Mathematics and economics: the case of Menger

Carl Menger's methodology describes reality as neatly organized, being constructed additively from strictly regular simple elements called pure types. Such a conception of the world's structure seems to invite mathematical treatment. Yet, his economics is not a mathematical one, and he even explicitly rejected mathematical approach to economics. This apparent puzzle is explained by Menger's failure to deliver in his methodological writings a realistic portrayal of what he was actually doing in his economics. His implicit ambition to retain the full meaning of the natural language concepts while using them simultaneously as theoretical concepts makes his economics dependent on the general human knowledge. Because the latter is mostly non-mathematical, so has to remain the former. This makes his economics both richer as well as fuzzier as compared with mathematical economics. This seems to be the result of a deliberate decision to keep his economic theory more realistic.