Logic of hegelian quantity

Abstract

Hegel’s Science of Logic presents in the Logic of Being, in the 2nd Section, Quantity, as a philosophy of modern mathematics. The stage of development of modern sciences in general, and of mathematics in particular, allow Hegel to make a diagnosis of the advances and limits reached so far, which points out the contradictions of the concept of quantity/quantum. We initially reconstructed the theory of pure quantity and its continuous and discrete moments; then, the dialectic of the extensive and intensive quantum, with the moments of number that culminate in the contradiction of infinitesimal calculus; finally, in the quantitative relationship, the overcoming of the speculative deficit of the mathematical relationships itself is articulated, giving rise, in this sense, to the conceptual aspect of quantity as quality. In other words, Hegel immanently deduces qualitative dialectic in quantity itself, so that with this explanation the quantitative logic is qualitatively determined, that is, mathematics has a speculative logical sense.