Epistemological Residuals and Knowledge Fractals: An Asymptotic Model for Social Science Methodology

Debates over quantitative and qualitative methods often assume that one can replace the other. This article develops a conceptual model of epistemological residuals: aspects of a problem space that remain underdetermined after formalization, measurement, or model construction. Using Godelian incompleteness and quantum uncertainty as structural analogies, the article argues that quantitative methods stabilize bounded subspaces of inquiry, whereas qualitative judgment interprets residual questions of meaning, validity, and value. The resulting asymptotic model reframes mixed methods as iterative coordination between formal reduction and communal interpretation, with implications for measurement, governance, and AI alignment.