Ideal Language and Kinship Structure
Ernest Gellner
Philosophy of Science, Vol. 24, No. 3. (Jul., 1957), pp. 235-242.
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IDEAL LANGUAGE AND ICIMSHIP STRUCTURE*
ERNEST GELLNER
University of Lonclon
This paper is inter-disciplinary. Its disadvantage is that the author is not
sufficiently conversant with the disciplines it is inter. He may however, like
Lord TVavell, claim that at least the thread that binds them is his own.
The paper is of philosophic interest in that it is inspired by, and hopes to shed
some light on, the notion of an ideal language. It is of interest to social anthropologjr
in that its main subject is kinship structure. It may be of interest to
mathematicians in setting a task.
Ideal Language. The notion of an ideal language played an important part in
philosophy earlier in this century. The notion lacks clarity-though clarity is
just one of the things an ideal language hopes to provide-but certain features
nevertheless seem to emerge: an ideal language must be unambiguous. This
means, amongst other things, that it observes the rule "one thing, one name";
no two things may have the same name, nor may two names be given to one
thing. Secondly, an ideal language is no deceiver, it does not mislead; permissible
and impermissible inferences and transitions are clearly evident from the very
notation. Thirdly, an ideal language does not distort the nature of reality; the
notation clearly shows what is due to the notation and what is due to fact. It
equally shows up the possibly related boundary between what is logically necessary
and what is contingent.
The above is not clear. But then, nor are the reasons ~vhichled to the abandonment
of this ideal. I shall return to both.
Kinship Structure. Kinship structure theory is an important and well developed
social anthropology. I t is well developed for a number of reasons. The kind of
question originally asked about primitive societies were often connected with
kinship; kinship structure is an aspect of society which is more tangible and
stateable with accuracy than most; kinship lends itself to comparison between
societies.
In fact, "kinship structure" means two separate things, though, as will emerge,
ailthropologists are right in not normally separating them. I shall:A
society consists of people, male and female, any pair of whom can mate
(with certain obvious qualificatioiis concerning age) as far as biology is concerned.
In actual fact, matings are not random in any society. In other words, actual
matings are a sub-class of biologically possible matings. Kinship-structure in
the jrst sense means the specification of how that sub-class is selected, in other
words which matings, or rather which kinds of matings, actually occur. For
instance in a strictly monogamous society with no pre- or extra-marital relations
or re-marriage, the actual matings woi~ldbe such that if A and B mate, then this
precludes any mating of A with B' or of B with A'.
* Received March, 1956.
235
236 ERNEST GELLNER
The second sense of "kinship-structure" is the correlation of social roles (which
are not logically entailed by biologically-defined relationships) with kinship
roles defined within the first sense of the term. For instance, the assertion that
the provider or protector of the woman is ex officio her biological mate. Kinship
structure in this sense specifies which roles, with what rigidity and to what
extent, are so to speak functions of the biological kinship position of the agent
(or vice versa). I t will also contain negative assertions to the effect that such and
such a role is not related to kinship. I t is, for instance, often said that industrial
society differs from most agrarian societies in that fewer roles are functions of
kinship.
The first and second sense of kinship-structure are logically distinct. Nevertheless
anthropologists are right in lumping them together, this being inevitable.
The reason for this is that many important limitations of matings (kinship
structure sense 1) operate in terms of social roles; for instance, in one society I
know a man may not marry a woman who was suckled by the same breast as
he (though it belong to a mere wet-nurse of either/or both "siblings of milk,"
as they are called). I t followsthat the tasks of the first and second kind of kinship
study can only be carried out pari passu, and can be separated neither in the
study nor in the presentation of material.
Contemporary social anthropologists, perhaps because they are anxious to
assert to social nature and the autonomy of their discipline vis-a-vis physical or
biological disciplines, tend to stress their concern with the second aspect of
kinship, sometimes almost to the point of implying that the first does not concern
them. But this cannot be so for the degree of overlap-admittedly incomplete-between
social and physical kinship is precisely one of the most interesting
things in the subject, and one to which the investigation of which social anthropologists
are committed by the 'functionalist' theory that social kinship structure
is explained by its serving the basic needs connected with procreation.
I shall nomi try to indicate what I think would count as an ideal language for
kinship structure theory.
In many languages a man is named by some locution such as "John, son of
Peter". Sometimes it is extended to something like "John, son of Peter, son of
Stephen". There is no necessary upper limit to this kind of thing. Nor is there
any reason why only the ancestors in the direct male line should be specified.
All ancestors, male and female, up to a certain point back could be specified,
and moreover specified according to a fixed order which would indicate just
who they were, biologically speaking, in relation to the person to be named.
No society, as far as I know, possesses anything like so complete a system of
naming its members. That, however, is no reason why such a system should
be devised.
If such a scheme were devised, we should then have a way of naming human
individuals such that their very name would promptly place them within their
biological logical space. Is one justified in calling this a kind of logical space?
I think so. The fact that man is born of woman and has a man for father is not a
logical truth; it is "merely" a synthetic, empirical truth of biology, though
IDEAL LANGUAGE AND ICIRTSI~IPSTRUCTURE 237
allowing for parthenogenesis as good a generalisation as ever we shall find. But
for the purposes of the social sciences, it can be taken as a logical truth defining
certain universal relations between objects they are investigating (namely,
human beings). In certain contexts "Mother's son" is indeed synonymous with
"man"; there are some languages in which "son of man" is used in the sense of
"man".
I t is now worth specifying some of the difficulties that would have to be overcome
in order that the above objective is attained.
1) If an individual's "name" in our ideal naming system consists of or at
least contains an ordered list of his ancestors, one has to take into account that
the names of those ancestors, or at least some of them, will be similarly complex.
Concretely, if John's name contains the sequence GHK each letter of which
names one of his ancestors, it is likely that G, H, and K may also in fact be
ordered strings of names. Hence there must be some device for indicating whether
a symbol occurs as part of a name other than the "total" name, or whether it
occurs atomically. Or alternatively, if the constituents of John's name build up
from his ancestors' names so that the preceding distinction vanishes, (every
symbol occurring in both ways) then some rule must still be made specifying
in what way one may break up John's name and get the names of ancestors,
rather than strings of symbols naming no one. If this system were ever applied
to an actually existing group of human beings, ancestors of a certain generation
past would have to be "primitive" ancestors and be assigned "primitive" names.
Though I do not think that if the present device xere ever worked out, its use,
if any, would be in actually naming people-people's names would be too impossibly
long. On the other hand if the device is to be sound it is necessary that
it should, however cumbersomely, be in principle so applicable.
Incidentally, the names nrould indicate the person's ancestors but never his
descendants. After all, he may not have any, or he may acquire some after
naming. The least a good name must do is not to depend on the empirical fortunes
of the man named. This is what distinguishes names from descriptions. I t is a
curious fact that it is logically true (in our sense) that we all have ancestors,
but not even factually true that we all have descendants. Those philosophers
unfortunate enough not to be able to tell the direction of time, and who sometimes
look for guidance in abstruse things such as entropy, may if they wish use
this more homely fact to guide them.
2) If the construction of an individual's name involved nothing but the ordering
of the names of his ancestors, the consequence would be that all siblings would
have the same name. This ~~youldcause confusion in his and the next generation,
and a violation of the principle "one name, one thing" in both the first and the
subsequent generations. Hence a device is again necessary for obviating it. I t
must in principle be possible. For instance, if GHKL is a string of names of
ancestors specifying in good order the common ancestors of Paul and Peter,
then Paul might be IGHKI; and Peter 2GHI<L, Paul being the elder. Of course,
a subtler device may be needed to prevent chaos when Paul's and Peter's name
enter as constituents into their descendants' names. At each stage in this enu-
238 ERNEST GELLNEI?
meration of difficultiesthe best I can do (and not always that) isto indicate possible
minimal tricks that would do the job; to devise methods that would not lead
to confusion when operating simultaneously is beyond both my ability and the
scope of the present paper.
3) The fact that there are two sexesis probably itself a nuisance in our scheme.
I suspect that it ~vouldbe necessary to treat only members of one sex as individuals
proper in our scheme, members of the other sex being only admitted by
courtesy but ultimately eliminable and definable in terms of the first, (in a
manner analogous perhaps to the one in which real numbers are ultimately definable
in terms of rational ones). I suspect moreover that the basic sex should
more conveniently be female, in view of the fact that it is harder for an individual
to be ignorant of the identity of his mother than of the identity of his father.
In other words, the basic language of kinship structure -would be matrilineal
rather than patrilineal, though ultimately it mould convey information about
all the antecedent lineages of a named individual. A device for making men "derivative"
might be something like this; if Joan has three sons and Joan's name
is J, their names mould be JIX, J2X, and J3X where X conveys the necessary
information about their respective fathers or father and in turn their ancestry.
Perhaps this amounts less to making men 'derivative' than to ensuring that
the sex of a person should be evident from the structure of his name. I t -would
also mean that male names would never be primitive names in the above sense.
Names constructed by making tu7o people of the same sex the parents of an
individual would then not be well-constructed terms of our language. The reason
which makes me suspect that one of the other sex would have to be made "derivative"
is that if such a language were really constructed by a mathematician,
it ~vouldprobably owe something to set theory, rhich (I believe) presupposes
that the individuals dealt with are homogeneous in the sense that if X is in a
certain logical relationship with Y, that any Z can also meaningfully, if not
always truthfully, be said to be in that relation with Y. (Is it not when this
condition fails that the famous antinomies arise?)
I t may be that our notation will require type-restrictions, for it must be made
nonsense (not just false) for a man to mate with a man, or for a mail to be his
own offspring, etc. Biological impossibility must be made into a logical impossibility
of our notation. Our notation must express the underlying biological presuppositions
of kinship as logical truths inherent and manifest in the symbolism
so that the social facts of kinship emerge against this background as asserted,
synthetic truths. Note incidentally, that if this language were devised, "individuals"
in a logical system ~vouldfor once mean individuals, rather than meaning
nothing or anything.
If I may digress a little; I have always found it hard to think of system of
mathematical logic in other than kinship terms, with axioms marrying transformation
rules to generate a fertile progeny of theorems in a timeless may, wit,h
formation rules guarding against the occurrence of miscegenation. Admittedly,
in this world unnatural unions are not merely permitted but apparently fertilefor
theorems and transformation-rules are sometimes hard to distinguish. (I
IDEAL LANGUAGE AND RINSI-IIP STRUCTCRE 239
leave psychoanalytic interpretation of this fancy to others.) A possible answer to
the philosophical question of what purely formal systems "really are" seems to
me that they are artificial systems of causation, imaginary worlds of which the
initial elements are postulated and so are the "causal" rules by which other
elements come into being. This interpretation of "what formal logical systems
really are" seems to be supported by the fact that actually constructed and
operating machines mirror logical systems. The consequence of such a philosophy
of logic would be that logic would be a study of possible causal systems. I t seems
very paradoxical thus to make causation more fundamental than logical necessity.
. . ..
One might add that if logic has sometimes borrowed its imagery or terminology
from kinship (e.g. the "ancestral" of Quine's), then my recommendation that
it aid kinship theory gives it an opportunity to repay an old debt. (It will be
sad if only the logical parts of this paper are tolerable to anthropologists, and
only the anthropological parts tolerable to logicians. The life of a pontifex need
not be an easy one).
4) No grave difficulty should arise from the fact that in real life many ancestors
are not known. The system of naming should be so devised that it allows
variables instead of actual names as parts of complex names.
Sofar, we have not a language but a system of naming (which is not a language)
We must now add things that can be said of the things named. Now we are
fortunate that in our logical space there is only one kind of logical relation.
It holds, when it holds, between groups of three individuals of the system. It
is a "triadic relation". It is the relation "A (male) and B (female)begat C (either
sex)". Any individual in the system is either directly related, or indirectly related,
or not related at all in this way, to every other individual in the system. If A
is related (directly or indirectly) to B, and B is similarly related to C, then A is
related to C. In other words our one logical relation in its extended indirect and
dyadic sense is transitive. This second relation is definable in terms of the first
and introduces nothing fundamentally new1. In view of this we are at liberty
to say either that two elements in a system may be unrelated, or alternatively
that if this is so, they do not form part of the same system. Which of these alternatives
we choose will depend on whether we wish to make our "system"
correspond, in the real world, to "relatives" or to "society".
Now if the above system of naming has been constructed to my specifications,
then there is no need for our one logical relation to exist in the basic vocabulary of
the system. Just this would be the beauty of our achievement, the attaining of
what philosophers who wanted an ideal language had hoped for; namely, that
logical necessary relationships should be "shown", be evident, from the very
Strictly speaking, two steps are involved. We begin with our ordered triads. Then a
dyadic relation of ' being directly related' is defined in terms of the triadic relation, quite
simply: "any member of a triad is directly related to each of the other two. (Df.)" We then
define 'being indirectly related' in the following way: 'Tf A is related directly or indirectly
to B, and B is related similarly to C, then A and C are (at least) indirectly related. (Df.)".
This last definition is not circular.
240 ERNEST GELLNER
notation, so that only synthetic, factual truths need actually be asserted. Note
that in one sense, once people are named according to our scheme, they all have
names with the same structure or 'form' irrespective of mhat their kinship organisation
is; but just this provides the conlnlon logical form (mirroring the biological
basis), and only reflects that we all have two parents, four grandparents, eight. ..
etc. The first way differences in that comnlon pattern arise-and hence information
can be conveyed-is that in societies inbred to any degree, certain kinds of
repetitive patterns mill occurwithin the names. Secondly, information concerning,
for instance, what counts as incest in a society will be conveyed by stating that
people bearing names with a certain repetition-containing structure count, in
that society, as offspring of incestuous unions.
One difficulty arises through so to speak the timelessness of our names. In
using our naming system, the fact that a society permitted "one man-many
women" marriages would be conveyed by the cornpossibility of names whose
structure revealed the same father but different mothers. But obviously such
names are compossible even in a society which does not allow of such marriages,
in view of the fact that one man may marry a number of women in succession.
If something corresponding to the date of birth were introduced into our "names"
this mould really undesirably complicate the names, by introducing something
other than biological relation into the logical, necessary-connection-generating
part of the notation. I think information of this kind x~ouldalways have to be
conveyed with help of "synthetically" attributed sociological predicates, in
addition to the predication "occur" or "there exist". Names conveying one
father but different mothers are, for instance, compossible in our society (owing
both to illegitimacy and to successive marriages) and in a polygamous one.
Onemight distinguish thetwo cases by asserting, synthetically, that in our society,
when such two names occur this implies that either one or both are illegitimate
or they are the offspring of successive marriages, whereas this entailment does
not hold in the other society. (Note that it is no weakness of the notation that
the names cannot convey whether their bearer is a bastard or legitimate. That
distinction is indeed not a biological but a sociologicalone, and must be conveyed
by the sociological predicates attributed to the names.)
Implications for Social Anthropology. How ~vouldthe truths of kindship-structure
theory be conveyed in such a language (for the construction of which this article
claims to be no more than a prolegomenon)? The truths of mhat I called the
first kind of kinship theory-the specification of which of biologically possible
unions actually occur-would be conveyed by stating that, in a given society,
only names of such and such structure actually occur. (For instance: such and
such repetitions of the variables comprising a name would be barred, or favoured,
or obligatory.) Truths of the second kind of kinship theory would be conveyed
by attributing sociologicalpredicates to names of a certain kind, or alternatil-ely
by denying connection between predicates of that kind and any of the permissible
kinds of names. Truths of the first kind of kinship theory which can only be
states with help of sociologicalpredicates could also be stated, though in a slightly
more complicated way.
IDEAL LANGUAGE AND ICISSHIP STRUCTURE 241
Would all this be of any actual use to social anthropology? Almost certainly
not in naming actual people, though it is just possible that we might one day
name members of a society according to certain rules derived from our system,
and then feed the names to a machine that ~ ~ o u l doblige by telling us the kinshipstructure.
Unfortunately, by the time we had so named the individuals concerned
we should know as much about their kinship structure as any machine
could tell us. On the other hand, it is possible that the language devised might
help analytically, by providing a guaranteed exhaustive classification of possible
kinship structure and even bring out empirically unperceived similarities, as
topology may show similarities or intuitively dissimilar knots.
Actual rules of naming and the inheritance of names in societies could be
stated and compared by showing which parts of our ideal and complete names
are left out, or on which parts or series within the ideal name the real name
depends. Similarly inheritance rules could be stated and compared with the
help of our language. In the case of what anthropologists call classificatory
kinship terminology, (a name for a kind of terminologies in actual use in certain
societies) their functioning would be conveyed in our scheme by stating that
all names (in our sense) of a certain structure are equivalent to one kinship
term in that society's language. (For instance, in a classificatory terminology
one term may serve for "father" and for any "paternal uncle".)
I t is also possible-I speak diffidently for my ignorance of demography is
even greater than that of logic and anthropology-that it would facilitate a
general theory of connection between demographic trends and kinship structure.
There obviously is a connection between the fields. To take a simple example,
on certain assumptions, a society in which one man may marry many women is
more likely to grow in population than a society in which only women may
marry a number of partners.
Of course, I imagine that demographers do in an ad hoc manner relate their
analyses to kinship structure, but our language might make it possible to state
an over-all theory. For instance, if the assumption were made that fecundity,
childbearing age and perhaps some other variables are constant, a general
theory might relate demographic trends to various kinds of kinship structure.
(The causal connection between demographic and kinship facts may of course
operate in both directions.) I t might even be possible to devise general schemes
for extrapolating into the past from the present size and structure of societies
and thus obtaining an aid towards reconstructing the history of illiterate peoples
and checking on their own often far-reaching kinship legends. Again, the scheme
might be of use in genetics. Whether any of these possibilities would actually
be useful I abstain from guessing. There are, however, sufficiently numerous
social scientists able and anxious to mathematicize their discipline and they
might care to have a try. The actual working out of the rules of such a notation
is a matter sufficiently complex, technical and difficult not to be usefully attempted
in the same place as the verbal specification of what is required and the
discussion of the implications of the attempt, which is essentially what is attempted
in this paper.
242 BRSEST GELLSETZ
Philosophical Implications. If the above scheme of an ideal language in the limited
but empirical field of kinship theory were actually realised, or if even it were
accepted that it is realisable, this mould show that an "ideal language" satisying
at least some of the specifications of that aspiration can be made to work over a
limited but not trivial field. In a way the carrying out of the scheme could count
as a 'formalisation' of kinship theory; but as it would actually 'mirror' the
subject matter of that theory, it \vould also count as an ideal language in the
above sense.
As I have said, the reasons which led to the abandonment of the pursuit of
an ideal language have not been made clearer than that notion itself. Historically,
it seems to have been caused by the failure of the people originally inspired by
that ideal to provide either samples of an ideal language or even satisfactory
recommendations for constructing one. I t was felt, perhaps rightly, that this
failure contained a profound and important intimation of something-though
I know not what. In consequence, philosophers of the relevant tradition turned
their backs on ideal language and indulged in a study of "ordinary language",
a pursuit whose exclusive usefulness is not to my mind conclusively established.
If the scheme propounded in this paper worked or were workable, reflection on
the difference between limited fields or the limited fields where it can work and
"the world in general" might throw more light on why an "ideal language in
general" cannot be obtained. This device may be similar to Wittgenstein's
'language games' but perhaps superior in not being a game. This use of the idea
gives it a certain philosophic interest even if it should not find other application.