71
A TRANSFORMATIONAL ANALYSIS OF THE KAPAUKU KINSHIP SYSTEM
Keith T. Kernan
Introduction
Although one of the important subdivisions of American anthropology
has always been anthropological linguistics, the theories and methodologies
of structural linguistics have, until recently, never been applied to the
study of anthropology's main concern, culture. Anthropological linguists
have, in the main, been merely linguists who studied and described the lan-
guages of rather exotic cultural groups. While these same men often were in-
terested in and described other aspects of the culture also, the methodology
used and the theoretical point of view taken were unrelated to their theoret-
ical assumptions about language. For theoretical models to be used for the
understanding of culture itself, these investigators turned to other sciences.
Evolutionists such as Morgan adopted their theories from the biological sci-
ences. The structure-functionalists traced their intellectual heritage back
to the French sociologists; while the Boasians rejected all theoretical models
and contented themselves with description and historical reconstruction.
Sapir, Whorf, and their followers were, of course, interested in the relation-
ship between language, culture and cogni tion. They did not analyze culture
from the point of view of linguistic theory, however. Rather they attempted
to demonstrate the influence of language upon thought and culture.
Recently, however, a number of anthropologists have begun using both
contemporary linguistic methodology and theory. (Cf. Romney and D'Andrade
196ha, and Hammel 1965a.) The techniques of analysis of ethnoscience have
their basis in the methodology of linguistics. The ethnoscientists are at-
tempting to discover the culturally relevant semantic categories in the soci-
ety under investigation.  To do so, they use linguistic data and linguistic
methodology. Their primary concern, however, is not with the language as
linguistic data, but, rather, with using language as an avenue for understand-
ing the cognitive categories of the people of the culture being studied and,
therefore, understanding the culture itself. The avowed purpose is to de-
scribe the culture from the point of view of the participants in that culture
in such a way that the description can be replicated by other investigators
using the same techniques. It is primarily a methodology for ethnography
that has been borrowed from linguistics. As such, it makes few theoretical
assumptions and most certainly does not attempt to apply the theories of con-
temporary, transformational linguistics to cultural data.
The type of kinship analysis done by Romney (1964b), Hammel (1965b),
and particularly by Lounsbury (1964 and 1965), however, (though closely re-
lated to ethnoscience in its development and referred to by Hammel as compo-
nential analysis 1965b) differs in an important respect from the other work
utilizing lingui'stic methods being done in American anthropology. These re-
searchers work with the methodology used in linguistic transformational anal-
ysis and much of tlleir theoretical orientation is that of the transformational
school of linguistics. What these men are doing essentially is analyzing the
formal structure of nonlinguistic aspects of culture.   They have used linguis-
tic data such as kinship terminologies, however, what they are in effect
72
analyzing is not the linguistic aspect of the kin terms but rather the inter-
nal structuring of the system. Their basic data are both kin terms and kin
types. The structure that they discover is one of relationship between the
lingtistic units, the kin terms, and the kin types which fall within each
term. An important aspect of the relationship between kin terms and kin types
is the relationship between the kin types themselves. The methodology used to
discover this structure is borrowed from the field of linguistics. In one of
the early articles which dealt.with this type of structural analysis of cul-
tural data, Lounsbury (1956:9) states: "The aim of this paper is to point
out a relatively simple problem in semantics which can be analysed by means
of techniques analogous to those already developed in linguistics . .
Both language and at least some other aspects of culture, then, can be ana-
lyzed by means of similar techniques. The point we wish to make here is that
both culture and language may be analyzed by using similar methodologies be-
cause they are structured in much the same manner. To demonstrate this and
to exemplify the techniques used in thi.s type of work, we shall analyse the
formal structure of the kinship system of the Kapaukans using data collected
by Pospisil (1960).
A Transformat'ional Analysi s of Kapauku Kinship Terminology
The Notation and the Calculus
Transformational analysis of kinship systems requires a system of no-
tation which is more primitive than the one traditionally used.   Hammel
(1965b) and Romney (1964b) have developed a notational system which fills
this need. Although the system still has limitations, it is superior to the
one that has been used in the past in that it indicates each biological fac-
tor in the expression.  For example, in the old notation "brother," which con-
tains two biological elements, was indicated by the single letter "B."   Under
the new system "brother" is indicated by three symbols; one which indicates
the sex of ego if it is relevant, one which indicates a sibling link, and one
which indicates that the sibling is male. The notation employed here includes
four operators and e ight elements.
Notation
Operators:
+     indicates
-     indicates
=     indicates
0     indicates
a step up by one generation.
a step down by one generation.
an affinal link.
a sibling link.
Elements:
a     indicates an individual of any sex.
b,c   indicates an individual of any sex provided that the sex
indicated by (b) is different from the sex indicated by (c).
d     indicates an individual of any sex provided that all of the
(d's) in any one expression indicate persons of the same sex.
m     indicates an individual of male sex.
f     indicates an individual of female sex.
e     as superscript indicates elder than ego.
y     as superscript indicates younger than ego.
73
Logical Statements:
>  indicates "transforms to."
<  indicates "transforms from.."
(Sore of the statements in this analysis are bi-directional,
i.e. of the form, <>.)
Examples:
MFB (any sex ego) is written as a4f+mOm: FFZS;
(male speaking) is written as m+m+mOf-m;
sibling of the same sex is written as dOd;
sibling of the opposite sex is written as bOc;
parent (any sex ego) is written as aea, etc.
Comments:
The Kapauku are a patrilineal, polygynous society. From the
data given by Pospisil, it seems clear that children of the same father
are considered to be full siblings.  The sibling link may, therefore, be
written redundantly as +m-. The expressions ama... and ...awa appear in
the analysis. These are to be read as indicating two individuals of op-
posite sex who are spouses.
Rules
I. a)b, c, d, f, m but the reverse is not true.
b,c,d>f,m (subject to the definitions of b,c, and d) but the reverse
is not true.
(Rule I is a substitution rule for elements, not a transformational
rule.)
II. d>+d- AOd (For any element, substitute a sibling of the same sex as
that element.)
(a) restriction--this rule does not apply to the d of do... or ...od
of affinal expressions.
III.O>+aOa-  (For a sibling operator, go up one generation, substitute a
pair of siblings of any sex, and then come down one generation.)
(a) restriction--this rule does not apply to expressions which con-
tain an 0 operator but no other operators.
IV. /R/ (Read the expression backwards, from right to left, and change
all + operators to - operators and vice versa. This rule may' be
termed a rule of reciprocity.)
(a) restriction--this rule cannot be applied to expressions or roots
containing one - operator and no other operators.
(b) restriction--this rule cannot be applied to expressions which
contain an elder or younger distinction.
(c) restriction--this rule cannot be applied to roots which end with
...+dOd.
(Restriction (c) is not necessary for certain expressions. In such
cases, however, the proper expansions can be reached even though the
restriction is employed. Since it is necessary for the proper expan-
sion of other roots, it is presented in its present form without fur-
ther qualifications for the sake of parsimony.)
V.  ...b >..c=b    (For any terminal element of a specific sex substitute
an element of the opposite sex and a spouse of the substituting
74
element.)
(a) restriction--this rule can only be applied to roots which con-
tain at least two + operators or one + operator and one a operator,
and no other kinds of operators.
(b) restriction--this rule cannot be applied to affinal kin of 0
generation.  [Rule VI makes this restriction necessary.]
VI. b=c+a>b=cOb (For anv narent of a snouse, substitute a sibling of
the opposite sex from that spoouse.)
(a) restriction--this ruile can only be aoplied when b=c+a occurs by
itself.
General Restriction
None of the above rules can be applied to expressions which contain
one + or one e operator and no other operator.
Roots and Expansions
In Table I, the root expressions, as defined above, are listed along
with the Kapauku kin term. The number before each term corresponds to
Pospisil's number for the term. In the second column, the expansions are
listed. The rule or rules which have been applied to the root to generate
the expression are given in the third column.
It should be stated at this point that Pospisil does not present his
data by giving the kin term and listing the kin types under it.   Rather, he
describes the types which fall under the term and gives several examples.
All of the expressions which have been generated by application of the rules
in Table I from any particular term and root conform to his description of
that term and expression set. Unfortunately, Pospisil does not state the
collateral limits of his kin terms but merely indicates that they may be ex-
tended to any degree of collaterality. Presunably, this means that anyone to
whom ego can trace an actual genealogical relationship is called by some one
of the kin terms listed. For practical reasons, the expansions in Table I go
no farther than the farthest removed kinsman from ego given by Pospisil in
his examples for that term. By further application of the rules of transfor-
mation, however, all individuals that could possibly exist in any ego's kin-
ship universe could be generated under the proper term. Column four gives
the number of the term under which compliments of the term in question occur.
Column five gives the number of the term with which the term in question over-
laps.
In column three, when two rules appear it means that the rule on the
left has been applied to the expression which has been generated by applica-
tion of the rule on the right to the root expression. The same principle ap-
plies to lists of more than two rules; i.e. apply the rule to the right to
the root, then apply the next rule to the left on the resultant expression,
and so on.
Expansions which are redundant (e.g. a+aOa+a+aOa+a) have not been
generated in Table I unless they are a necessary preliminary step to further
expansions.
Table I
Term and Root         Expansions            Rule       Complements   Overlaps
in          with
(1) Ani Pigoka
a+a+a+a+a
25-32 expressions
under rule I, e.g.
m+m+m+m+m, f+f+m+f+m,
m+m+f+m+f, etc.
a-a-a-a-a                 I
25=32 expressions when    I
rule I is applied after
rule IV has been applied,
e.g. f-f-f-f-f, m-f-m-f-m,
m-m-m-m-mi, etc.
a+a+a+a+a a
26u64 expressions when    I
rule I is applied, e.g.
m+m+M+M+mOm, f+m+f+m+fOm,
f+f+f+f+mOf, etc.
a-a-a-a-a
26464 expressions when    I
rule I is applied, e.g.
mOf-m-f-f-f, etc.
a+a?a+a?a+aOa-a
28m256 expressions when   I
rule I is applied, e.g.
m+in+pmm+m+inmO-m,
f+m+f+m+f+mOf-f, etc.
a+aa-a-a-a-a-a
2 8256 expressions when   I
rule I is applied, e.g.
m+inOn-m-in-m-m-in,
f+mOf--m-f-m-f-m, etc.
a+a+a+a+a-a* *
25-32 expressions when    I
rule I is applied, e.g.
m+m+m+m+mmf , f+m+f+t+fnm,
etc. (This is not 2  since
the a to the left of the a
operator def ines what the
final a will be.)
a-a-a-a-a=a
I
[v.
E. IV
[1.
., II
Nv, II
I, IV, II
III, II
I, III, II
lII, IV, II
I, III, IV, II
V
I, V
V, IV
(1)
(1)
(1)
(1)
(1)
(1)
(1) (22)
(22)
"This expression is not redundant since the Kapauku are polygynous and
this individual ray be one of grandmother's co-wives rather than grandmother.
(1) (22)
(22)
76
Table I Continued
Term and Root         Expansions            Rule       Complements    Overlaps
in          with
(1) Ani Pigoka
a-a+a+a+a
(Cont.)
25%32 expressions when
rule I is applied, e.g.
Mm-m-m-m-=f,
m-f-m-f-f-rm, etc.
a+a+a+a#aOawa
26"64 expressions when
rule I is applied, e.g.
m+M+m+m+mOm=f,
m+f+m+f+mOfum, etc.
aca-a-a-a-a=a
26=64 expressions when
rule I is applied, e.g.
fOm-m-m-m-m-m=f,
mOm-f--m-f-m-f=mr, etc.
a+a+a+a+a+aOa-a=a
28=256 expressions when
rule I is applied, e.g.
mer+m+m+m+mOm-Munf,
m+f+m+f+m+fOm-fam, etc.
a+aOa-a-a-a-a-ava
28m256 expressions when
rule I is applied, e.g.
m+mOm-m-m-m-mr-muf,
m+fOm-f-m-fr-m-ffsm, etc.
ataaa-a-a-a
25 32 expressions when
rule I is applied.
aua+a+a+a+a
25-32 expressions when
rule I is applied.
a=a0a-a-a-a-a
26=64 expressions when
rule I is applied.
a=a+a+a+a+aOa
26=6  expressions when
rule I is applied.
a=a+aQa-a-a-a-a-a
28=256 expressions when
rule I is applied.
I,
I,
VI,
I,
I, V, IV
II
V, II
IV, II
V, IV, II
III, II
V, III, II
VI,III,IV, II
I,V,III,IV,II
IV, V
IV, V, IV
IV, VV II
IV,V,III,II
(1) (22)
(1) (22)
(1) (22)
(1) (22)
(1) (22)
(1) (22)
(1) (22)
(1) (22)
(1) (22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
77
Table I Continued
Complements   Overlaps
Term and Root         Expansions           Rule            in         with
-~~~~~~~~~~~~~i                                         with
aua+a+a+a+a+aOa-a
28" 256 expressions when
rule I is applied.
aZaa-a-a-a-asa
25a32 expressions when
rule I is apnlied.
awa+a+a+a+ana
25 u32 expressions when
rule I is applied.
ama0-a-a-a-ama
26*64 expressions when
rule I is applied.
ana+a+a+aOa a
26-64 expressions when
rule I is applied.
a=a+aOa-a-a-a-a-a=a
28=256 expressions when
rule I is applied.
a=a+a+a+a+a+aa-a=a
28 =256 expressions when
rule I is anplied.
2 =16 expressions when
rule I is applied to
root.
a-a-a-a
24.16 expressions when
rule I is apolied.
a+a+a+aOa
25.32 expressions when
rule I is applied.
aOa-a-a-a
25 32 expressions when
rule I is applied.
a+a+a+a+aOa -a
27=128 expressions when
rule I is applied.
Iv5,V,II,IV, (1) (22)
II
V, IV, V        (1) (22)
V, IV, V, IV (1) (22)
V, IV, V, II (1) (22)
V,IVJV,IXvII    (1) (22)
V,IV,V,III,II (1) (22)
vj,IV,V,III, (1) (22)
Iv,jI
I
IV
II
IV, II
III, II
(2)
(2)
(2)
(2)
(2)
(1) Ani Pigoka
a+a+a+a+a
(Cont. )
(2) Ani aija
a+a+a+a
(22)
(22)
(22)
(22)
(22)
(22)
(22)
78
Table I Continued
Term and Root          Expansions            Rule       Complements    Overlaps
in          with
(2) Ani aija
a+a+a+a
(Cont. )
a+aOa-a-a-a-a
27=128 expressions when
rule I is applied.
a+a+a+ana
24m16 exnressions when
rule I is applied.
a-a-a-a*a
24 16 expressions when
rule I is applied.
a+a+aaOawa
25_32 expressions when
rule I is applied.
aOa-a-a-ama
25 32 expressions when
rule I is applied.
a+a+a+a+aOa-ama
27-128 expressions when
rule I is applied.
a+aOa-a-a-a-a=a
27=128 expressions when
rule I is applied.
a=a-a-a-a
25=32 expressions when
rule I is applied.
ana+a+a+a
24=16 expressions when
rule I is applied.
asaOa-a-a-a
25w32 expressions when
rule I is applied.
a'wa+a+aaOa
2 '232 expressions when
rule I is applied.
ama+aca-a-a-a-a
27-128 expressions when
rule I is applied.
III, IV, II
V
V, IV
V, II
V, IV, II
V, III, II
V,III,IV, II
IV, V
IV, V, IV
IV, V, II
Iv,V, IV, II
I3V3V,Iij,II
(2)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(2) (22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
79
Table I Continued
Term and Root        Expansions           Rule      Complements   Overlaps
. .  ,               ,             .               S   . . .  D~~i   wit
ama+a+a+a+aOa-a
27-128 expressions when
rule I is applied.
a-a-a-a-a-a
24=16 expressions when
rule I is applied.
a-a+a+a+a-a
24u16 expressions when
rule I is applied.
a0aC-a-a-a-a
25 32 expressions when
rule I is apDlied.
a.a+a+a+aOama
25 32 expressions when
rule I is applied.
a,a+aCa-a-a-a-ata
2 %128 expressions when
rule I is applied.
ama+a+a+a+aOa-a?a
27m128 expressions when
rule I is applied.
23-8 expressions under
rule I.
a-a-a
23-8 expressions when
rule I is applied.
a+a+aOa
24=16 expressions when
rule I is applied.
aCa-a-a
24=16 expressions when
rule I is applied.
a+a+a+aOa-a
26.64 expressions when
rule I is applied.
IVV,5iII,5I,    (2) (22)
II
V. IV, v        (2) (22)
V, IV, V, IV (2) (22)
V, IV, V, II (2) (22)
V,IV,V,IV,II (2) (22)
V,IV,V,III,II (2) (22)
V,jiV,V,iII     (2) (22)
IV, II
I
(3)
IV
II
(3)
(3)
IV, II
III, II
(3)
(3)
(2) Ani aija
a+a+a+a
(Cont. )
(3) Ani muuma
a+a+a
(22)
(22)
(22)
(22)
(22)
(22)
(22)
80
Table I Continued
Term and Root         Expansions            Rule       Complements    Overlaps
in          with
(3) Ani muuTar
a+a+a
(Cont. )
a+a0a-a-a-a
,6
2 ,64 expressions when
rule I is applied.
a+a+aua
2 38 expressions when
rule I is applied.
a-a-a-a
23=8 expressions when
rule I is applied.
a+a+aOa=a
24=16 expressions when
rule I is applied.
aOa-a-a=a
24"16 expressi*ons when
rule I is applied.
a+a+a+aOa-ama
26=64 expressions when
rule I is applied.
a?a-a-a-a-a
26u64 expressions when
rule I is applied.
aua-a-a
23?8 expressions when
rule I is anplied.
at.a?a+a
23m8 expressions when
rule I is applied.
a=aOa-a-a
24=16 expressions when
rule I is applied.
a=a+a+aOa
24=16 expressions when
rule I is applied.
a=a+aOa-a-a-a
26=6 expressions when
rule I is applied.
III, Iv, II
V
V, IV
V, II
V, IV, II
V, III, II
V,III, IV,II
IV, V
IV5, V, lv
IV, V, II
IV,V,JIV, II
IV,V, III,II
(3)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(3) (22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
81
Table I Continued
Term and Root   Expansions            Rule       Complements   Overlaps
Term and Root        Expanslons            Rule           in          with
ana+a+a+aOa-a
26'64 expressions when
rule I is applied.
a-a-a-afta
23"8 expressions when
rule I is applied.
awa+a+aua
23*8 expressions when
rule I is applied.
aoaCa-a-a-a*a
24n16 expressions when
rule I is applied.
aoa+a+aOa=a
24=16 expressions when
rule I is applied.
ana+aOa-a-a-a-a
2 6=64 expressions when
rule I is applied.
a-a+a+a+aaa-ama
26=64 expressions when
rule I is applied.
Iv,V,III,IV, (3) (22)
II
v, IV, v         (3) (22)
V, IV, V, IV (3) (22)
V, IV, V, II    (3) (22)
V,IV,V,IV,II (3) (22)
V,IXT,V,III,Il (3) (22)
V,IVj,X,III,    (3) (22)
IV, II
f+fOm
m+fOm
a+f+aGa-m
23.8 expressions when
I
III
rule I is applied, e.g.
f+f?fOf-m, m?f+mOf-m, etc.
mOf-a                     IV
mOf-f
mOf-m
m+aa-f-a                  IV, III
23.8 expressions when
rule I is applied.
a+f+a+aca-a-m             III, III
25-32 express'ions when
rule I is applied.
(3) Ani muuma
a+a+a
(Cont.)
(22)
(22)
(22)
(22)
(22)
(22)
(22)
(h) Naama
a+fOm
(4)
(4)
(4)
(4)
(4)
82
Table I Continued
Term and Root         Expansions           Rule       Complements   Overlaps
in          with
m+a+aOa -a - -aa
25=32 expressions when
rule I is applied.
IV, III, II
(5) Ani ooka
a+mOf
(6) Ani joka
d-a
f +mOf                    I
m+mOf
(Further expansion
parallels that of 14, with
complements, however found-
in 5.)
m-mi
m-f
f-m
f-f
dOd-a
mOm-rn
mOm-f
fOf-im
f Of-f
a+aOa-d-a                  III, II
24=16 expressions when
rule I is appl'ed.
(This is not 2  since the
sex of the first d deter-
mines the sex of the second d.)
d+a+aOa-a-d-a
26=64 expressions when
rule I is applied.
(7) Niikai
a+f
(8) Niikab
a+fOf
IIII, III, II
m+f                       I
f+f
(No expansions are poss ible
due to the gereral restriction
given previously.)
I
mifOf
f+fOf
aThis term and many of
degrees of collaterality.
paper will only be carried
the terms to follow may be extended to further
As previously stated, however, expansions in this
out as far as Pospisil's examples.
bThis term is also applied to stepmother. All of stepmother's relatives
are called by the pertinent kinship terms for true maternal relatives.
(14) Naama
a+fOm
(Cont. )
(4)
I
I
(5)
(7, 9)
(8, 10)
II
I, II
(8, 10)
(8, 10)
(6)
(6)
83
Table I Continued
Term and Root         Expansions           Rule       Complements   Overlaps
in          with
(8) Ni ika
a+fOf
(Cont.)
(9) Naitai
a+m
a+f aOa-f
23m8 expressions when
rule I is applied.
m+m
III
I
f+m
(No expansions are possible
due to general restriction.)
(10) Naita
a+mOr
(11) Noone
a+bOc-a
m+mOm                     I
f+mOm
(Further expansion parallels
that of 8, with complements
in 6.)
23-8 expressions when
rule I is applied.
(6)
Se lf -rec iprocal
a+b+aOa-c-a
25*32 expressions when
rule I is applied.
a+b+a+aca-a-c-a
27m128 expressions when
rule I is applied.
III
Self -rec iprocal
III, III    Self-rec iprocal
(12) Ani i joka
a+fOf-a
(13) Ani paneka
b+m-c
m+fOf-m
m+fOf-f
f+fOf-f
f+fOf-m
a+f +aa-f-m
23-8 expressions when
rule I is applied.
m+m-fa
f+m-m
b+mOm-c
m+mOm-f
f+mOm-m
b+m+aOa-m-c
23.8 expressions when
rule I is applied.
I
III
I
I, II
III
Self-reciprocal
Self -rec iprocal
Self -rec iproca 1
Self -reciprocal
Self-reciprocal
Redundant for mOf.
(6)
(6)
84
Table I Continued
Term and RootExpanioComplements      Overlaps
Term and Root          Expansions             Rule            in          with
(1L) Ani Weneka
d+m-dy
(15) Nauiwa
m+m-m
(16) Anibai
f+m-fe
( 17) Anepa
d+mOm-d
m+m-mYm
f+m-fY
d+mOm-dy
m+mOm-my
f+mOmn-fY
d+m+aGa-m-dy
23*8 expressions when
rule I is applied.
m+m-me
m+mOnm~m
m+m+aOa-m-me
22=4 expressions when
rule I is applied.
f +m_fe
f +mOm-fe
f+ma+ao-m-f e
22=4 expressions when
rule I is applied.
a
f?TnOm-f
d+m+aOa-m-d
23ft8 expressions when
rule I is applied.
I
II
I, II
III, II
II
III, II
II
III, II
I
III
(15, 16)
(l5, 16)
(15, 16)
(14)
(1h)
(14)
(14)
(14)
(14)
Self-reciprocal
Self -rec iproca l
(18) Ani wapi
a+aOfwm
m+mOfgm
m+fOfwm
f +fOfwm
f mOfam
mufOa-a
mifOm-m
mu f Cm-f
mnf Of-f
m-fOf-m
a+a+aOa-f-im
23=8 expressions when
rule I is applied.
(17)
(17)
(17)
(17)
(17)
(17)
(1l,15,
16)
(14,15,
16)
I
IV
I, IV
III
(18)
(18)
(18)
aKinship terms 1-17 are extended to close relatives of the speaker's best
fr iend.
Table I Continued
Complements   Overlaps
Term and Root        Expansions            Rule           in          with
(18) Ani wapi
a+aOf-m
(Cont. )
(19) Naama i
a+aOmuf
m-f+aOa-a -a
23-8 expressions when
rule I is applied.
m+mOmnf
m+fOmwf
f+fOmf
f+mOm*f
fwmOa-a
fmmOm-m
f-mOm-f
f4mOf-f
f-imOf-m
a+a+aOa-m-f
24*16 expressions when
rule I is applied.
fm+aOa-a-a
24=16 expressions when
rule I is applied.
(20) Ani waka
bnc
(21) Ani
bOb c
geeka
f-mr
mrf
(No other rules apply.)
mOm-f
? Of-rn
c-bOb
f-mOrn
rn-fOf
I
I
IV
I, IV
Se lf -rec iproca 1
(21)
(21)
b+aOa-buc
23=8 expressions when
rule I is applied.
c.b+aOa-b
23-8 expressions whien
rule I is applied.
(22) Ani *aaka
ba c (-ea)
bwc+a
bu c+a+a
bsc+a+a+a, etc.
b-c+aOa
number of times to
IV, III
(18)
(19)
IV
I, IV
III
IV, III
(19)
(19)
(19)
III
IV, III
(21)
(21)
(22)
(22,
(22,
(22)
II
*Dhe n superscript indicates that +a may be added any
the right of the expression.
3)
2)
(3)
(2)
86
Table I Continued
Complements   Ove-rlaps
Term and Root         Expansions            Rule            in          with
in          with
(22) Ani baaka
b=c(+a)n
(Cont.)
23=8 expressions ihen
rule I is applied.
b=c+a+aOa
24-16 expressions when
rule I is applied.
bnc+a+a+aOa
25=32 expressions when
rule I is applied.
a-cob
a-a-cub
a-a-a-c*b, etc.
bnc+a+aOa-a
25m32 expressions when
rule I is applied.
aOa-c-b
23-8 expressions fwhen
rule I is applied.
aOa-a-cmb
24=16 expressions when
rule I is applied.
aOa-a-a-c-b
25-32 expressions when
rule I is applied.
bucOb
f=mOf
bOc-b
mOf -i
bnc+aO-aa
23-8 expressions when
rule I is applied.
ama0a-cmb
23m8 expressions when
rule I is applied.
b- c+a+aOa-awa
2 fu32 expressions when
rule I is applied.
II
II
IV
III, II
II, IV
2II, IV
II, IV
VI
I, VI
IV, VI
I, IV, VI
V, II
IV, V, II
V, III, II
(22, 3)
(22, 2)
(3)
(2)
(22)
(22,
(22,
(22)
3)
2)
(3)
(2)
(22)
(22, 3)
(22, 2)
(3)
(2)
(22)
(22)
(22)
(22)
(22)
87
Table I Continued
Term and Root         Expansions            Rule       Complements    Overlaps
in          with
(22) Ani Paaka   (Many further expansions              Complements of Would
b!c(+a)        are possible under this                these would be  over-
(Cont.)        root.  Pospisil gives no              in (22, 1.)      lap
further examples, however.)                           with (1)
(23) Ani-geeto   m=fOf=m                   I           Self-reciprocal
a=aOa=a        f=mOm=f
m=fOm=f
f=mOf-m
a-a+aOa-a=a               III         Self-reciprocal
24=16 expressions when
rule I is applied.
Conclusion
The preceding formal analysis illustrates a number of points, the
most important of which are that the Kapauku kinship system does have a struc-
ture and that this structure can be analyzed by using a methodology which is
analogous to that used by transformational linguistics for the analysis of
language.
Transformational theory views language as consisting of two interre-
lated levels; the deep structure, and the surface structure (cf. Chomsky
1965). As Chomsky points out, it is the central idea of transformational
grammar that these two levels are distinct and that the surface structure is
determined by the application of grammatical transformations to the deep
structure. The deep structure of a language consists of a highly restricted
(perhaps finite) set of basic strings. The basic strings are made up of ele-
mentary units, termed by Chomsky base phrase-markers, which are combined and
related by a system of rules. That is to say, basic strings (the underlying
deep structure of particular sentences) are generated by the application of
rules to base phrase-markers. Each of these sequences is the basis of the
sentence that it underlies. Surface structures are formed by the application
of grammatical transformations to these basic strings.
Perhaps we can put it more simply without distorting Chomsky's basic
points if we say that each sentence of a language has an underlying structure.
The sentence itself is (in a spoken language) a string of sounds. That is to
say, it is a physical occurrence. It takes the form that it does as the re-
sult of certain formal transformational rules that have been applied to the
underlying deep structure.
A particular sentence's deep structure, on the other hand, is the
structure which underlies the surface structure. Sentences are physically
manifested by the application of a limited number of transformational rules
to a restricted number of basic strings.
88
It should be clear that the preceding analysis of a kinship system is
directly comparable to a transformational analysis of a language. Three
basic elements have been delineated: root kin types, rules of expansion, and
expansions. These features are analogous to the linguistic features of deep
structure, transformational rules, and surface structure.
The basic strings of a language and the core kin types of a kinship
system are both restricted in number. Both are also further analyzable; the
basic strings in terms of phrase-marker rules (Chomsky 1965:17) and the core
kin types in terms of componential analysis (see Goodenough 1956). By the
application of transformational rules to the deep structure of either a sen-
tence or a kin term, the surface structure is generated. In our formal kin-
ship analysis we have applied six transformational rules to twenty-three
basic strings and have generated all of the possible kin types for each term.
We have accounted for a large body of data by application of a few simple
rules of transformation to a limited number of basic elements.
Now, it has already been pointed out above that this type of formal
analysis of kinship systems has been done by others and that these researchers
have stressed their reliance on linguistic methodology. The clear analogy
between this type of analysis and linguistic transformational analysis has
never been explicitly stated, however. It is not merely a case of nominalism
to talk about kinship systems in the same way that linguists talk about lan-
guages. Since both bodies of data are amenable to one kind of analysis, the
use of the same terminology is logical and can lead to the application of
method and theory in one discipline to data in the other. Moreover, linguis-
tic methodology and theor-y can be applied to more areas of culture than kin-
ship terminologies. Frake (1964) has done this in the area of religious
behavior and Pospisil (1965) to the classification of geographical features,
to name two recent examples. There is no reason to suppose that all of cul-
ture cannot be analyzed in terms of this type of methodology and theory.
NOTE
1I should like to thank Dr. E. A. Hammel for his helpful comments
concerning the formal analysis part of this paper. He, of course, is not
responsible for any of its shortcomings.
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89
HAMf'EL, E. A.
1965a Formal semantic analysis. E. A. Hammel, ed. American
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