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A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan and Murdock to the Present

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This paper addresses typological relationships among kinship terminologies determined from structural differences in the way kin terms are organized as systems of concepts. Viewing a terminology as a system of concepts makes evident the generative logic of a terminology that starts with properties shared across several terminologies and eventually includes properties specific to a single terminology. These structural properties lead to a typology in which structural differences between terminologies form the branch points. The typology highlights two primary dimensions along which terminologies may be distinguished: (1) structural differences between terminologies and (2) variation in the morphology of the lexemic form of kin terms. Variation in the former relates to change constrained in the cultural domain and change in the latter relates to change constrained in the linguistic domain.
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Title:
A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan and
Murdock to the Present
Journal Issue:
Structure and Dynamics, 6(1)
Author:
Read, Dwight W, University of California, Los Angeles
Publication Date:
2013
Publication Info:
Structure and Dynamics, Social Dynamics and Complexity, Institute for Mathematical Behavioral
Sciences, UC Irvine
Permalink:
http://www.escholarship.org/uc/item/0ss6j8sh
Author Bio:
Department of Anthropology
Keywords:
terminologies, typology, generative logic
Local Identifier:
imbs_socdyn_sdeas_17982
Abstract:
This paper addresses typological relationships among kinship terminologies determined from
structural differences in the way kin terms are organized as systems of concepts. Viewing a
terminology as a system of concepts makes evident the generative logic of a terminology that starts
with properties shared across several terminologies and eventually includes properties specific to
a single terminology. These structural properties lead to a typology in which structural differences
between terminologies form the branch points. The typology highlights two primary dimensions
along which terminologies may be distinguished: (1) structural differences between terminologies
and (2) variation in the morphology of the lexemic form of kin terms. Variation in the former relates
to change constrained in the cultural domain and change in the latter relates to change constrained
in the linguistic domain.
A New Approach to Forming a Typology of
Kinship Terminology Systems
From Morgan and Murdock to the Present
Dwight Read
Department of Anthropology
University of California, Los Angeles
Los Angeles, California, USA
dread@anthro.ucla.edu
This paper addresses typological relationships among kinship terminologies determined
from structural differences in the way kin terms are organized as systems of concepts.
Viewing a terminology as a system of concepts makes evident the generative logic of a
terminology that starts with properties shared across several terminologies and eventu-
ally includes properties specific to a single terminology. These structural properties lead
to a typology in which structural differences between terminologies form the branch
points. The typology highlights two primary dimensions along which terminologies may
be distinguished: (1) structural differences between terminologies and (2) variation in the
morphology of the lexemic form of kin terms. Variation in the former relates to change
constrained in the cultural domain and change in the latter relates to change constrained
in the linguistic domain.
Introduction
The typology frequently used for kinship terminologies traces back to distinctions made
by Lewis Henry Morgan, Robert H. Lowie, Peter Kirchhoff, Leslie Spier and George Pe-
ter Murdock. The typology is derived from difference in the ways that kin terms identify
or categorize what are presumed to be primary genealogical relations. Morgan (1871)
made a division between descriptive versus classificatory terminologies according to the
way the terminology incorporates lineal and collateral genealogical relations. Descriptive
terminologies were said to distinguish lineal from collateral relatives and classificatory
terminologies were those that did not. However, ambiguity arises in this definition, as
noted by Morgan in his discussion of Eskimo terminologies (pp. 267-277), when lineal
and collateral positions are distinguished in the middle three generations but not for more
distant generations so that, for example, the child of one’s ‘niece’/‘nephew’—a collateral
relative, is referred to as ‘granddaughter’/‘grandson’—a lineal relative.
Lowie (1928) (and independently Kirchhoff [1932]; see Murdock [1968] and
Trautmann [1981:83]) added a parallel/cross contrast derived from Krober (1909) to
Morgan’s lineal/collateral distinction and worked out a four-part division of terminolo-
gies based on distinctions made in the parental generation. He referred to his four-part
division by the expressions Generation, Bifurcate Merging, Bifurcate Collateral and Lin-
eal terminologies.1 Of these, Generation and Bifurcate Merging fit in with Morgan’s clas-
sificatory terminologies and Bifurcate Collateral and Lineal with his descriptive termi-
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1
nologies. Subsequently, Murdock (1949), building from the cross-cousin distinctions
used by Lowie (1928) to form a typology of kinship terminologies, focused on the differ-
ences in kin terms for genealogically close kin in ego’s generation. He added Sudanese
and Eskimo terminologies to the four terminology types—Hawaiian, Iroquois, Crow and
Omaha—discussed by Lowie. Murdock’s six types are based on differences in kin terms
for genealogical sibling and cousin relations, with each type named for an exemplar soci-
ety having that kind of terminology. Despite explicit definitions, these typologies are
based on only a few kin terms from one or two generations and so the same terminology
may be classified differently, depending on the choice of the generation for the kin terms
used in the classification.
The intersection of Morgan’s two types with Lowie’s four groups and Murdock’s
six groups yields the following organization for these typologies: Descriptive—includes
Sudanese (a Bifurcate Collateral terminology with different terms for each kind of
cousin) and Eskimo ( a Lineal terminology with a single term for cousins who are all dis-
tinguished from siblings) and Classificatory—includes Hawaiian (a Generation terminol-
ogy in which siblings and cousins are not distinguished), Iroquois (a Bifurcate Merging
terminology with parallel cousins distinguished from cross cousins), Crow (a Bifurcate
Merging terminology similar to Iroquois, but without a distinction between fathers sister
and fathers sisters daughter), and Omaha (a Bifurcate Merging terminology similar to
Iroquois but one in which mother’s brother and mother’s brother’s son are not distin-
guished). Subsequently, the Iroquois class of terminologies in Murdock’s (1949) classifi-
cation was divided into Iroquois versus Dravidian terminologies based on an analytical
(etic) difference in these terminologies between the way parallel and cross relations were
distinguished. More recently, refined subdivisions of Murdock’s six classes have been
made (see Dziebel 2007:211-254 and Pericliev 2011:20-127), including Murdock’s
(1970) own, more extensive typology derived from over 1000 terminologies.
The classification system has substantial drawbacks since it is based on class
definitions that incorporate a mix of structural properties such as lineal versus collateral
relations and genealogical properties such as the way genealogical cousins and siblings
are distinguished terminologically. Even more problematic, the definitions for the types
of terminologies refer to surface differences in terminologies and not to the structural
properties leading to the structural form of a terminology. As noted by David Kronenfeld
(2004: 260): “The kinds of attributes or information that structure some contrasts between
types are quite different from the kinds that structure other contrasts.” In addition, the dis-
tinctions used by Murdock to define his types are not adequate as terminologies are
classed together that are obviously dissimilar from each other. The !Kung san and the
American/English terminologies are both classified as Eskimo terminologies, for exam-
ple, yet the two terminologies differ on almost every aspect other than superficially simi-
lar distinctions among genealogical cousins, uncles and aunts. Other terminologies, such
as the Shipibo terminology, do not fit into the typology system at all (Behrens 1984).
Rather than using surface differences among terminologies based on mapping kin
terms onto genealogical relations, a typology should be based on the structural properties
that generate those surface differences. The generating processes are where we find “na-
Structure and Dynamics, 6(1) (2013)
2
ture’s joints” to which a typology should conform in order for it to satisfy the hallmark of
being a better classification (Kronenfeld 2006). Distinctions made at the surface level of
kin terms focus, instead, on the result of structuring processes. Consequently, the com-
monly used method of distinguishing among kin terms by mapping them onto genealogi-
cal relations will group together as similar what are structurally different terminologies
when different structuring processes yield kin terms with similar genealogical definitions.
In addition, the genealogical distinctions may not be sensitive to differences in structur-
ing processes. To deal with these considerations, we need to first determine what the
generative, structural properties are and then classify terminologies according to differ-
ences arising from the structuring processes that have been identified.
Structural Properties of Kinship Terminologies
The structural properties we need for classifying terminologies can be derived from the
way users of a kinship terminology determine kin relations directly from the kin terms
without necessary reference to genealogy; that is, from the way a kinship terminology is a
cultural construct with an internal logic that makes it possible to use kin terms computa-
tionally in a logically consistent manner as a way to determine kin relations among indi-
viduals. This does not mean that genealogy is irrelevant to understanding kinship sys-
tems, only that there is a logic that organizes kin terms into an idea system that does not
derive from genealogical relations. The cultural idea system encapsulated in a kinship
terminology does relate back to genealogy through mapping kin terms to genealogical
categories, but the mapping is constructed from the properties of the kin term idea system
and not from the properties of a genealogical space, as has already been demonstrated
(see Read 2001, 2007), and the genealogical categories associated with kin terms are pre-
dictable from the logic that organizes the kin terms into an idea system (see Read 2001:
Figure 5, 2007:338-339, Figure 3).
The way kinship relations are calculated directly by users of a kinship terminolo-
gies from kin term concepts was expressed succinctly by Anthony Good (1981) in his
discussion of the terminology for the Kondaiyankottai Maravar of India: “If ego knows
what term to use for alter A, and also knows what term A uses for alter B, he can easily
work out what term he himself should use for B” (Good 1981:113). Other ethnographers
(e.g., Behrens 1984; Dousset 2008; Levinson 2006; Radcliffe-Brown 1913, among oth-
ers) have made similar observations about calculating kin term relations between two
persons by referring to the kin term relation each has to a third person.
We can formalize this kind of computation by defining a kin term product (Read
1984) as follows: “If ego (properly) refers to alter 1 by the kin term L and alter 1 properly
refers to alter 2 by the kin term K, then by the product of K and L, denoted K o L, is
meant a kin term (if any) ego properly uses to refer to alter 2.” To illustrate, using
American/English kin terms, if ego (properly) refers to alter 1 as uncle (= L) and alter 1
properly refers to alter 2 as daughter (= K), then ego properly refers to alter 2 as cousin
(= K o L) and so daughter of uncle is cousin, or more formally, daughter o uncle =
cousin, as shown in Figure 1.
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From the kin term product we may “read off” the relative product, “my uncle’s
daughter is my cousin.” Whereas a relative product has to do with the product of genea-
logical relations between persons constructed from parent-child and spouse relations, the
kin term product is defined over kin terms. The kin term product calculations make it
evident that “there are formal, structural relationships in the terminology which do not
derive from particular, behavioral uses to which the terminology may be put. … [and so]
the structure should not be represented by means of a pseudo-genealogical diagram”
(Good 1981:113). Instead, we can display diagrammatically the structural relationships
among the kin terms by computing all possible kin term products using the kin terms that
express the “relationships within the elementary family, viz. The relation of parent
and child, that of husband and wife, and that between siblings” (Radcliffe-Brown 1950:6;
see also Murdock 1949:93-94). For the American/English terminology (hereafter AKT),
we obtain, through elicitation (Leaf 1971, 2006), kin term product equations that deter-
mine the structure of the AKT by starting with the concept of self and then repeatedly tak-
ing products with the primary kin terms father, mother, son, daughter, husband and wife.
For example, we elicit the kin term grandfather from English speakers by asking: If ego
refers to alter 1 by the kin term father and alter 1 refers to alter 2 by the kin term father,
then what is the kin term ego uses properly to refer to alter 2? When we are informed that
ego would refer to alter 2 by the kin term grandfather, we have elicited the kin term
product equation father of father = grandfather. Similarly, we find that father of mother
= grandfather by asking: If ego refers to alter 1 by the kin term mother and alter 1 refers
to alter 2 by the kin term father, then what is the kin term ego uses to refer to alter 2? Be-
cause we are informed that ego would refer to alter 2 by the kin term grandfather, we
now have the kin term product equation father of mother = grandfather. We continue in
Alter 1
ego Alter 2
uncle daughter
cousin
Kin Term Product
daughter of uncle is cousin
Figure 1: Kin term product equation for the kin terms
uncle, daughter and cousin.
Structure and Dynamics, 6(1) (2013)
4
this manner and elicit other kin term product equations such as: mother of father =
grandmother = mother of mother, son of father = brother = son of mother, daughter of
father = sister = daughter of mother, and so on.
We can elicit the kin term product equations systematically, beginning with the
kin terms that express the primary relations as identified by Radcliffe-Brown. Thus we
begin by asking, “If ego refers to alter 1 by a primary kin term and alter 1 refers to alter 2
by a primary kin term, then what is the kin term, if any, ego uses to refer to alter 2.” The
reply is likely to be a kin term that is not one of the primary kin terms. We continue in
this manner, systematically, until we have formed all possible questions using the primary
kin terms both for reference to alter 1 and for reference to alter 2. For any kin term, L,
received in reply that is not a primary kin term, we then ask all possible questions of the
form “If ego (properly) refers to alter 1 by the kin term L and alter 1 (properly) refers to
alter 2 by a primary kin term K, then what is the kin term ego (properly) uses to refer to
alter 2?”, where L is one of the kin terms that has just been elicited and K is one of the
primary kin terms. We will receive as a reply either (1) a kin term we have not elicited so
far; e.g., for the AKT, when we use the kin term L = grandfather and K = son and ask
“How do you refer to son of grandfather?”, we would obtain the previously unsolicited
kin term uncle, (2) a kin term we have already elicited; e.g., when we use the kin term L
= cousin and K = son, we may receive the reply, cousin, an already elicited kin term, or
(3) in some cases the reply may be that there is no such kin term; e.g., when we use the
kin term L = father-in-law and K = father, then we would receive the reply that there is
no kin term corresponding to the kin term product father of father-in-law. For a sequence
of kin terms such as grandfather, great grandfather, great great grandfather, in the
AKT, it would be evident that the kin term sequence continues with a regular pattern for
forming each of the kin term expressions. In this way, the elicitation procedure makes it
possible not only to determine the kin terms making up the kinship terminology, but also
its conceptual boundaries.
Along with the kin terms making up the terminology, we have also elicited a
structure for the terminology through the products with the primary kin terms. We can
display this structure by starting with a node labeled by the self concept, then letting each
of the primary kin terms and each of the elicited kin terms be a node in the graph of the
structure. We show the connections among the nodes by drawing an arrow from a kin
term L to the kin term elicited when forming a kin term product of the kin term L with a
primary kin term K. We distinguish products with different primary terms through an
arrow form (shape of arrow head, kind of line used for the shaft) specific to a single pri-
mary kin term. For example, corresponding to the kin term product equation son of fa-
ther = brother, we draw an arrow corresponding to the primary term son from the kin
term father to the kin term brother, as shown in Figure 2.
Figure 2 shows the kin term map we obtain for the AKT from this elicitation pro-
cedure. All kin terms are represented by a node in the structure and the arrows from any
kin term, L, point to the kin terms obtained when taking a product with the primary kin
terms and the kin term L. For example, arrows corresponding to son and daughter point
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from the kin term aunt to the kin term 1st cousin due to the fact that (son or daughter) of
aunt is 1st cousin. The equal sign, used to indicate a product with the spouse term, links
aunt and uncle since spouse of aunt is uncle and spouse of uncle is aunt.
By comparing kin term maps for different terminologies we make evident struc-
tural differences among kinship terminologies. The kin term map for the Shipibo termi-
nology (see Figure 3; the Shipibo are a horticultural group in eastern Peru) differs strik-
ingly from the kin term map for the AKT (compare Figures 2 and 3) and we can immedi-
ately see structural differences such as the horizontal symmetry that only occurs in the
Shipibo terminology versus the “ladder-like” vertical structures for the lineal terms and
the descending collateral terms in the AKT. The kin term map for the !Kung san termi-
nology (see Figure 4) is equally striking in its differences from the kin term maps for the
AKT and the Shipibo terminology. Yet another kin term map that also shows structural
properties unlike these three terminologies can be seen with the kin term map for the Kar-
iera terminology (see Figure 5). These differences in terminology structure can be related
to differences in some aspects of their respective forms of social organization.
Relationship Between Terminology Structure and Social Organization
The ladder-like structure in the AKT (see Figure 2), which is derived from a sin-
gle line of ascending parent products and descending child products, makes evident the
Figure 2: Kin term map for the American Kinship Terminology, based on the primary kin terms
father, mother, son, daughter, and spouse. Male terms are black, female terms are grey, and neu-
tral terms are bold and in black (here and in the other figures). Etc indicates that the kin term
map continues in the same way without any structural changes.
Structure and Dynamics, 6(1) (2013)
6
way in which the terminology conceptually expresses a lineal structure reflected in the
(previously traditional) practice among English speakers of a woman and her children
taking on the name of her husband even though lineal descent groups are not culturally
recognized. The terminology already provides a structural model for vertical relations,
hence the lineal device of tracing to a common ancestor for defining the vertical
dimension is not needed. Horizontally, the terminology structures kin into “lines.” Ac-
cordingly, one measure of kinship “closeness” would be the number of lines that are
crossed to reach a term for someone in one’s own generation: siblings are closer relatives
than first cousins, who are closer relatives than second cousins, and so on. By this crite-
rion, nephews and nieces should be closer relatives than aunts and uncles and this is the
case in Canadian immigration law for sponsorship: “The relationship between the Spon-
sor and the Sponsored Person … must be one of the following … [b]rother, sister,
nephew, niece …” (Anonymous 2012, emphasis added). Though parents are also in-
cluded as possible Sponsored Persons, uncles and aunts are not.
The symmetry of the Shipibo terminology (see Figure 3) is reflected in the sym-
metry of the women’s designs used to decorate pottery, clothing, faces and other parts of
the body: “the intricate permutations of symmetry and tessellations were common knowl-
Figure 3: Kin term map for the Shipibo kinship terminology. The parental terms
are papa (‘father’) and tita (‘mother’) and reciprocally bake (‘child’). Ea is the
central, self position. The kin terms pui and huetsa depend on the sex of speaker.
The suffix, -f, has been added to denote the usage of these terms by a female
speaker. Kin terms are from Behrens 1984.
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7
edge and skills ... with which the Shipibo women artists effortlessly expelled from their
imaginations the most affecting and intricate arrays” (Roe 2004:240, emphasis added).
The symmetry is expressed through a continuous line depicting the forms making up the
symmetry of the design, a continuity that relates to therapeutic aspects of curing and be-
witching shamanistic practices (Roe 2004:254).
Another dimension for the Shipibo where we find a parallel between the structure
of terminologies and other conceptualizations is in their distinction between, and integra-
tion of, a male and a female domain. While many terminologies have terms whose mean-
ing depends on the sex of speaker, these usually reflect a structural division into male
terms and female terms (see Read 2007; when the same lexeme is used by both males and
females, difference in meaning arises from whether the meaning is by reference to the
male structure or to the female structure of kin terms). The male-female distinction
among the Shipibo kin terms has a different structural basis. A single structure accounts
for all the terms, whether male marked or female marked, but unambiguous mapping of
the terms onto genealogical positions requires, for some of the terms, that the sex of
speaker be taken into account. It is precisely for these terms where the meaning of a term
depends on the sex of speaker. To put it another way, the terminology includes both sepa-
ration of male from female and their integration within the framework of a single struc-
ture. The same pattern is widespread in Shipibo life, as they are “[t]ied together by a per-
vasive sexual division of labor, an iron embrace of segregation of tools, tasks, and spaces,
but united by their mutual complementarity” (Roe 2004:255, emphasis added).
Structure 1
Structure 2
tun!ga (ws)
!ku!na (ms)
!ku!na (ws)
tun (ms)
=
=
tsu //ga
Male Terms Female Terms
ba
(!father")
tai
(!mother")
[male self, female self]tsin
(!younger sibling")
!ko (!older brother")
!kwi (!older sister")
reciprocal terms:
!tum
(!son-in-law")
/otsu
(!daughter-in-law")
!hai
(!daughter")
!ha
(!son")
[tsiu
(!wife"),
!kwa
(!husband")]
/otsu
(!mother-in-law")
!tum
(!father-in-law")
Family Terms!-in-law" Terms
n!unba
(!father" of /otsu,
!tum)
n!untai
(!mother" of /otsu,
!tum)
=
=
=
=
=
Name giver/
Name receiver
=
ba (!father")
tai (!mother")
!hai (!daughter")
!ha (!son")
=
!spouse"
tsin (!younger sibling")
Figure 4: Kin term map for the !Kung san kinship terminology. Structure 1 has the
kin terms for the family positions and Structure 2 encompasses all other kinship posi-
tions. The two structures are linked by the name-giver/name-receiver relationship.
Kin terms are from Marshall 1976.
Structure and Dynamics, 6(1) (2013)
8
This division into male versus female also relates to designs versus figures: “Thus
the Shipibo … form yet another representative of the cross-cultural trend statement men :
figural :: women : geometric designs(Roe 2004:275). The association of women with
pattern expressed through design includes patterning in kinship and other aspects of cul-
tural knowledge: "Women are repositories of traditional knowledge and I found that,
when I asked men questions about kinship, language or folklore, they often deferred to
their wives on these matters" (Behrens 1984:372).
The very different kin term map for the !Kung san (see Figure 4) emphasizes the
horizontal dimension formed through sibling and spouse links and eliminates the vertical
dimension through not having kin terms defined by kin term products such as ba of ba
(‘father’ of ‘father’). Instead, the vertical dimension is expressed through the name giver/
kundal (ʻdaughterʼ)
=ñuba (ʻspouseʼ)
toa (ʻmotherʼ)
maiñga (ʻsonʼ)
mama (ʻfatherʼ)
turdu
mari
=
kumbali
kaja
margara
ñuba
=
kandari
=
tamimaeli kabali
=
toa
=
kaga
mama nganga
=
kundal
=
kuling
maiñga ngaraia
=
maeli*
=
tamimaeli tami*
=
mari (ʻdescending sisterʼ)margara (ʻdescending brotherʼ)
kaja (ʻascending brotherʼ)turdu (ʻascending sisterʼ)
Figure 5: Kin term map for the Kariera terminology from the perspective of a male
speaker. Terminology has both parental (mama [‘father’], nganga [‘mother’]) and sibling
(kaja [‘elder or ascending brother’], turdu [‘elder or ascending sister’]) primary terms.
The term ñuba [‘cross-cousin’] is used structurally for the spouse relation. Black: male
marked terms; gray: female marked terms; and bold: neutral terms. The diagram is modi-
fied from Radcliffe-Brown 1913: Table 1.
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9
name receiver relationship that divorces the terminology from a genealogical structure.
Conceptually removing the vertical dimension and replacing it with a horizontal
dimension could hardly be structurally more complete and still have the functionality of a
viable kinship terminology. The horizontal dimension for the kin terms carries over ex-
plicitly to the structure of residence groups. Residence groups are composed of families
linked to one another through sibling and spouse links (Lee 1979, see especially Figure
3.6) and are the opposite of descent groups based on a vertical dimension formed through
tracing to a common ancestor. The residence group is neither unilineally nor cognitively
a descent group, as it is not the vertical dimension of ancestry that determines member-
ship, but the horizontal dimension of sibling hood and spouse hood emphasized in the
kinship terminology.
Finally, the relationship between the self-centered kinship terminology of the Kar-
iera and their socio-centered social organization as a four-section system is well-known.
The section system derives from “collapsing” the structure shown in Figure 5 vertically
into two levels: 0, ±2 generation terms versus ±1 generation terms and horizontally into
the first and fourth column of terms versus the second and third columns of terms, where
the combined columns are composed of terms linked by a sibling relation. The intersec-
tion of these two “collapsings” yields four sets of kin terms that then divide the domain of
kin into four groups. This is not yet a section system as it must be shown that the divi-
sion of kin into four groups is the same regardless of the reference person. That the sub-
jective grouping made by a single individual is an objective grouping for everyone is
proven mathematically in Leaf and Read (2012). Thus the four-section system can be
viewed as resulting from the Kariera recognizing a structure for the social organization of
their society that emerges from the structural properties of their kinship terminology.
The associations between terminological structure and structures found in the
forms of social organization seen in these examples is not a simple one of A causes B.
Neither the terminology structure of the Kariera causes them to have a four-section sys-
tem nor does the symmetry of the Shipibo terminology cause them to employ symmetry
extensively in designs drawn by women. Rather, the connection is through patterning
made available to them through the structure of their terminology. Patterning in one do-
main can be transformed into pattern in another domain. There is asymmetry in this rela-
tionship, though, as it is unlikely that patterning in designs or patterning in residence
groups determines whether an ensemble of persons will have a kinship terminology with
structure similar to already existing patterning in other domains. What these examples
imply is that we, as culture-bearers, are aware, at some cognitive level, of patterning in
the structure of our system of kinship relations that then becomes the basis, or a model,
for constructing similar patterning in other domains (cf. Bennardo and Read 2007).
Generation of Structure
The structural differences among these kin term maps raises the question: Do the struc-
tural differences arise from factors extrinsic or intrinsic to the terminology? The answer is
determined by asking yet another question: Can the structural form of a kinship terminol-
ogy be generated, using kin term products, from a set of primary kin terms and structural
Structure and Dynamics, 6(1) (2013)
10
equations satisfied by the kin term products? The answer is yes, hence the structural dif-
ferences are intrinsic. How the question is answered for each terminology provides us
with the basis for forming a typology of kinship terminologies according to the
generative structural logic underlying the form of a kinship terminology. While our for-
mal representation of that generative structural logic is not at the level of the cognizant
awareness of culture bearers, there must be neurological processes and functioning
through which this structural logic is implemented. Whereas the kin term map provides
us with a description of structure, the generative logic informs us that that structure arises
from neurological processes acting on neurological representations corresponding to the
primary concepts and relations structuring the system of kinship ideas and concepts
expressed through a kinship terminology. Just as the grammar of a language is not a lit-
eral representation of what is occurring at the neurological level but expresses linguistic
organization and structure produced through neurological processes, the same is must be
true of the generative logic of a terminology. The computations we make are our way of
representing to ourselves the outcomes of neurological processes even though do not yet
know precisely what mental representations and what neurological processes are involved
when we make a computation such as child of uncle is cousin. That we make such com-
putations, and especially the fact that we agree on what such computations yield, requires
that our overt, symbolic representations in the form of kin terms that we can manipulate
consciously reflects something that is happening at a deeper, neurological level. We are
not imposing structure on kinship terminologies when we uncover a generative logic, but
making evident what already exists at the cognitive/neurological level.
The generative logic of kinship terminologies has now been worked out for
enough terminologies to outline a typology for terminologies based on structural proper-
ties. Comparisons of terminology structures already provides new insights into relation-
ships among kinship terminologies and to aspects of social systems related to the
generative logic of kinship terminologies as discussed above.
One important result is that there is no universal structural form from which all
extant kinship terminologies are evolutionarily derived (contra Allen 2008). Instead,
there are at least three different structural forms for kinship terminologies, no one of
which can be evolutionarily derived from the other two. The common basis for termi-
nologies is not a particular structure but commonality in the way in which kinship termi-
nology structures are generated (Read 2007; Leaf and Read 2012). Examples of these
three different structures are provided by the AKT, the Kariera and the !Kung san termi-
nologies. Of these three terminologies, the !Kung san differs from the other two by hav-
ing two structures joined through a naming relationship created when a newborn child is
given the name of a close relation (Marshall 1976) (compare Figure 4 with Figures 2 and
5). In this terminology, kin term relations more distant than immediate family relations
(see Structure 2 in Figure 4) do not have a fixed genealogical relation to a new born
(Marshall 1976), hence these terms do not have a simple genealogical definition.2 In-
stead, a child has a close relation with his/her name giver and then has kin relations with
other individuals by reckoning kin relations from the perspective of one’s name giver,
using Structure 2 in Figure 4 (Marshall 1976).
Read: A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan an...
11
For the other two terminologies, the Kariera terminology differs structurally from
the AKT by having sibling terms, kaja and turdu, as generating terms, whereas brother or
sister in the AKT are compound terms defined through the kin term product (son or
daughter) of (father or mother). More precisely, the AKT has a single ascending kin term
generator, parent (Read 1984; Read and Behrens 1990), whereas the Kariera terminology
has both mama (‘father’) and kaja (‘elder or ascending brother’) as generating terms for
the structure of male-marked ascending kin terms and structurally introduces female
marked terms through an isomorphic copy of the structure of male marked terms (Leaf
and Read 2012). This implies that the AKT can be transformed into the Kariera termi-
nology (and vice-versa) only by redefining what are the primary terms from which each
of the two structural forms can be generated, which is not a structural transformation but
a redefinition of generating element(s).
Despite the structural differences among these three terminologies, there is a uni-
versal generative sequence for the construction of a kinship terminology structure, start-
ing with self and one (or two) ascending generators. This sequence is as follows, using
the idea that the structure of a kinship terminology is a series of layers.
1. Center Position
The center position of the terminology is a self position, which may be sex marked de-
pending on the terminology (see Figure 6A).
2. Ascending Structure
Form a structure of ascending terms, where an ascending term expresses a kinship rela-
tion between ego and an alter who is before ego in a birth order sense. The primary as-
cending terms consist of a set of parental terms = {‘father’, ‘mother’, ‘parent’} and some-
times a set of sibling terms = {‘older or ascending brother’, ‘older or ascending sister’,
‘older or ascending sibling’}. (The single quotes indicate that the English words are the
closest translation of the kin term being considered.) All terminologies use a parental
term as an ascending generating term and generally use the kin term product to generate a
structure of ascending terms, beginning with the self position (see Figure 6 B; the !Kung
san terminology is an exception). The extensiveness of the ascending structure varies
from the !Kung san terminology with an ascending structure consisting of a single step
(see Structure 1 in Figure 4) to an unending ascending structure as occurs withe the AKT
and several of the other European terminologies. The classificatory terminologies differ
by using a sibling term, as well as the parental term, to generate the structure of ascend-
ing terms.
Any limitations on the vertical extensiveness of the ascending structure are
expressed through structural equations satisfied by kin term products using the primary
ascending terms. The AKT has no such structural equations whereas the Shipibo termi-
nology has the equation papa of papa of papa of papa = papa of papa of papa that pro-
vides a conceptual, vertical boundary for the ascending kin term structure. Terminologies
with a sibling term as a generator will have structural equations such as ‘older brother’ of
‘older brother’ = ‘older brother’ expressing the reflexive property of a sibling term and an
equation such as ‘father’ of ‘older brother’ = ‘father’ expressing the structural relationship
Structure and Dynamics, 6(1) (2013)
12
between an ascending generating term such as ‘father’ and a sibling generating term such
as ‘older brother’.
3. Descending Structure
The next layer is a descending structure isomorphic to the ascending structure, meaning
that the descending structure has the same number of generators as the ascending struc-
ture. The descending structure uses the same self term as does the ascending structure.
Each structural equation for the ascending structure is repeated as a structural equation
for the descending structure, but written with the corresponding descending generator in
place of an ascending generator (see Figure 6C). Thus, the AKT has a descending struc-
ture with generating term, child, in place of the generating term parent for the ascending
Figure 6: Outline of the first part of the procedure for generating a kinship terminology, illus-
trated with the American Kinship Terminology. (A) Self concept forms the central position of a
terminology structure. (B) An ascending structure is generated from {self, parent}. (C) A de-
scending structure based on {self, child} is generated isomorphic to the ascending structure. (D)
The structural equation parent of child = self defines parent and self to be reciprocal kin terms.
Cross products between ascending and descending terms are formed and reduced using the equa-
tion for reciprocal generating terms. Each generated position corresponds to a kin term or a pair
of kin terms, in the American Kinship Terminology.
Read: A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan an...
13
structure. There is no structural equation for the descending structure in the AKT since
its ascending structure has no structural equation.
4. Reciprocity
Reciprocity, a central concept for kinship systems, is structurally expressed between an
ascending generator and a descending generator by a structural equation of the form (as-
cending generating term) of (descending generating term) = self or, for the AKT the
equation parent of child = self (see Figure 6D). The equation for the AKT is motivated
by kin term products. If ego refers to alter 1 by the kin term child and alter 1 refers to
alter 2 by the kin term parent, then alter 2 must be ego since in the construction at this
point we do not yet have affinal relations and so ego refers to alter 2 by the term self,
hence the equation parent of child = self. We also include all possible products between
the ascending and the descending generating terms (see Figure 6D). For the AKT, the kin
term products defined in this manner correspond to kin terms in the kinship terminology;
e.g., child of parent = [brother, sister], child of parent of parent = [uncle, aunt], child of
child of parent of parent = cousin, and so on.
5. Sex Marking
Next, sex differences among kin terms are introduced through one of two means. (A) In-
troduce sex marking attributes, call them M (male) and F (female), into the set of generat-
ing terms with appropriate structural equations such as M o M = M = M o F, F o F = F =
F o M, and K o M = K o F= K, for any kin term K. Sex marking is represented by a
product such as M o K or F o K. For example, in the AKT, parent becomes sex marked
by forming and labeling the products M o parent = father and F o parent = mother. (B)
Form an isomorphic copy of the ascending and descending structure, with the initial
structure interpreted as male marked terms and the isomorphic copy as female marked
terms (or vice-versa). The two structures are joined to form a single structure using ter-
minology specific structural equations. This procedure is ubiquitous among the classifi-
catory terminologies and occurs with some of the descriptive terminologies such as the
Polish terminology (Lee, personal communication). There are several different ways the
two structures can be joined and three of these ways create the Kariera-like terminologies
(Leaf and Read 2012), the Polynesian and other Oceanic terminologies (Read 2013), and
the Dravidian terminologies (Read 2010).
6. Affinal Terms
Lastly, affinal terms are introduced, either by introducing a spouse generating term in the
structure (along with appropriate structural equations such as S o S = S [read: “spouse of
spouse is spouse”] and S o P= S [read: “spouse of parent is parent”], where S is the
spouse generating term and P is the ascending generating term), or by identifying an ex-
isting term as a spouse term as occurs in terminologies such as the Kariera terminology
where ñuna (‘cross-cousin’) is the term used to refer to spouse by a male or a female
speaker (see Figure 5).
7. Rules For Local Structure
Structure and Dynamics, 6(1) (2013)
14
Additional structural properties may be introduced, such as, for the AKT where limita-
tions are placed on which terms remain sex marked and there are structural rules for the
elaborated cousin terms. In the AKT, a kin term, K, remains sex marked only if S o K is
a kin term (read: “Spouse of K is a kin term”) or S o Kr is a kin term (read: “Spouse of
the reciprocal term for K is a kin term”); e.g., the sex marked kin terms father, mother,
son and daughter are in the AKT since spouse of father = mother, spouse of mother = fa-
ther and son and daughter are the reciprocal terms for father and mother. In contrast,
cousin is not sex marked since spouse of cousin is (logically) not a kin term.
8. Cultural Modifications
Finally, local modification of the terminology may be made using cultural criteria exter-
nal to the terminology, such as the kin term ‘younger brother’ of ‘mother’ in the Tongan
terminology is introduced for reasons relating to inheritance (Bennardo and Read 2007).
With this as background, we can now outline an initial typology for kinship ter-
minologies.
Typology for Terminologies
Level 1: Variation in the content of Generating Sets
The first division in the typology will be based on differences in the content of the gener-
ating set for the ascending structure. We will distinguish between terminologies with a
single parental (ascending) generating term and terminologies with both a parental gener-
ating term and an ascending sibling generating term. This distinction corresponds to
Morgan’s descriptive versus classificatory terminologies, respectively (Read 2007; Read
and Behrens 1990; Bennardo and Read 2007; Leaf and Read 2012). The correspondence
between generating sets and descriptive and classificatory terminologies (often referred to
as bifurcate merging terminologies) arises for the following two reasons. First, when
there is a single parental generating term, it logically follows that collateral kin term posi-
tions will be distinguished from lineal kin term positions as long as there is no structural
equation of the form descending generator of ascending generator = self (see Figures 2-
3). Second, when there is both a parental generating term and a sibling generating term,
the kin term product equations ‘brother’ of ‘father’ = ‘father’ and ‘sister’ of ‘mother’ =
‘mother’ that characterize classificatory terminologies (see Figure 5) are the logical con-
sequence of the general procedure for generating a kinship terminology as discussed
above (for details, see Read and Behrens 1990; Bennardo and Read 2007; Read 2007;
Leaf and Read 2012).
That the concept of sibling can give rise to a generating term is corroborated by
ethnographic observations of indigenous groups with classificatory terminologies such as
the Kaluli of New Guinea who, when working out kin relations, “frequently invoke a sib-
ling relationship as the link that explains the application of a term--’I call him brother be-
cause my father calls his father brother.’ … the sibling relationship takes precedence over
descent whenever the principles are in conflict” (Schieffelin 1976:54, 55, emphasis in the
original). Similarly, the Tangu of New Guinea consider that “siblingship is the determi-
nant that descent [parent-child links] might have been expected to be … descent was
Read: A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan an...
15
probably always calculated from siblingship and siblingship rather than descent al-
ways provided the definitive norms of social behavior” (Burridge 1959/60:128, 130). In
the Polynesian and Oceanic area there are numerous references to the centrality of sib-
lings, especially siblings of opposite sex, in a group’s cultural conceptualizations regard-
ing kin relations (Marshall 1983).
Not all terminologies are descriptive or classificatory. The !Kung san terminol-
ogy is neither one nor the other since the terms for the family relations are not used to
generate additional kin terms; for example, there is neither a kin term corresponding to ba
(‘father’) of ba (‘father’) nor to tai (‘mother’) of tai (‘mother’). Instead, as discussed
above, the terminology has two disjoint structures linked by the name giver/name re-
ceiver relationship made active when naming a newborn child. Consequently, there are
two sets of generating elements, each corresponding to one of these two structures.
Since there is no structural transformation connecting these three structural forms,
we include (at least) three distinct root structures for kinship terminologies: (1) descrip-
tive terminology structures with a single parental generating term, (2) classificatory ter-
minology structures with a parental generating term and a sibling generating term, and (3)
other terminology structures such as the !Kung san terminology. Under (3), we leave
open the possibility that other structural forms may be identified as the generative logic
for a wider variety of terminologies is worked out.
Now consider variants on the generating set for the ascending structure. First we
consider the descriptive terminologies.
Descriptive Terminologies
Level 2a: Sex Marking of Generating Terms
Variants include:
(1) a generating set where the parental term is not sex marked;
e.g., {self, parent} is the generating set for the AKT ascending structure and parent is not
sex marked (see Figure 2),
(2) a generating set where the self term and the parental term are already sex
marked, so that there will (initially) be generating sets for the ascending male terms
and for the ascending female terms;
e.g., {male self, papa (‘father’)}, {male self, bap (‘father’)}, and {male self, ojciec (‘fa-
ther’)} are the respective generating sets for the male ascending terms in the Shipibo
(Figure 3), Punjabi (Figure 7), and Polish terminology (Figure 8). The corresponding
generating sets for the ascending female terms for these three terminologies are {female
self, tita (‘mother’)}, {female self, ma (‘mother’)}, and {female self, matka (‘mother’)},
respectively.
Level 2b: Ascending Structural Equations
The ascending structure may have different structural equations. For example, the
Shipibo terminology has the boundary condition (using ba [‘father’]): ba of ba of ba of
Structure and Dynamics, 6(1) (2013)
16
ba = ba of ba of ba. The Punjabi terminology has a different boundary condition (using
bap [‘father’]): bap of bap of bap of bap of bap = 0. The difference in boundary condi-
tions relates to differences in whether ancestors are considered to be relatives in the sense
of kin terms used to refer to them (Shipibo) or not (Punjabi) (Leaf and Read 2012).
Level 3: Sex Marking of Kin Terms
At the next level in the typology are differences in the way sex marking of kin terms is
implemented, depending on whether the initial generating elements are sex marked. For
the AKT, what are initially neutral generating terms are bifurcated into sex marked terms;
e.g., parent [mother, father] by incorporating sex marking elements as discussed
above so that mother = F o parent and father = M o parent. In the Polish, Shipibo and
Punjabi terminologies, the ascending + descending structure based on male terms and the
isomorphic copy of this structure based on female terms are already disjoint structures of
male terms and female terms. For terminologies like this, the sex marked terms initially
form disjoint sets and so they must be joined to form a single structure of male marked
and female marked terms. There are several ways that this has been implemented, de-
pending on the cultural context, with each way based on the fact that the structure of
terms marked with a single sex includes a sex marked self position, either male self or
female self depending on whether it is part of a structure of male terms or a structure of
female terms.
Figure 7: Kinship map for the Punjabi terminology (Leaf 1971). The diagram uses a kinship
map rather than a kin term map. The kinship map contains the same structural information as
does the kin term map, but is constructed directly from the elicitation procedure using the method
given in Leaf 2006. Note that the patrilateral terms extend upward one more generation than do
the matrilateral terms.
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17
One way a single structure is formed is by taking the set union of the two struc-
tures and introducing a covering self term for the male self and female self terms, so that
self = [
female self, male self] becomes the central position in both the structure of male
terms and in the structure of female terms. Then structural equations are added, as ap-
propriate, for products of male marked generating terms and female marked generating
terms. Examples of using this method for joining the structures are the Shipibo terminol-
ogy (Figure 3) and the Punjabi terminology (Figure 7).3
A second way, which applies to the Polish terminology, is through interpreting
each of male self and female self as a kin term from the viewpoint of a speaker with the
opposite sex of the sex marked self term. For the Polish terminology structure, female
self is interpreted as żona (‘wife’) for a male speaker and male self is interpreted as mąż
(‘husband’) for a female speaker. żona is formally represented by the kin term product
equation żona = female self of male self and mąż by the kin term product equation mąż =
male self of female self (see Figure 8). Thus neither żona nor mąż are additional, primary
generating terms.
Additional differences may be introduced in the typology relating to the way affi-
nal terms and other structural properties are introduced into the terminology structure.
These are not discussed here but see Read 2007; Read and Behrens 1990; and Leaf and
Read 2012 for details.
Classificatory Terminologies
Level 2a: Sex Marking of Generating Terms
ojciec
bratanka
syn
dziad
stryj
brat
stryjeczny siostra
wujeczna
matka
siostrzenica
co!rka
wnuczka
babka
[m, f]
m f
fm
wujstryjna
stryjenkamstryjenka
stryjecazny
dziad
stryjecazny
babka
siostra
stryjeczna
wujna pociot
ciotka
brat
wujeczny
siostra szwagler
prababka
pradziad
cioteczna
babka ze
strony cjca
cioteczny
dziad ze
strony cjca
cioteczna
babka
cioteczny
dziad
wujecny
dziad
wujecna
babka
siostra
cioteczna
ze strony
cjca
brat
cioteczny
ze strony
cjca
brat
cioteczny
siostra
cioteczna
siostrzenica siostrzeniec
siostrzenica
syn
siostrzenicy
co!rka
siostrzenicy
syn
bratanka
co!rka
bratanek
bratanicy
co!rka
bratanicy
syn
bratanica synsynowa
wnuk
pra-
wnuk
pra-
wnuczka
brat
bratowa
co!rka zien,c!
ojciec
matka
syn
co!rka
"wife!
"husband!
Figure 8: Kin term map of the Polish terminology. Primary generating terms are ojciec (‘father’)
and male self. Based on personal communications with Jacob Lee (2004, 2009).
Structure and Dynamics, 6(1) (2013)
18
Classificatory terminologies consider to date are based on sex marked generating terms,
including the self term, though it may yet be found that some classificatory terminologies
make use of non-sex marked generating terms.
Level 2b: Ascending Structural Equations
For classificatory terminologies, the ascending structural equations imply (see Bennardo
and Read 2007; Leaf and Read 2012 for details), when constructing the isomorphic de-
scending structure, both the equations ‘brother’ of ‘father’ = ‘father’ and ‘son’ of
‘brother’ = ‘son’ and an ‘older’/‘younger’ distinction (more accurately, an ‘ascending’/
‘descending’ distinction; see Leaf and Read 2012) for ‘brother’ terms. Inclusion of a sib-
ling generating term accounts for the the distinction between descriptive and classifica-
tory terminologies and this difference in a generating set provides an unambiguous defi-
nition for each of these two classes of terminologies in place of Morgan’s ambiguous
definition based on difference as to whether the kin terms distinguish collateral from lin-
eal relations.
Level 3: Sex Marking of Kin Terms
Sex marking of kin terms is by making an isomorphic copy of the structure of ascending
+ descending kin terms. To date, three ways have been determined for joining the struc-
ture of male terms and of female terms into a single structure.
Variant (1)--Oceanic Terminologies with male self for a female speaker and fe-
male self for a male speaker interpreted as ‘cross-sex sibling’ terms. As a consequence,
there is no ‘older’/‘younger’ distinction for ‘cross-sex sibling’ terms. This leads to many
of the Oceanic classificatory terminologies (see Figure 9). Additional variants relate to
alternative ways in which reciprocity of the sibling terms is defined structurally and ac-
count for variation in the structural form of the sibling terms in the Polynesian terminolo-
gies that, in turn, leads to a historical reconstruction consistent with the geographical and
time sequence for the colonization of the Polynesian Islands (Read 2013).
Variant (2)--Australian Kariera-like terminologies with and ‘older/’younger’ dis-
tinction for sibling terms regardless of sex of speaker. The linkage between the structures
of male marked and female marked terms is through the ‘older/younger same sex sibling’
terms. In this case there will be an ‘older’/‘younger’ distinction for ‘cross-sex sibling’
terms as occurs in the Kariera terminology (Figure 5). The logic of generating the termi-
nology has two sub-variants: (A) terminologies where the equation ‘spouse’ = ‘cross-
cousin’ is necessary for the logic of the terminology structure; e.g., the Kariera and other,
similar Australian terminologies, and (B) terminologies that reverse the structural posi-
tion for the male and female ‘cross-cousin’ terms in sub-variant (A) and thereby remove
‘spouse’ = ‘cross-cousin’ as a necessary equation for the logic of the terminology struc-
ture. The Iroquois terminology with its lack of a ‘cross-cousin’ marriage rule is generated
in this manner.
Variant (3)--Dravidian terminologies (see Figure 10) in which there are ‘older/
younger cross-cousin’ terms. The male and female structures are made into a single
structure by introducing self as a covering term for female self and male self: self [fe-
Read: A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan an...
19
male self, male self]. An isomorphic copy of the structure of female + male terms be
comes a structure of affinal terms for the terminology and then the structure of female +
male terms is structurally joined with the structure of affinal male + affinal female terms
through spouse kin term products between terms in the structure of female+male terms
and the term in the corresponding position in the structure of affinal male+female terms.
*tua-fafine [(ms) “sister”]
*tua-fafine [“daughter”]
*tina(na) [“mother"]
**fosa [“son”]
*tama(na) [“father"]
*tua-!a"ane [(ws) “brother”]
*tuaka(na) [“elder same sex sibling”]
*tahina [“younger same sex sibling”]
*tuaka(na)*tahina
*tupuna
*tama(na) *tina(na)*tu"a-tina**masaki-ta!a
*tama *tama-"a-fine
*"o-fafine *!ilamutu
*makupuna
*tahina*tuaka(na)
*tupuna
*makupuna
**fosa
*tua-!a"ane
*tua-fafine
**faka-fotu
Male Structure Female Structure
Figure 9: Kin term map for the *Proto-Polynesian terminology reconstructed linguistically from
changes in the morphological form of kin terms. However, the structural form is assumed and
not demonstrated. Feasible evolutionary changes in structure, the geographical pattern of set-
tlement of the Pacific Islands and the current distribution of structurally different terminologies
imply that there are two root terminologies and the structure shown here is derivative, not a root
terminology (Read 2013). There is a hidden male self position beneath the box in the male
structure and a hidden female self position beneath the box in the female structure. Except for
the two long, curved-dotted arrows in the center of the figure, all arrows pointing to or originat-
ing at the center position for each of the two structures involve the male self and the female self
position. For example, in the male structure, the horizontal, double-headed arrow pointing to
*tahina originates at the male self position (i.e., *tahina of male self = *tahina) and the horizon-
tal, double-headed arrow originating at *tahina points to male self (i.e., *tuaka(na) of *tahina is
male self). Terms in boxes show the connection between the male structure and the female
structure via male self becoming *tua-ŋaʔane (‘brother’) for the female self position and female
self becoming *tua-fafine (‘sister’) for the male self position.
Structure and Dynamics, 6(1) (2013)
20
For example, wife’ of ‘older brother/younger brother’ of self =older sister/younger sister
of ‘spouse’ of self in the Dravidian terminologies (see Read 2010 for details). The con-
struction sequence shows that the Dravidian terminologies have an emergent ‘cross-
cousin’ marriage structure and this accounts for the substantial difference discussed by
Dumont (1953) for what is meant by a ‘cross-cousin’ marriage rule when comparing the
Kariera terminology with the Dravidian terminologies.
Conclusion
The kin term products that culture-bearers use in computing kin relationships make it
evident that there is structure to the terms in a kinship terminologies independent of map-
ping kin terms onto genealogical positions. We make that structure visually evident
through a kin term map. We then work out whether there is a generative logic for the
kinship terminology structure. If so (and this has been the case for all terminologies con-
sidered to date), we are determining, through generating terms, structural equations, and
structural ways to join distinct structures into a single structure, the structural properties
that give rise to the structural form of a terminology through kin term products. This
makan
appa
annan
tampi
[I , i]akka
makal
amma
peran petti
attai maman
mayni
kolunti
attan
maccinan
marumakan marumakal
pattan patti
=
=
==
tankacci
= =
akka
tankacci
annan
tampi
appa makan amma makal
Figure 10: Kin term map of a Dravidian terminology from the perspective of female self.
The male perspectives is the same except for reversing the terms in the -1 generation. Hori-
zontal arrows on the extreme right and left side of the kin term map wrap around to the other
side. Reflexive arrows not shown. Solid arrow heads are ascending generating terms and
open arrow heads are descending generating terms. The “=” denotes terms connected by a
kin term product with a spouse term. Kin terms are from Trautmann 1981.
Read: A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan an...
21
Generating Set:
Parental Term
Generating Set
Parental Term
Sibling Term
Kinship Terminologies
Generating Sets
(1) Parental Term
Sibling Term
(2) Older/Younger
G = {I, P} G = {I
M
, F}
American
Kinship
Terminology
Polish
Kinship
Terminology
Equations
SFFF = FF
SSFF = SF
Punjabi
Kinship
Terminology Shipibo
Kinship
Terminology
G = {I
M
, F, B}
Equations
BI
F
= B
bI
F
= b
ZI
M
= Z
zI
M
= z
Kariera
Kinship Terminology
Marriage Rule
Sp = “X-Cousin”
*Proto Polynesian
Kinship Terminology
Equations
I
M
I
F
= Brother (ws)
I
F
I
M
= Sister (ms)
Dravidian
KinshipTerminology
Equations
W[B, b] = [Z, z]H
H[Z, z] = [B, b]W
[Z, z]F = MHi = MWI
[B, b]M = FWI= FHi
G
1
= {I, F, Sib} G
2
= {O, Y}
Level 0
Level 1
Level 2
Level 3
Self
child
parent
[brother, sister]
[nephew, niece]
[grandnephew,
grandniece]
grandchild
Etc.
grandparent
Etc.
[uncle, aunt]
cousin
Etc.
Etc.
Structure 1
Structure 2
tun!ga (ws)
!ku!na (ms)
!ku!na (ws)
tun (ms)
=
=
tsu //ga
Male Terms Female Terms
ba
(!father")
tai
(!mother")
[male self, female self]tsin
(!younger sibling")
!ko (!older brother")
!kwi (!older sister")
reciprocal terms:
!tum
(!son-in-law")
/otsu
(!daughter-in-law")
!hai
(!daughter")
!ha
(!son")
[tsiu
(!wife"),
!kwa
(!husband")]
/otsu
(!mother-in-law")
!tum
(!father-in-law")
Family Terms!-in-law" Terms
n!unba
(!father" of /otsu,
!tum)
n!untai
(!mother" of /otsu,
!tum)
=
=
=
=
=
Name giver/
Name receiver
=
ba (!father")
tai (!mother")
!hai (!daughter")
!ha (!son")
=
!spouse"
tsin (!younger sibling")
!Kung san
Kinship Terminology
*tua-fafine [(ms) “sister”]
*tua-fafine [“daughter”]
*tina(na) [“mother"]
**fosa [“son”]
*tama(na) [“father"]
*tua-!a"ane [(ws) “brother”]
*tuaka(na) [“elder same sex sibling”]
*tahina [“younger same sex sibling”]
*tuaka(na)*tahina
*tupuna
*tama(na) *tina(na)*tu"a-tina**masaki-ta!a
*tama *tama-"a-fine
*"o-fafine *!ilamutu
*makupuna
*tahina*tuaka(na)
*tupuna
*makupuna
**fosa
*tua-!a"ane
*tua-fafine
**faka-fotu
Male Structure Female Structure
makan
appa
annan
tampi
[I ,i]akka
makal
amma
peran petti
attai maman
mayni
kolunti
attan
maccinan
marumakan marumakal
pattan patti
=
=
==
tankacci
= =
akka
tankacci
annan
tampi
appa makan amma makal
Descriptive Terminologies
Classificatory Terminologies
Other Terminologies
male mera
bap
bhai
patija
dada
pardada
tai-chacha
putar
ma
pohta
parota
nakardada
nakarparota
female mera bhain
bhanji
nani
parnani
masi
putri
doti
pardoti
nakardoti
Emergent Marriage Rule
[Z, z]F = MH
Figure 11: Typology for descriptive, classificatory and other terminologies. Level 1:
Variation in generating set for the terminology. Level 2: Variation in sex marking of gen-
erating terms. Level 3: Variation in sex marking of kin terms and linking disjoint struc-
tures of male marked and female marked kin terms.
Structure and Dynamics, 6(1) (2013)
22
provides us with the foundation for working out a typology of kinship terminologies
based on the properties responsible for the structural differences among kinship termi-
nologies, hence to a typology that ensures that the terminologies grouped together in the
typology are homogeneous with respect to the structural properties that determine the
form of a kinship terminology (see Figure 11). This makes possible a more meaningful,
cross-cultural comparison of kinship terminologies and provides a sounder foundation
than has been available previously for working out the relationship between terminology
structure and form of social organization as discussed above. Structural comparison in-
vites diachronic and not just synchronic comparison. Some changes in structure are more
plausible than others; e.g., dropping the rule in the AKT for terms where sex marking is
preserved could, from a structural viewpoint, easily be dropped, thereby leading to a ter-
minology with all kin terms sex marked.4 Changing a Kariera-like terminology with
terms that incorporate an ‘older/younger‘ distinction for sibling regardless of the sex of
speaker to a Polynesian-like terminology in which that distinction only occurs among
same-sex sibling terms is not a matter of “erasing” the distinction on opposite -sex sibling
terms, but requires restructuring the way the structure of male terms and the structure of
female terms are joined together to form a single structure, hence is a structurally more
complex transformation. Just as evolutionary patterns can be worked out linguistically
from changes in word forms, evolutionary patterns can be worked out from changes in
structural forms, as Read (2013) has shown for the Polynesian terminologies. Even more
broadly, working out the structural logic of a terminology makes explicit what is meant
by the oft-repeated claim that culture is a constructed reality, for the kin relations
expressed through a kinship terminology are both “real” for the users of the terminology,
yet constructed through a generative logic acting on the cultural knowledge embedded in
a kinship terminology.
1 In genealogical equation form the types are as follows; Generation: FB= F = MB, FZ = M =
MZ; Bifurcate Merging: FB = F MB, MZ = M FZ; Bifurcate Collateral: FB F MB, FZ
M MZ; and Lineal: FB = MB F, FZ = MZ M.
2 Structure 2 has the structural form of the tetradic structure defined by Allen (1998), but differs
since it neither encompasses the entire society as is assumed by Allen for the tetradic structure nor
is it sociocentric. Allen assumes that kinship terminologies are derived from something like the
sociocentric four-section system that is part of the Kariera social organization, but the Kariera
four-section system is derived from the kinship terminology and not the reverse (Leaf and Read
2012). No extant kinship terminology has yet been identified that has a structure reflecting the
tetradic structure that is allegedly the root of all kinship terminologies. We do not need to posit
root terminology structures without evidence since the structural forms represented by the AKT,
Kariera and !Kung san terminologies are the structural consequence of straightforward differ-
ences that have ethnographic support, such as whether a sibling term is a generating term or not
(descriptive versus classificatory terminologies) or whether the terminology structure distin-
guishes between terms relating to the family space and terms relating to other positions along
with a structural means for connecting these two structures together (the !Kung san terminology
with the naming relationship). There is no a priori reason why there must be a single, root termi-
nology structure for all kinship terminologies as multiple origins with different structural forms is
possible.
Read: A New Approach to Forming a Typology of Kinship Terminology Systems: From Morgan an...
23
3 When working out the structure of kinship terminologies initially, the various structural proper-
ties and distinctions discussed here had to be worked out abductively from structures displayed in
kin term maps. In doing this, I drew upon my knowledge as a mathematician regarding generat-
ing structures as abstract algebras since the set of kin terms from a terminology along with the kin
term product satisfy the definition of an abstract algebra. Some of the kinship structural proper-
ties correspond to properties of abstract algebras, such as the structure of ascending and descend-
ing terms having the form of an algebra known as a semigroup; in particular, the structure shown
in Figure 6D is known as a bicyclic semigroup in the semigroup literature. Other structural prop-
erties are specific to the domain of kinship terminologies. The abduction process is aided by the
fact that a wrong guess as to a structural property is made evident through the fact that the struc-
ture generated using that wrong guess diverges from the kin term map as its structural implica-
tions are worked out. Trying to generate a classificatory terminology, for example, using a single
ascending generating element fails to generate fundamental properties of the classificatory termi-
nologies such as the terminologically recognized ‘older or ascending’/‘younger or descending’
sibling terms without engaging in ad hoc procedures such as simply imposing that distinction
even though there is no ethnographic evidence showing that the users of the terminology concep-
tualize sibling terms in that manner. The properties discussed here are those that have been found
to “work” in that they generate the structure of the terminology without ad hoc equations or other
properties being added to force agreement between the analytically generated structure and the
empirically observed structure displayed in the kin term map (contra Jones 2011). The argument
being made here is falsifiable in a Popperian sense. One only needs to find a terminology with
structure that cannot be generated except by including properties motivated solely as a way to
force agreement between the generated structure and the empirical structure.
4 We have not considered the reasons why the sex rule exists for the AKT in the first place and
those reasons may place constraints on possible changes in the sex rule independent of the fact
that such a change does not pose any significant structural constraints. The kinship domain is a
complex one where multiple cultural idea systems come into play (Leaf and Read 2012) and this
affects the likelihood of structural changes regardless of their feasibility.
Structure and Dynamics, 6(1) (2013)
24
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Structure and Dynamics, 6(1) (2013)
26
... The fact that this modus operandi (the products of kin terms) appears as culturally salient and apparently universally distributed suggests to Read (2012Read ( : 14-15, 2018a: 77) that a kinship terminology neither simply consists in a list (a collection or an addition) of vernacular kin terms corresponding to categories of genealogically "predetermined" relationships, as it is generally assumed, nor is it modeled on the logic of biological relations, but represents: 12 […] a conceptual system that expresses what are the kin relations as they are understood in a particular society and how kin relations may be computed among the individual sharing the same kinship terminology (Read 2007) […] (Read 2012: 15). This system … has an underlying computational logic that enables culture bearers to make kin term computations in a consistent and noncontradictory manner without reference to genealogical definitions of kin terms (Read 2018a: 77). ...
... To these primary terms, one needs to add the central position of self, or myself, considered as a same level generating element with the other primary terms. So, according to Read, the American terminology only needs (my)self, parent (father and mother), child (daughter and son) and spouse (husband and wife) in order to be empirically generated using kin term products (Read 2018a: 98) and graphically represented (Read 2007(Read , 2012(Read , 2014(Read , 2018a. ...
... Morgan (1871: 470) stated, as we mentioned earlier (chapter 1), that the primary relationships, making up the familial circle, were historically, the first to have been assigned specific terms, and these have to be logically considered as the primary terms. For his part, Read (2018a: 77) assumes that the primary terms structuring kinship systems through their mutual products, … are terms for the family relations, and he adds (2014: 65) that, … from an evolutionary viewpoint, these primitive conceptual relations had their origin in the evolving mental/cognitive capacities of the precursors of modern Homo sapiens (Read, Lane and Van der Leeuw 2009;Read 2010b, Read 2012). ...
... The analysis presented here follows the argument for the generative logic of kinship terminology structures laid out in six parts in Read (2007Read ( , 2014 and in Leaf and Read (2012). The six parts are as follows. ...
... Typically, groups with Iroquois terminologies do not have 'cross-cousin' marriage rules. (Note that the Hadza terminology does not have the structural form of an Iroquois terminology, underscoring the fact that Murdock's kinship terminology classification is based too much on superficial similarities that may be the consequence of dissimilar generative processes; see Read 2014 for an outline of an alternative typology of kinship terminologies based on the generative logic of kinship terminologies.) Another qualitative, cultural difference occurs with the !Kung San joking/ avoidance characterization of kin terms that plays a central role in !Kung San kinship behavior (Marshall 1976), yet neither has a counterpart in Hadza nor Kariera kinship relations and behavior. ...
... It has been developed by Dwight Read in two versions. One uses basic algebra represented with set theory notation or a graphic form (Read 1984(Read , 2000(Read , 2001(Read , 2007(Read , 2010(Read , 2013(Read , 2018Leaf and Read 2012). The other is a computer program that can be used by anthropologists without Read's mathematical background. ...
... "Crow-Omaha problem," i.e., why these terminologies skew oblique lineal kin-terms intergenerationally. And his proposal for a new typology based on structural features rather than ethnonymic designations resonates with several later arguments (e.g., Trautmann and Barnes 1998;Read 2013). Reawakened interest in Crow-Omaha systems (e.g., Trautmann and Whiteley 2012;Read 2018;Trautmann and Whiteley 2018;Parkin 2019;Whiteley and McConvell forthcoming) has much to gain from Popov's argument, whether or not evolutionary irreversibility of stage transformations is accepted as a general matter (for arguments con and pro, see, e.g., Trautmann 2001 andGodelier 2011, respectively). ...
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