The Genius of Kinship: The Phenomenon of Human Kinship and the G ...

The awareness of kinship theorists of the history of mathematical logic starts with MacFarlane: His work was eulogized by Rodney Needham (see, e.g., Neeham, 1971a, pp. xxii-xxv),⁵ and even republished in Ballonoff's volume Genetics and Social Structure (1974). De Morgan's seminal publication received a different trajectory: his logic of relations was developed by Charles Peirce (1873, 1897a, 1897b), Ernst Schröder (1895), Bertrand Russell (1903), Rudolf Carnap (1929), Alfred Tarski (1941a), J. C. C. McKinsey (1940, 1946), and Alexander R. Bednarek and Stanislaw M. Ulam (1978, 1990), and it entered the classical textbooks of symbolic logic as a promising but under-developed field. The logic of relations explicitly allows for the quantification over classes, an operation not available to other foundational figures in modern logic such as George Boole and Gottlob Frege, who continued to analyze propositions like “x is an ancestor of y” in terms of abstract classes and properties (see Lucey, 1979).

According to Gottschall (1980, p. 238), Bednarek and Ulam actually fulfill De Morgan's “trenchant prophecy” by classifying his logic of relations. Outside of the spheres of analytical philosophy, formal logic and abstract algebra, Joseph Greenberg's youthful interest in logical positivism took him to Carnap, whose brief notes on kin relations inspired Greenberg's rarely cited work The Logical Analysis of Kinship (Greenberg, 1949). Again, De Morgan was left out, for neither Greenberg nor his reviewer (Borgers, 1949) gave a single mention of him. None of the programmatic works on the algebraic analysis of kinship published in the last 20 years (see, e.g., Boyd, 1966; Gould, 2000; Lehman, 1993, 2001; Levin, 1974, 1978; Liu, 1986; Read, 1974, 1984, 2001; H. White, 1963) contains any acknowledgment of De Morgan's pioneering effort or makes any reference to Peirce, Schröder, Russell, Tarski, McKinsey, Bednarek, and Ulam. Trautmann's Lewis H. Morgan and the Invention of Kinship (1987) also failed to bring to light the existence of L. H. Morgan's namesake. Alternatively, the only monographic study of De Morgan's contribution, namely Augustus De Morgan and the Logic of Relations (Merrill, 1990), quite predictably contains no references