Abstract

Levins and Lewontin have contributed significantly to our philosophical understanding of the structures, processes, and purposes of biological mathematical theorizing and modeling. Here I explore their separate and joint pleas to avoid making abstract and ideal scientific models ontologically independent by confusing or conflating our scientific models and the world. I differentiate two views of theorizing and modeling, orthodox and dialectical, in order to examine Levins and Lewontin’s, among others, advocacy of the latter view. I compare the positions of these two views with respect to four points regarding ontological assumptions: (1) the origin of ontological assumptions, (2) the relation of such assumptions to the formal models of the same theory, (3) their use in integrating and negotiating different formal models of distinct theories, and (4) their employment in explanatory activity. Dialectical is here used in both its Hegelian–Marxist sense of opposition and tension between alternative positions and in its Platonic sense of dialogue between advocates of distinct theories. I investigate three case studies, from Levins and Lewontin as well as from a recent paper of mine, that show the relevance and power of the dialectical understanding of theorizing and modeling.