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![Page 1: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/1.jpg)
Mathematical Modeling of the Logical Structure of Kinship Terminologies
Dwight Read
Department of Anthropology
UCLA
UC4-Human Complexity Talk Friday Oct 22, 2010 1:30-3:20 PM
![Page 2: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/2.jpg)
What will be shown• Cultural basis for kinship
– Genealogical Basis (Problems)– System of symbols (kin terms)
• A kinship terminology is a computational system.• A kinship terminology has a generative structure.• Genealogical kin term definitions can be predicted.• Logical explanation of terminology features.• Basis for major structural differences between kinship terminologies.• Kinship space integrates family space, genealogical space and kin term
space
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A Cultural Encounter
• Neighbor: “What kind of research do you do?”• Reply: “I do research on the structure of kinship
terminologies..”• Neighbor: “What are kinship terminologies?”• Reply: “These are the words we use to refer to our
relatives -- brother, sister, mother. I’m interested in explaining why other groups have very different ways to refer to their relatives”
• Neighbor: “I thought everyone referred to their relatives the way we do.”
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Cultural basis for kinship
![Page 5: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/5.jpg)
Cultural KinshipS
ocial Behavior
Terminological Structure (kin term map) based on:Linguistic symbols + product operation
(multiple structures)
Trobriand
American
biologicalkinship
Kin selection, inclusive fitness
genealogicalkinship
Type of relative
culturalkinship
Social identityRoles
Tracing preserved,Structural form
preserved
abstraction
Products preserved, Structural form not
preserved
abstraction
Genetic Tracing (pedigree) based on:Genetic reproduction
genetic mother
genetic father
Genealogical Tracing (genealogy) based on:Culturally recognized motherhood and fatherhood
genea-logical father
genea-logical mother
Cultural kinship is not biological kinship:“All human societies have kinship, that is, they all impose some privileged cultural order over the biological universals of sexual relations and continuous human reproduction through birth” (Parkin 1997, p. 3, emphasis added)
Cultural kinship is not biological kinship:“All human societies have kinship, that is, they all impose some privileged cultural order over the biological universals of sexual relations and continuous human reproduction through birth” (Parkin 1997, p. 3, emphasis added)
Hunter-gatherer society: !Kung san (Botswana) has around 500 persons
Genealogical tracing: 500 genealogical paths from ego to all society members
!Kung san kinship terminology has 17 kin terms
7 terms used for the nuclear family4 terms for other consanguines 2 terms for husband/wife4 terms for other affines
Terminology simplifies from 500 genealogical paths to 17 kin terms
Hunter-gatherer society: !Kung san (Botswana) has around 500 persons
Genealogical tracing: 500 genealogical paths from ego to all society members
!Kung san kinship terminology has 17 kin terms
7 terms used for the nuclear family4 terms for other consanguines 2 terms for husband/wife4 terms for other affines
Terminology simplifies from 500 genealogical paths to 17 kin terms
![Page 6: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/6.jpg)
Genealogical Basis (Problems)
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Definition of Kinship
“I define kinship, therefore, [as] a relationship which is determined, and can be described, by means of genealogies” (W. H. R. Rivers 1924: 53).
“Kinship is conventionally defined as relationships between persons based on descent [parent-child links] or marriage” (Linda Stone 2000: 5)
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Family Tree (Genealogy)
ego
fatherfathermothermother auntaunt uncleuncle
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Genealogical Perspective
==
=
ego
= =
ego
Genealogical Grid (partial)
Underlying logic
1. fs = ms = b, fd = md = z2. sf = df, sm = dm3. bz = z, zb = b4. sb = s = db, bf = f = zf5. sz = d = dz, bm = m = zm
Terminology (AKT)Father, Mother, Uncle,Aunt, Son, Daughter, Cousin, etc.
AuntFatherMotherAunt Uncle Uncle Uncle
SonDaughter
Sister Brother
Analytic Methods:Componential Analysis
Rewrite Rules
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American Kin Terms and Genealogy
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!Kung San of the Kalahari Desert
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!Kung san Camp
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!Kung san Terms and Genealogy
Implied definition: !un!a’a = {ff, mf} txuma = {fm, mm}
Implied definition: !un!a’a = {ff, mf} txuma = {fm, mm}
Problem: Does not match usage of kin terms.
Problem: Does not match usage of kin terms.
“I found that different persons used different terms in a given [genealogical] relationship …It was Toma who … told me what he had assumed everyone knew, that the term ‘followed the name’” (Lorna Marshall 1976: 202)
“I found that different persons used different terms in a given [genealogical] relationship …It was Toma who … told me what he had assumed everyone knew, that the term ‘followed the name’” (Lorna Marshall 1976: 202)
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!Kung san Terminology
American/English Kin Terms !Kung San Kin Terms (approximate)
Grandfather, Great uncle !gun!aGrandson, Great nephewMale cousin (1st, 2nd, 3rd, etc)Male __cousin twice removed, etc
Grandmother, Great aunt //gaGranddaughter, Great nieceFemale cousin (1st, 2nd, 3rd, etc)Female __cousin twice removed, etc
Uncle, nephew, tsuMale __cousin once removedMale __cousin 3 times removed, etc
Aunt, niece tunFemale __cousin once removedFemale __cousin 3 times removed, etc
Mother taiFather baBrother (older) !goSister (older) !kwiBrother (younger), Sister (younger) tsiSon !haDaughter ≠khai
!, //, ≠ -- click sounds
These four !Kung san terms are not based on the genealogical relationship of the relative to ego, but on the generational relationship of the relative to ego’s name giver.
These four !Kung san terms are not based on the genealogical relationship of the relative to ego, but on the generational relationship of the relative to ego’s name giver.
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Who is the Father? “[their]indigenous theories of procreation have no place
for [the genitor or genetic father], and attribute the onset of gestation to action by a spirit. One group, the Murinbata, recognize another social role, the ‘firestick father,’ the individual who, they believe, directs the spirit to the mother. But the ‘firestick father’ is neither believed to be a genitor, nor is necessarily identical with the genetic father. The distinction between the genetic father and the ‘firestick father’ is shown by the fact that the ‘firestick father’ is sometimes a woman” (J. A. Barnes 1964:296, from Bronislaw Malinowski 1913).
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Procreation ≠ Kinship
“In parts of Melanesia … the family to which a child belongs is not determined by the physiological act of birth, but depends on the performance of some social act; in one island the man who pays the midwife becomes the father of the child and his wife becomes the mother; in another the father is the man who plants a leaf of the cycas-tree before the door of the house. These are only dramatic examples of a widespread practice whereby fatherhood and motherhood depend, not on procreation and parturition, but on social convention, and it is evident that blood-relationship is quite inadequate as a means of defining kinship.” (W. H. R. Rivers 1924: 53-54)
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System of symbols (kin terms)
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Kinship Identification and Calculation
Gao [a Nyae Nyae !Kung] had never been to Khadum [to the north of
the Nyae Nyae region] before. The !Kung who lived there at once
called him ju dole [dole: ‘bad’, ‘worthless’, ‘potentially harmful’]. He
was in haste to say that he had heard that the father of one of the
people at Khadum had the same name as his father and that another
had a brother named Gao. `Oh,’ said the Khadum people in effect, `so
you are Gao’s !gun!a . . .. (Lorna Marshall 1976:242)
[!gun!a -- kin term for persons in a name giver-name receiver relationship]
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Gao’s Calculation
Gao
Gao’s father
Unidentifiedperson A
A’s father
Unidentifiedperson B
B’s brother’sname is Gao
(same name)
!gun!a kin relationship
!gun!a
?? = tun
Gao (ego)
Gao
B
tsi (“brother”)
Gao … was in haste to say that he had heard that
the father of one of the people at Khadum had the
same name as his father and that another had a
brother named Gao. `Oh,’ said the Khadum people
in effect, `so you are Gao’s !gun!a . . .”
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A kinship terminology is a computational system.
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Kin Term Reckoning“Kinship reckoning on Rossel [New Guinea] does not rely on knowledge of kin-type strings
[genealogical pathways]. . . . What is essential in order to apply a kin term to an individual
X, is to know how someone else, of a determinate kinship type to oneself, refers to X. From
that knowledge alone, a correct appellation can be deduced. For example, suppose
someone I call a tîdê ‘sister’ calls X a tp:ee ‘my child,’ then I can call X a chênê ‘my
nephew,’ without having the faintest idea of my genealogical connection to X.” (Levinson
2002:18, emphasis added)
Relationship between concepts: tp:ee of tîdê is chênê
Call this a kin term product of the terms tp:ee and tîdê
Relationship between concepts: tp:ee of tîdê is chênê
Call this a kin term product of the terms tp:ee and tîdê
tp:ee
Person XchênêEgo
someone
tîdê daughter
Person X???Ego
someone
aunt
cousin
Relationship between concepts: daughter of aunt is cousin
Call this a kin term product of the terms daughter and aunt
Relationship between concepts: daughter of aunt is cousin
Call this a kin term product of the terms daughter and aunt
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Kin Term Product (example)
aunt son
Ego
Person X
Person Y???
cousin
Product of kin terms: Son of Aunt = Cousin
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Kin Term Product: Formal Definition
Let K and L be kin terms in a given kinship terminology, T. Let
ego, alter1 and alter2 be three persons each of whose cultural
repertoire includes the kinship terminology, T. The kin term
product of K and L, denoted K o L, is a kin term, M, if any, that
ego may (properly) use to refer to alter2 when ego (properly) uses
the kin term L to refer to alter1 and alter1 (properly) uses the kin
term K to refer to alter2.
L K
ego
alter1
alter2M
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Construction of a Kin Term Map: American Kinship Terminology
Self
Father Mother
Grandfather Grandmother
Son
Brother
And so on…..
product with father term
product with mother term
product with son term
![Page 25: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/25.jpg)
Kin Term Map: American Kinship Terminology
Nephew of Grandmother = ?Nephew of Grandmother = ?
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Shipibo (Horticulturalists)
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Kin Term Map: Shipibo Terminology
Shipibo: Horticultural group in Peru
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Comparison: AKT and Shipibo
American Kinship Terminology
Shipibo Kinship Terminology
![Page 29: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/29.jpg)
A kinship terminology has a generative structure (cultural
theory)
![Page 30: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/30.jpg)
Inductively Derive Cultural Theory Expressed in the Kin Term Map
Simplify the structure by removing one structural layer at a time
• Affinal layer
• Sex marking layer
• Descendant and reciprocal term layer
• Core ascendant structure
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Remove Affinal Terms, Sex Marking of Terms
Remove affinal terms (=)
Combine terms in structurally equivalent positions
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Remove Descending Structure, Identify Core Concepts
Remove [son daughter]= child and kin term products of form child of ______ .Reduce ascending structure to core concepts.
X
[Father, Mother]
Self
XXX
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Simplified kin term map
[Father, Mother]
Self
Kin Term Product: parent of parent
ego
alter1
parent m, f
Generate New Kin Term Concepts From the Core Concepts
Parent
Self
Use the kin term product to generate a new concept: parent of parentUse the kin term product to generate a new concept: parent of parent
Give the new concept a name: grandparentGive the new concept a name: grandparent
We have constructed the primary meaning of grandparent. Grandparent is the kin term ego uses for alter2 when ego refers to alter1 as parent and alter1 refers to alter2 as parent.
We have constructed the primary meaning of grandparent. Grandparent is the kin term ego uses for alter2 when ego refers to alter1 as parent and alter1 refers to alter2 as parent.
alter2
parent
= grandparentparent of parent
Parent of Parent
Generated Structure
m, f
mm, mf, fm, ff
genealogical relation m -- mother f -- father
Grandparent = mother’s mother, mother’s father, father’s mother, or father’s fatherGrandparent = mother’s mother, mother’s father, father’s mother, or father’s father
We have also generated the genealogical definition of grandparent.We have also generated the genealogical definition of grandparent.
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Continue Forming New Kin Term Concepts
Parent
Self
Next we construct parent of grandparent = parent of parent of parent in the same manner, and so on.
Next we construct parent of grandparent = parent of parent of parent in the same manner, and so on.
Parent of Parent
Generated Structure
[Father, Mother]
Self
Simplified kin term map
![Page 35: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/35.jpg)
Generate Core Ascending Structure
Set of Symbols S = {Self, Parent}. Form all possible products with Parent: Parent, Parent of Parent = Parent2, Parent of Parent2 = Parent3, and so on
Self
Parent
Parent2
Self
Parent
Grandparent
Etc
Isomorphicstructures
(ascending structure)
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Generate Descending Structure Descending set of symbols S* = {Self, Child}. Form all possible products with Child: Child, Child of Child = Child2, Child of Child2 = Child3, and so on
Parent2
Self
Parent
Child Child2
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Reciprocity of Terms
Generating set {Self, Parent, Child}
Reciprocal Equation
= Self
ego, alter1, alter2 blood related
ego must be alter2,
Parent of Child = Self
My childMy parent
Parent and child are reciprocal kin terms
Parent
alter2
alter1
Child
ego ??
so ego refers to alter2 as self and Parent of Child = Self
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Ego
someone
child
Generate Ascending and Descending Structure
Descending generating term = child Reciprocal terms: parent of child = self
child
child of child of parent of parentchild of parent of parent
child of child
child of child of parentchild of parent
parent of parent
parent
self
[brother, sister] [nephew, niece]
grandchild
[uncle, aunt] cousingrandparent
parent
= Person X
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Structure is Isomorphic to Reduced Kin Term Map
P2
I
P
C
C2PCP
CP2 C2P2
C2
I SelfP [Father, Mother] = ParentC [Son, Daughter] = Child
Isomorphic
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Sex Marking, Spouse ElementSex Marking: Add sex markers, M and F, to algebra.
Affinal Terms: Add spouse generating element, S, to algebra, along with spouse structural equations:
SS = I (Spouse of Spouse = Self)
SP = P (Spouse of Parent = Parent)Reciprocal equation: CS = C (Child of Spouse = Spouse)
P2S = 0 (Parent of Parent of Spouse is not a kin term)Reciprocal equation: SC2 = 0 (Spouse of Grandchild is not a kin term)
PSC = 0 (Parent of Spouse of Child is not a kin term)
SCP = CPS (Spouse of Sibling = Sibling of Spouse = Sibling-in-law)
Structural RulesSex Marking of kin termsCousin nomenclature
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Construction Steps
Self
Parent
Grandparent
Etc
(1) Self, Parent: ascending terms
(2) Self , Child: descending terms
Self
Parent
Grandparent
Etc
Grandchild Child Etc
(3) Reciprocal Terms: Parent of Child is Self
Grandchild Child Etc
[Nephew, Niece][Brother,Sister] Etc
Cousin [Uncle, Aunt] Etc
Self
Parent
Grandparent
Etc Etc
Cousin,CousinUncle,Aunt Etc
Nephew, NieceBrother,Sister Etc
Gson,GDaughter Son,Daughter EtcSelf
Father,Mother
GFather,GMother
Etc Etc
(4) Sex Marking
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Construction Steps (cont’d) (5) Spouse Term
Spouse of Spouse = SelfSpouse of Parent = ParentSpouse of Sibling = Sibling of Spouse = Sibling-in-lawParent of Parent of Spouse is not a kin termParent of Spouse of Child is not a kin term
(6) Sex Marking Rule: If spouse of a kin term is a kin term then that kin term and its reciprocal kin term stay sex marked. Otherwise, sex marking is removed.
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Isomorphism Between AKT and Generated Structure
Algebraic Structure Kin Term MapIsomorphism
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Kin term genealogical definitions can be
predicted.
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Predicted Kin Term Definitions
STEP 1: Instantiation: I {ego}P {f, m}C {s, d}S {h, w}
Where: f = genealogical fatherm = genealogical mothers = genealogical sond = genealogical daughterh = husbandw = wife
STEP 2: Construct set products corresponding to symbol products: e.g. CP = {s,d} {f, m} = {fs, fd, ms, md} = {b, z}
RESULT: Predicted genealogical diagram
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Logical explanation of terminology features.
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An Oddity in Our Terminology
• Kinship terminologies change through time: cousin became “ith cousin j-times removed”
• “in-law” appears to be the way we mark a relation by marriage
• There is nothing strange about the words “aunt-in-law” or “uncle-in -law”
• But husband of aunt is not uncle-in-law and wife of uncle is not aunt-in-law.
• Why not?
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Husband of Aunt = Uncle?Wife of Uncle = Aunt?
Algebraic Structure Kin Term MapIsomorphism
Spouse of Spouse = SelfSpouse of Parent = ParentSpouse of Sibling = Sibling of Spouse = Sibling-in-lawParent of Parent of Spouse is not a kin termParent of Spouse of Child is not a kin term
Spouse of Spouse = SelfSpouse of Parent = ParentSpouse of Sibling = Sibling of Spouse = Sibling-in-lawParent of Parent of Spouse is not a kin termParent of Spouse of Child is not a kin term
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An Oddity in Our Terminology
• Kinship terminologies change through time: cousin became “ith cousin j-times removed”
• “in-law” appears to be the way we mark a relation by marriage
• There is nothing strange about the words “aunt-in-law” or “uncle-in -law”
• But husband of aunt is not uncle-in-law and wife of uncle is not aunt-in-law.
• Why not?• Answer: The logic of the terminology implies husband
of aunt = uncle and wife of uncle = aunt
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Basis for major structural differences between kinship
terminologies.
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Kin Term Map: Kariera Terminology
Kariera (hunter-gatherer group)
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Simplify: Remove Affinal Relations
Remove terms connected by “=“
“older brother”
“younger brother”
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Simplify: Male Terms
Include “male self” term
“older brother” “younger brother”
“older brother”
“younger brother”
“father”
“son”
Restrict to male marked terms.
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Remove Descending Structure
“older brother”
“father”
“son”X
X
X
XX
Ascending structure Remove descending terms
“younger brother”“older brother”
“father”
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“older brother”
“father”
“son”
Remove Ascending Products
Remove product Maeli = Mama of Mama
“older brother”
“father”
“son”
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“older brother”
“father”
“son”
Core Structure
Generating Terms: Mama, Kaja
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“older brother”
“father”
“son”
Comparison of Core Structures
Kariera Core Structure
[Brother, Sister]
[Father, Mother]
Self
Parent Child
[Son, Daughter]
American Core Structure With
Brother = Son of Father product
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Comparison of Sibling Concepts
self
father mother
daughterson
brother sister
English: brother = son of father, mothersister = daughter of father, mother
Sibling as a derived concept
Descriptive Terminologies
[self, self]
Mama(‘father’)
Kaja(‘o brother’)Margara(‘y brother’)
Manga(‘son’)
Nganga(‘mother’)
Turdu(‘o sister’)Mari(‘y sister’)
Kundal(‘daughter’)
Sibling as a primary concept
Classificatory Terminologies
Kariera:‘older brother’/’younger brother’‘older sister’/’younger sister’Are primary concepts
“Among the Tangu (New Guinea), “a person’s descent is of small significance to him but that relationships with sibling are of vital importance. Briefly, that siblingship is the determinant that descent might have been expected to be” (Burridge 1959: 128).
“Among the Tangu (New Guinea), “a person’s descent is of small significance to him but that relationships with sibling are of vital importance. Briefly, that siblingship is the determinant that descent might have been expected to be” (Burridge 1959: 128).
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Structure with Sibling Generator
Ascending generating terms: {male self, father, Brother}
Ascending Structural Equations: (1) father of male self = father(2) Brother of Brother = Brother(3) father of Brother = fatherDescending generating terms:
{male self, son, brother}Descending Structural Equations(1*) son of male self = son(2*) brother of brother = brother(3*) son of brother = sonReciprocal Structural Equations(4) Father of son = male self(5) Son of father = male self(6) Brother of brother = male self = brother of Brother
Reciprocal equation: Brother of father = father
Older, Younger Sibling: Brother (ascending), brother (descending)
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Kinship space integrates family space, genealogical space and kin term space
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Kinship Space
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Family Space
(A) Family space based on filiation and marriage
(B) Family space based on filiation, siblingship and marriage
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Genealogical Space
==
=
ego
= =
ego
Genealogical Grid (partial)
Underlying logic
1. fs = ms = b, fd = md = z2. sf = df, sm = dm3. bz = z, zb = b4. sb = s = db, bf = f = zf5. sz = d = dz, bm = m = zm
Terminology (AKT)Father, Mother, Uncle,Aunt, Son, Daughter, Cousin, etc.
AuntFatherMotherAunt Uncle Uncle Uncle
SonDaughter
Sister Brother
Analytic Methods:Componential Analysis
Rewrite Rules
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Kin Term Space
![Page 65: Mathematical Modeling of the Logical Structure of Kinship Terminologies Dwight Read Department of Anthropology UCLA UC4-Human Complexity Talk Friday Oct.](https://reader035.fdocuments.net/reader035/viewer/2022081520/56649e385503460f94b295d6/html5/thumbnails/65.jpg)
Kinship Space
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Summary
• A kinship terminology is a computational system.
• The generative structure of a terminology
• Prediction of term definitions.
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Nephew ofGrandmother = ?
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Summary (cont’d)
• Basis for differences in kinship terminologies
• Explanation of terminology features.
• Account for differences among terminologies
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Conclusion• We have shown that while reproduction underlies kinship, the relation between
biological fact and cultural construct is well-expressed by Robert Parkin’s comment: “All human societies have kinship, that is, they all impose some privileged cultural order
over the biological universals of sexual relations and continuous human reproduction through birth”
• Kinship terminologies have structure based on a set of symbols (the kin terms), a binary product defined over those symbols (the kin term product) and structural equations that give a terminology its particular structure; that is, terminologies have the form of algebraic structures and can be mathematically analyzed using algebraic concepts.
• Mathematical analysis of terminologies leads to new ethnographic insights into the broad issue of what we mean by kinship and how kinship is lived in the societies we study as anthropologists.
• Questions?
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Shipibo Terminology
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Spouse S-in-law,D-in-law
B-in-law,Z-in-lawF-in-law,M-in-law
Construction Steps (cont’d) (5) Spouse Term
Self
Father = Mother
Gfather = GMother
Etc
CousinUncle = Aunt Etc
Nephew, NieceBrother,Sister Etc
Gson,GDaughter Son,Daughter Etc
Etc
Spouse of Spouse = SelfSpouse of Parent = ParentParent of Parent of Spouse is not a kin termSpouse of Sibling = Sibling of Spouse = Sibling-in-law
(6) Sex Marking Rule: If spouse of a kin term is a kin term then that kin term and its reciprocal kin term stay sex marked. Otherwise, sex marking is removed.
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Tiwi Mother“… when my informant said, ‘My mother fed me when I was small until my brother was born, but often my mother beat me so hard I ran away. But Polly, that’s my mother, would come after me and bring me back,’ I found it unwise and invalid to assume that my informant was referring to any specific number of ‘mothers’…. Even in cases where my informant knew that I knew the exact genealogical relationship between her and her real mother and her mothers ‘one-granny’ sisters [other women that the informant would call ‘mother’], she rarely made discrimination unless I demanded it. In the specific instance quoted above, I found that she was referring to three ‘mothers,’ only one of whom was named ‘Polly’.”(Jane Goodale 1971:73)
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Keesing’s Definition:Genealogical Network
“’Kinship,’ then, is the network of relationships created by genealogical connections, and by social ties (e.g., those based on adoption) modeled on the ‘natural’ relations of genealogical parenthood” (Keesing, p. 13)
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Schneider’s View
“One must take the native’s own categories, the native’s units, the native’s organization, and articulation of those categories and follow their definitions, their symbolic and meaningful divisions wherever they may lead. When they lead across the lines of ‘kinship’ into politics, economics, education, ritual, and religion, one must follow them there and include those areas within the domains which the particular culture has laid out” (Schneider 1972:51)
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Reference versus Address
• Reference: "She's my cousin on my mother's side" • Address: "Uncle Frank, thanks for the present!”• Terms of address are more variable: mom, mommy,
mother, mama, mum,… • Form of address may signal the nature of the relationship
with the kin person: ‘mother’ is more formal than ‘mom’ when addressing someone
• Terms of reference often have genealogical definitions: Uncle is father’s brother, mother’s brother, father’s sister’s husband, mother’s sister husband
• Genealogical definitions may be used to make the kind of relation more precise: “He’s my uncle -- my mother’s brother”
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Genealogical GridDevised as a universal diagram for
expressing genealogical definitions of kin terms
Problem: (1) Assumes kin are
first of all determined from reproduction
(2) Does not allow for relative age to be part of kin terms
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Read’s View
• Genealogical tracing is based upon a genealogical father and a genealogical mother whose definition is culture specific and used by culture bearers when tracing a linkage between an ego and an alter. A genealogical parent may, but need not, be genitor/genetrix; a genealogical parent may, but need not be, pater/mater.
• Kinship relations are determined via the categorizations that constitute the kinship terminology and the conceptual linkages among the categorizations.
• There are two ways in which a link between individuals may be conceptualized: (1) a link via genealogical tracing and (2) a link via kin term categorization. Neither can be wholly reduced to the other.
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Predicted Kin Term Definitions
STEP 1: Instantiation: I --> {ego}P --> {f, m}C --> {s, d}S --> {h, w}
Where: f = genealogical fatherm = genealogical mothers = genealogical sond = genealogical daughterh = husbandw = wife
STEP 2: Construct set products corresponding to symbol products: e.g. CP = {f, m}{s,d} = {fs, fd, ms, md} = {b, z]
RESULT: Predicted genealogical diagram
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Polysemic Meaning of Mother, Father (American
Terminology)John said: “That woman is my mother” Two meanings, depending on the
circumstances:(1)John is identifying the woman who gave
birth to him(2)John is referring to the woman with whom
he has a kin relationship labeled by the linguistic expression “mother”; for example, John might be adopted and is referring to the woman who is his mother by virtue of adoption
Kin term products are based on kin terms used to indicate the relation linking speaker and referent person
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Definition: Kin Term ProductLet K and L be kin terms in a given kinship
terminology, T. Let ego, alter1 and alter2 be
three persons each of whose cultural repertoire
includes the kinship terminology, T. The kin
term product of K and L, denoted K o L, is a
kin term, M, if any, that ego may (properly) use
to refer to alter2 when ego (properly) uses the
kin term L to refer to alter1 and alter1
(properly) uses the kin term K to refer to
alter2. L K
ego
alter1
alter2M
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