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The Logical Analysis of Kinship

Published online by Cambridge University Press:  14 March 2022

Joseph H. Greenberg
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Extract

The present attempt to indicate the general manner in which the kinship system of a people can be stated as an interpreted axiomatic system, with utilization of the symbolism of modern mathematical logic, is intended as a demonstration of the applicability of contemporary logical methods to problems in the social sciences. Aside from the obvious general advantages in the way of clarity and logical rigour to be gained by an application of axiomatic method, there emerges as by-products a convenient system of kinship symbolization and what is believed to be a solution to the long-standing controversy concerning the use of the terms ‘descriptive’ and ‘classificatory’ in reference to kinship systems. Since kinship terms are words in languages, the present exposition is perhaps of interest in that it shows how meaning in a semantic field of related terms can be defined by logical methods. So all the directional or temporal terms in a specific language might be treated as kinship terms are here. The possibility of a systematic treatment of the semantic aspects of linguistics which so far have resisted this type of treatment should be of interest to linguists.

Type
Research Article
Information
Philosophy of Science , Volume 16 , Issue 1 , January 1949 , pp. 58 - 64
Copyright
Copyright © Philosophy of Science Association 1949

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Footnotes

1

The present treatment was partly suggested by R. Carnap's discussion of kinship in his Abriss der Logistik. I have also been struck by the frequent recourse to illustrations from kinship in logical discussion, particularly in relational theory. In the case of ‘ancestral relation,’ the term itself is taken from kinship and is, as a matter of fact, utilized here in the definition of a kin group descended from a common ancestor (a ‘clan’).

Previous applications of axiomatic method of which I am aware are: J. H. Woodger's The Axiomatic Method in Biology (Cambridge, 1937), the same writer's ‘Formalization of a Psychological Theory’ Erkenntnis 7: 195–8 (1937) and C. E. Shannon's ‘A Symbolic Analysis of Relay and Switching Circuits.‘ Transactions, American Institute of Electric Engineering 57: 713–23 (1938).

I am indebted to Wilfrid Sellars and Gerhard Kalisch for helpful criticism.

References

2 See now H. Reichenbach's treatment of the semantics of tense in Elements of Symbolic Logic (New York, 1947) 287–299.

3 For some of the primitive ideas introduced below, for example, O ‘older than’, an alternative treatment would involve the introduction of the following primitive ideas: 1) F ‘following in time,’ in terms of which F̄ ‘preceding’ and S ‘simultaneous’, the negation of the sum of the relations F and F̄, could be defined 2) t ‘the time of discourse’ 3) B, the relation of the birth of an individual to the individual, 4) D, the relation of the death of an individual to the individual. Then ‘x is older than y’ becomes ‘the birth of x precedes the birth of y’. The class λ (see Def. 3 below), consisting of those living at the time of discourse, might be defined as the class of those whose birth does not follow and whose death does not precede the time of discourse.

For most kinship systems the alternative followed in the text seems preferable.

4 There has been reported from Nigeria and other areas of West Africa the institution of woman marriage by which a woman becomes a ‘father’ to children by a slave girl whom she ‘marries.’ The physiological father is a man hired for the purpose. In this instance we may interpret ‘sociological male’ as including women—they are few in number—who practice this institution.

5 Among the Toda tribe of southern India, a polyandrous society, sociological paternity is determined by performance of a special ceremony (the bow ceremony). Occasionally the man who performs this ceremony is not one of the woman's husbands. He is, nevertheless, the father of the child from whom the child inherits property.

6 Where divorce and remarriage of the same couple can take place, we must introduce the further primitive ideas M′ ‘second marriage,’ D′ ‘second divorce’ and if necessary M″ ‘third marriage,’ D″ ‘third divorce’ etc. Then our definition of N ‘currently married’ will read:

We can, of course, extend this by the addition of as many alternations as we find necessary. There will be further primitive propositions concerning the relations of inclusion among these new primitive ideas:

7 This does not occur anywhere, to my knowledge.

8 The present treatment which defines δ in terms of λ will probably be adequate in all instances inasmuch as kinship systems do not make provision for the unborn. Thus the universe of discourse consists only of those individuals not born up to the moment of discourse. If the unborn are to be considered, then two classes, say v ‘the unborn,’ and λ ‘the living’ must be assumed and a third, δ ‘the dead,‘ then defined in terms of them. An alternative procedure is outlined in footnote 3.