¹ Leonard Bloomfield, Language, chapters 2 and 9 (New York, 1933).

² For the difference between ‘designation’ and ‘signification’ see §5.

³ Charles W. Morris, Foundations of the theory of signs (International Encyclopedia of Unified Science, Vol. 1, No. 2; Chicago, 1938); Signs, language and behavior (New York, 1946).

⁴ Charles F. Hockett, Problems of morphemic analysis, Lg. 23.321–43, esp. 333 ff. (1947).

⁵ Cf. my Oneida verb morphology 11–6, 35–45 (Yale University Publications in Anthropology 48; New Haven, 1953).

⁶ Zellig S. Harris, Componential analysis of a Hebrew paradigm, Lg. 24.87 (1948).

⁷ Cf. Roman Jakobson, Beitrag zur allgemeinen Kasuslehre, Travaux du Cercle linguistique de Prague 6.240–88 (1936) ; Thomas A. Sebeok, Finnish and Hungarian case systems: Their form and function (Acta Instituti Hungarici Universitatis Holmiensis, Series B, Linguistica 3; Stockholm, 1946); John Lotz, The semantic analysis of the nominal bases in Hungarian, Travaux du Cercle linguistique de Copenhague 5.185–197 (1949); William L. Wonderly, Semantic components in Kechua person morphemes, Lg. 28.366–76 (1952); Zellig S. Harris, Lg. 24.87–91 (1948).

⁸ Lewis H. Morgan, Systems of consanguinity and affinity of the human family 195–9, 293–382 (Smithsonian Contributions to Knowledge, Vol. 17; Washington, 1871).

⁹ An English example will illustrate the use of these terms. In our kinship system father's brother, mother's brother, father's sister's husband, and mother's sister's husband are four kin types belonging to the kin class uncle. For definitions and further discussion of these terms see §10.

¹⁰ Primary kin types are those within the nuclear family. Since an individual normally becomes a member of (at least) two nuclear families—that of his parents and siblings, in which he finds himself as a child, and that of his spouse and offspring, which he establishes as an adult—it results that a primary relative of a primary relative is not necessarily also a primary relative. Some are; e.g. Ms = B, FW may = M. Some are not; e.g. MB and BW. The latter are secondary kin types. Similarly, a primary of a primary of a primary, which does not reduce to either a primary or a secondary, is a tertiary kin type; and so forth. Cf. George Peter Murdock, Social structure 92–7 (New York, 1949). The degree of a kin type is given, in our notation, by the number of letters used in its abbreviation.

¹¹ FMB is not given by Morgan. From Sss — raktíki it can be reconstructed, by reciprocity, as atipat. From FSss = irári/irátsti it can be reconstructed, by reciprocity and succession, as atías.

¹² From FSds = atías, by reciprocity and succession.

¹³ From *FMB = atías, by sibling relationship.

¹⁴ From *MMB = tiwátsiriks, by sibling relationship. For the double signification of atíra see §7.4.

¹⁵ From MBsss = tíwat, by reciprocity and sibling relationship.

¹⁶ Parallel collateral extension from MMS. Cf. fn. 14.

¹⁷ From FSds = atías and FSdd = atíra, by reciprocity. Morgan gives MMBs as tiwátsiriks, which is inconsistent with the classification of the reciprocals FSds and FSdd. This is hardly to be interpreted as reflecting alternative principles of classification, but rather must be an isolated exception. Generally the child of an “uncle” is “child”. The succession “uncle” > “uncle”, in place of “uncle” > “child” is a known type of mutation in a Crowtype kinship system when rules of residence are changing from matrilocal to patrilocal. It is a shift from ‘Crow’ principles of classification to ‘Omaha’ principles of classification. In the Republican Pawnee data this must be an isolated instance of some informant's MMB having retained his parental residence after marriage, bringing his wife with him rather than going to live with his wife's family. That this must represent a single instance rather than a continuing new practice is indicated by the succession in the next and continuing generations where it goes “uncle” > “child” > “grandchild”. As a result of this one exception the MMB agnatic line is displaced one classificatory generation upward in Morgan's data. We have deleted this divergent line from our data, and have filled it out by utilizing Morgan's data on reciprocals.

¹⁸ The ambiguities in Morgan's data here, when he employs the terms ‘great grandson’ and ‘great granddaughter’ in defining kin types, are resolved in his special remarks on the Pawnee, op.cit. 196–7, and also by the data for the more exactly specified reciprocal types FFFB and MMMB, tiwátsiriks.

¹⁹ The ambiguities here and in the following, which inhere in the terms ‘grandson’ and ‘granddaughter’, are resolved by the example of the specifically given MBss, MBds, MBsd, MBdd.

²⁰ See fn. 11 on the reciprocal type FMB.

²¹ Morgan's ambiguous terms ‘FB great-grandson’ and ‘FB great-granddaughter’ are taken to include all eight possibilities, FB(s/d)(s/d)(s/d), because of the precedent furnished by (B/S)('grandson'/'granddaughter') = (B/S) (s/d) (s/d) = raktíki; cf. fn. 19. Similarly, ‘MS great-grandson’ and ‘MS great-granddaughter’ are taken as including MS(s/d)(s/d)(s/d).

²² The ambiguous ‘FFB great-great-grandson’ and ‘FFB great-great-granddaughter’ are taken, on the same precedent, to include FFBs(s/d)(s/d)(s/d). Similarly, ‘MMS great-great-grandson’ and ‘MMS great-great-granddaughter’ are taken as MMSd (s/d)(s/d)(s/d). Cf. fns. 19 and 21.

²³ Foundations 3–9, 21–7; SLB 17–20 (cf. fn. 3). In the earlier work Morris used the term ‘semantical rule’ in place of ‘significatum’.

²⁴ Journal of the Royal Anthropological Institute 39.77–84 (1909); reprinted in A. L. Kroeber, The nature of culture 175–81 (Chicago, 1952).

²⁵ ‘Degree of collaterally’ between a pair of consanguineal kinsmen is equal to the number of generations up a descent line of the higher-generation member of the pair, or of either if of same generation, up to their common ancestor. It is thus a reciprocal constant: the degree of collaterally of the first with respect to the second is equal to that of the second with respect to the first, regardless of which is taken as Ego. Degree of collaterally, thus defined, is the primary dimension of our English kinship system. Lineal kinsmen (ancestors and descendente), as well as oneself, are of zero degree collaterally; uncles and aunts, brothers and sisters, and nephews and nieces, as we use these kinship terms in English, are of first degree collaterality; while cousins are of second and higher degrees of collaterally.

²⁶ For the definition of ‘uterine’ and ‘agnatic’ see §7. The term ‘parallel· is sometimes understood as a cover term to include both of these : those to whom consanguinity can be traced entirely through connecting kinsmen of one sex. Sometimes, however, it applies only to kinsmen of the same generation, with the requirement that to be ‘parallel· the parents through whom they are related must be merely consanguineal kinsmen (not necessarily themselves parallel) of the same sex. It is in this latter sense that it is applicable in the kinship systems of the Iroquois, the Cree, the Dakota, and other so-called Iroquoistype systems of North America.

²⁷ These are ‘elementary’ only in a relative sense, being simpler than the derived dimensions which are used later. For a reduction of kinship dimensions to elementals see Joseph H. Greenberg, The logical analysis of kinship, Philosophy of science 16.58–64 (1949).

²⁸ Note that the formula juxtaposes symbols in two manners: with intervening dot, and without. Juxtaposition without the dot indicates a dependency relationship analogous to our genitive construction. The meaning of A ⁰ cannot be defined absolutely as can the meaning of ♂. It is relative to a chosen reference point. If no other reference point is prefixed, it is understood to be Ego. Thus, A ⁰ is to be read, Ego's agnatic kinsman of the same generation as he. Some other reference point may be stated, however, as in U⁺A ⁰. This is to be read as Ego's ascending-generation uterine kinsmen's agnatic kinsmen of same generation as they.

Juxtaposition with intervening dot indicates the Boolean class product. X·'Y is the class of things which are both X and Y, i.e. the intersection of the two given classes. Dot products are commutative. That is, X·Y = Y·X. Simple juxtapositions are not comnutative. XY ≠ YX.

We shall have occasion also to use the Boolean sum. X + Y is the class of things which are either X or Y. Cf. George Boole, The mathematical analysis of logic (Cambridge, 1847).

²⁹ Nondot juxtapositions, being noncommutative, require inversion of order when taking reciprocals. Dot products, being commutative, may be written in any order, ♂ = male, ♂^-1 — a male's. Generation reciprocals change sign. Zero-generation is self-reciprocal.

³⁰ Gene Weltfish, oral communication.

³¹ Neither could kinsmen of such types be uterinely or agnatically connected to Ego by virtue of some other line of connection. For this to be the case, there would have to have been a practice of first-cross-cousin marriage, which however is exceedingly rare for peoples with Crow-type kinship systems, and which for the Pawnee would have been incestuous.

³² ‘Levirate’ is the practice whereby, when a man dies and leaves a widow, his brother (usually a younger brother) is obliged to take the widow to wife.

³³ Some of these, which make use of the relative-age distinction, simply extend their ‘elder brother’ term to the “uncle” types and their ‘younger brother’ term to the “nephew” types.

³⁴ This is the entire “child” class to a male. To a female it is only half of the “child” class. Cf. §7.5.

³⁵ Systems 196–7.

³⁶ Lev Šternberg, Semja i rod u narodov severo-vostočnoi Azii (Leningrad, 1933) ; Josef Haekel, Das Dreiclansystem, Sitzungsberichte der anthropologischen Gesellschaft in Wien, Jahrgang 1937-38.11-3 (issued with Mitteilungen d. A. G. in Wien, Vol. 68; 1938) ; Alexander Slawik, Zum Problem des Bärenfestes der Ainu und Giljaken, Wiener Beiträge zur Kulturgeschichte und Linguistik 9.189–203 (1952).

³⁷ William H. Gilbert Jr., Eastern Cherokee social organization, Social anthropology of North American tribes 283–338 (ed. Fred Eggan; Chicago, 1937, 1955) ; William H. Gilbert, The eastern Cherokees, Bureau of American Ethnology, Bulletin 133.169–414 (1943).

³⁸ It is obvious that if such a rule were consistently in operation, the society could consist of seven and only seven lineages. Perhaps it is not fortuitous that the Cherokee have seven sibs.

³⁹ The various discussions provoked by Kroeber's paper form a literature relevant to the ‘language and culture‘ problem. For a review of this, and another anthropologist's opinions, see A. R. Radcliffe-Brown, The study of kinship systems, Journal of the Royal Anthropological Institute 71.2 ff. (1941), reprinted as chapter 3 of Structure and function in primitive society (Glencoe, Ill., 1952), esp. 59 ff.

⁴⁰ George A. Dorsey and James R. Murie, Notes on Skidi Pawnee society (Field Museum of Natural History, Anthropological Series, Vol. 27, No. 2; Chicago, 1940); Alexander Lesser, Levirate and fraternal polyandry among the Pawnees, Man 30.98–101 (1930); id., The Pawnee ghost dance hand game (Columbia University Contributions to Anthropology, Vol. 16; N. Y., 1933). For additional bibliography on the Pawnee, see G. P. Murdock, Ethnographic bibliography of North America² 80–1 and 198 (New Haven, 1953).

⁴¹ The famous case is that of the Natchez. Cf. John R. Swanton, Indian tribes of the lower Mississippi Valley and adjacent coast of the Gulf of Mexico 100–8 (Smithsonian Institution, Bureau of American Ethnology, Bulletin 43; Washington, 1911); C. W. M. Hart, A reconsideration of Natchez social structure, American anthropologist 45.374–86 (1943).

⁴² Lesser, The Pawnee ghost dance hand game 42.

⁴³ I have discussed these in more detail in Psycholinguistics: A survey of theory and research problems 171–7 (C. E. Osgood and T. A. Sebeok, editors; Indiana University Publications in Anthropology and Linguistics, Memoir 10; 1954).

⁴⁴ Bloomfield, Language 139.

⁴⁵ Cf. Martin Joos, The description of language design, Journal of the Acoustical Society of America 22.701–8 (1950), esp. 708.

⁴⁶ As examples of such studies see Ward H. Goodenough, Property, kin, and community on Truk (Yale University Publications in Anthropology, No. 46; New Haven, 1951), and the papers by various authors in Fred Eggan (ed.), Social anthropology of North American tribes (Chicago, 1937, 1955).

⁴⁷ Works on Pawnee linguistics which may be consulted: J. Dunbar, The Pawnee language (appendix to G. B. Grinnell, Pawnee hero stories and folk-tales² 409–37; New York, 1893); Gene Weltfish, The vision story of Fox-Boy, a South Band Pawnee text, International journal of American linguistics 9.44–75 (1936); id., Caddoan texts (Publications of the American Ethnological Society, Vol. 17; N. Y. 1937).

⁴⁸ Cf. Bloomfield, Language 76–8.

⁴⁹ As in Bloomfield, Language 162; E. A. Nida, A system for the description of semantic elements, Word 7.1–14 (1951) ; and W. L. Wonderly, Semantic components in Kechua person morphemes, Lg. 28.366–76 (1952). In the latter two works, semes and sememes are not restricted to the meanings of morphs and morphemes, but may sometimes be identified with semantic components. In our suggested application of the terms, there could be no equating of sememe with semantic component any more than there is of equating phoneme with phonetic component.

⁵⁰ I am indebted to Roger W. Brown for these suggestions, which he offered in discussion of an earlier version of this paper at a Linguistic Forum meeting, Linguistic Institute, University of Michigan, in the summer of 1954.

⁵¹ The simpler approach has had a wide utility in phonemics. One may raise the question whether in the future it may be necessary to alter these procedures, especially in relating data on perception of phonemes to data on acoustics.