A combination of some sort is needed, and working metaphysics, understood as makeshift tool, might help. This already happens in practice, as it is evident from the somewhat clumsy efforts of international organizations such as the UN, which cannot be said to have a uniform persistent metaphysical basis to operate from. This Cartesian view I would think does not automatically follow from the use of mathematics as a tool, and is thus to be considered an additional feature. Scientific terminology tends to reflect such an opinion. In my next response I will start with a somewhat detailed discussion of Dialectical Materialism as a proposition for an epistemological point of view, and in further responses I intend to follow this with shorter comments on others.
Belief alone can comprehend belief.