The second difficulty addresses the epistemological status of the claim that there is a structural equivalence between the mathematical and the non-mathematical domains. On what grounds do we know that such equivalence holds? Someone may say that the equivalence is normatively imposed in order for the application process to get off the ground. But this suggestion leads to a dilemma. Either it is just assumed that we know that the equivalence holds, and the epistemological question is begged (given that the grounds for this are in question), or it is assumed that we do not know that the equivalence holds—and that is why we have to impose the condition—in which case the latter is clearly groundless. However, it may be argued that there is no problem here, since we establish the isomorphism by examining the physical theories of the material objects under consideration. But the problem is that in order to formulate these physical theories we typically use mathematics. And the issue is precisely to explain this use, that is, to provide some understanding of the grounds in terms of which we come to know that the relevant mathematical structures are isomorphic to the physical ones.