Deductions from "Axiomatic Theory"
Herbert L. Costner, Robert K. Leik · American Sociological Review · 1964
Axiomatic theories, following Zetterberg, derive propositions according to the logic of classes. This procedure is valid if postulated relationships are perfect, but is subject to serious error when postulates are stated, or derivations are tested via correlation or association coefficients with absolute values less than unity. Given variables A, B, and C, with rAB and rBo treated as independent, the potential range of rAo is explored. If no further assumptions are made, r*AB+r2BC1 is a necessary and sufficient condition for validation of the axiomatic deductions. But when asymmetric, causal relations in a closed system are assumed, axiomatic deductions are validated regardless of the magnitude of the independent correlations. A similar examination of systems of association, as measured by Q, is undertaken, including operating curves specifying the range of QAC for varying magnitudes of QAB and QBo, and for varying marginal conditions.