ABSTRACT
This chapter investigates the relationship between ‘mathematical argumentation’ and ‘notional speculation’ in Georg Wilhelm Friedrich Hegel’s philosophy. Hegel saw his philosophy as a form of science out of which the speculative notion could be attained. He stood in critical opposition to the numerous philosophical attempts to make mathematics the methodological model for philosophy. He illustrates how the deficiency of ‘construction’ and ‘proof as ways of explanation are to be understood by using the example of a theorem proved qua construction. For Hegel, however, the ‘construction’ is at first limited to the geometrist’s incomprehensible operations with ‘temporary material’. His interpretation of Schelling is such that construction is not the equation of intuition and notion, but rather the sensed reflection of an archetype. If one were to attempt to say what significance Hegel’s philosophy of nature plays for contemporary natural science, one would encounter great difficulties. For almost a century research about Hegel has simply ignored his philosophy of nature.
