On the articulation of systematic-dialectical methodology and mathematics

In their published works, both Hegel and Marx made use of a form of a historical as well as a systematic dialectic. There is more room for quantification in Marx’s system than there is in Hegel’s because the imperative of exchange that is paramount to Marx determines the concepts required for Marx’s dialectics as ontologically quantitative abstractions-in-practice. Hegel’s system, by contrast, does not allow for the existence of such entities because his determination of the subject of mathematics as an external reflection on many distinguishable but divisible elements, forbids immediate quantitative representations of anything without first devising a suitable Measure that reunites external Quantity with internal Quality. Since Marx’s schemes of reproduction, i.e. his models for the renewal and expansion of capital deal exclusively with the aforementioned abstractions-in-practice, they can be reconstructed in such a way that they are fully defendable dialectically. This requires the model’s assumptions to either formally recap a dialectically arrived at result, temporarily abstract from some tendency that was already exhibited dialectically, remind the reader that some not yet exhibited entities must be considered absent at the level of abstraction the model pertains to or to anticipate the presence of not yet exhibited mechanisms crucial to the unhindered working out of a tendency that was exhibited as necessary to the working of the system as a whole. When assumptions can be presented like that, there are no fundamental obstacles to the integration of systematic dialectics and mathematics or mathematical modeling