Tools or Toys?
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Under “problem orientated research” I understand the kind of research where scientists try to answer a particular empirical research question. If a scientist follows a problem orientated research strategy then the problem is fixed and the methods should be chosen or disposed of as appropriate. From what has been said before about the specific conditions for modeling in the social sciences, two obvious conclusions follow:
A possible exception to this rule is the science of economics, where there seem to be few methodological alternatives to modeling. It almost seems as if in economics, any answer of an economical question needs to be rendered in the form of a model in order to be acceptable to the community. (I am not in a position to judge whether what appears to be the common understanding of economists about their science is misguided or not. Therefore, I am just mentioning this fact.)
But even in those cases where the kind of research question does not preclude a mathematical approach prima facie, modeling is not always worth the effort. If a model can neither be validated empirically nor vindicated theoretically then there is no point in modeling.