in the dependent clause of the coming transitive (or intransitive) independent clause could be similarly handled. See, however, our adding of these allosyntagmatic elements to the Cashibo matrix, in (10) above.

²⁸ See Waterhouse §1.1.2. Larson's paper contains a zero allotagma of tense. For discussion of hesitation at setting up a totally-zero morpheme, see Eugene A. Nida, Morphology ² 46 fn. 44 (Ann Arbor, 1949). Note also bibliographical discussion in my Language 3.64–65.

²⁹ Pickett 58, also 61.

³⁰ Data abstracted from Colin C. Delgaty, Tzotzil verb phrase structure, in Mayan studies I, Linguistic series of the Summer Institute of Linguistics 5.82–126 (1960).

³¹ A few of the irregularities might disappear after checking further with an informant. This possibility does not negate our method. On the contrary, if our approach forces irregularities into attention for checking, it is useful to us in that respect as well.

³² As I indicated for phonology in my article More on grammatical prerequisites, Word 8.120 (1952).

³³ Language, 3.30–39; and my article Language as particle, wave, and field, Texas quarterly 2.2.37–54 (1959).

³⁴ Pickett 91 discusses constructions as waves with nuclei.

³⁵ Some graphic displays of contrasts—semantic or structural—between inflectional morphemes of paradigms have been given by other authors. See, for example, John Lotz, The semantic analysis of the nominal bases in Hungarian, Travaux du Cercle Linguistique de Copenhague 5.185–97 (1949).

³⁶ See Charles F. Hockett, Two models of grammatical description, Word 10.210–31 (1954), §1.1. The word-in-paradigm approach is recognized by him as deserving 'the same consideration ' as item-and-process and item-and-arrangement. But Hockett gives 'apologies for not having worked such consideration of WP into the paper.' No theoretical basis for a possible treatment is suggested.

The objection to WP referred to by Hockett—that the paradigm approach is not sufficiently general to organize ‘efficiently the facts of a language like Chinese ‘—is met in our treatment through matrices and tagmemic formulas to represent dimensional components of constructions on levels higher than the word. A simple paradigm may be merely a one-vector special instance of a matrix of one grammatical level.

³⁷ For some of the distortion involved in any one separate view, see my Language 3.59–65.

³⁸ Gaps and errors need filling and correcting here, as they do for any approach.

³⁹ Zoque: Phonemics and morphology, IJAL 17.2–3 (1951).

⁴⁰ Begun in my Language l.§5.53, 3.§11.52.