Regarding the exclusive use of mathematical modeling in economics, there is a deeper objection.  Leaving aside the fact that a mathematical result has nothing to say, as such, about reality and that to do so requires an always risky interpretation, any mathematical truth is a necessary truth, that is, the final result of a mathematical process is already inherent in the initial definitions and hypotheses. This is not, of course, to rule out mathematics; it is rather not to claim any mathematical authority for, more or less arbitrary, presuppositions and interpretations.
JA

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