Austrians tend to closely define marginal utility as a non-quantifiable ordinal relationship. Much of mainstream economics rests upon the assumption that utility can be safely proxied by quantifiable phenomena.
Would there be value in proving that utility is not quantifiable under normal algebraic means? For instance, utility probably fails the Abelian and monoid tests for rings (I provide no formal proof). Could this be used as a critique of econometric models which proxy quantities to derive algebraic formulations? Much of Austrian critique of quantity proxies for utility rely on proof in the vernacular (such as Rothbard’s arguments in Man, Economy, and State).
Just because the Austrian schools criticizes the applicability of algebraic modeling in catallactics, does not mean that math cannot be used to properly critique other schools of thought within their own domains.
Furthermore, the math developed in the last century regarding set theory, sequences, and relations may be sufficiently powerful to help clarify and formalize many of the Austrian models and arguments without burdening the models themselves.
Thoughts?