Suppose a secular academic discipline (AD) endeavors to develop an epistemology. This study's formal theory shows efforts, which in aggregate, are not inclusive of any mathematical formalism result in epistemology that are vacuously formulated; mathematical formalism (mf) is, as such, not a luxury, rather is a necessary parameter of any epistemology that is robustly (non-vacuously) formulated. Suppose a concept or principle (COPR) is solely rooted in language, that is, is not natively mathematical. Only mf that are non-parametrically formulated (mfn), such as, Set Theory are robust to a formalization of the COPR. Suppose, contrarily that a COPR is natively mathematical; either mf that are parametrically formulated (mfp), such as, Differential Calculus, or mfn are robust to a parameterization of the COPR. Applying the foregoing, any and all applications of mfp to a core concern of Economics, namely "what is rationality (WIR)?" are inherently vacuous. The rationale is straightforward, namely ideally, "how exactly to implement rationality (HIR)?", which neoclassical theory parameterizes as, `value maximization' ought to be derived from a parameterization, a priori, of the concept of rationality. In the skipping of the WIR question to the HIR question, rationality, which first and foremost is a parameter of man - non-satiation with respect to `wealth' is, first and foremost, a parameter of man - is itself not parameterized. The vacuousness of the resulting neoclassical characterization of rationality is evident in the implication that there does not exist any person or time-invariant parameterization of rationality. With respect, as such, to rationality, asymptotically, the neoclassical standard is, `anything goes'. In presence of the evidence, there is arrival at epistemological and paradigm grounds for an alternative to each of neoclassical theory and neoclassical mathematics. For concreteness of the necessity of new mathematical formalism, with calculus shown, in this study, to be inappropriate to a parameterization of rationality - because only mfn are appropriate to the objective - noting that the concept of rationality is foundational to all of the Social Sciences and Humanities (SSH), neoclassical theory lacks mathematical formalism that are appropriate to the development of the epistemology of either economics or any of the other disciplines that make up the SSH. Since Philosophy refines language, all truly philosophical questions are rooted in language, are not natively mathematically specified. In presence of the foregoing, and additional evidence in support of the axiom that logic is non-robust to the development or progression of epistemology - logic refines existing epistemology, points out gaps or cracks in existing epistemology, and incentivizes the direction of, or extensions to epistemology, but is unable itself to actualize the changes that it points out to be desirable or necessary - ideally Philosophy journals become receptive to studies which, having applied logic arguments towards critiques of epistemology, additionally, apply solely mfn towards the development or progression of an epistemology. As is historically implored by Frege, if the response is, as such, there is arrival at a robust and appropriate progression to the relevance of Philosophy to the welfare of man.