The Nature of the Structures of Applied Mathematics and the Metatheoretical Justification for the Mathematical Modeling

The classical (set-theoretic) concept of structure has become essential for every contemporary account of a scientific theory, but also for the metatheoretical accounts dealing with the adequacy of such theories and their methods. In the latter category of accounts, and in particular, the structural metamodels designed for the applicability of mathematics have struggled over the last decade to justify the use of mathematical models in sciences beyond their 'indispensability' in terms of either method or concepts/entities. In this paper, I argue that these metamodels employ structures of different natures and epistemologies, and this diversity does pose a serious problem to the intended justification.