The nature and procedure of the formation of the primary terms of non-philosophy, of its non-conceptual symbols, starting from philosophical concepts concerned with philosophical intuitiveness and naïveté.
Axiomatics is initially a scientific object. It is the organization of a theory or a fragment of a theory in order to empty the terms of their empirical or regional contents and to explicitly reveal the logical apparatus which connects them and becomes through this their only contents. There is a philosophical reflection on the axiomatic (Aristotle), but there are few examples of axiomatization in philosophy itself, if not perhaps in Descartes’ Responses, Spinoza’s Ethics and Fichte’s Science of Knowledge. In all these cases it is a matter of an ontological axiomatization, still largely intuitive. In the sciences, more or less complete attempts at axiomatization were made in particular by Hilbert in geometry, by Jean-Louis Destouches in quantum physics—i.e. above all in fields where unexpected innovations (non-Euclidean geometries, Heisenberg’s ‘uncertainty’ principle) required theoretical reorganization to legitimate their rigor. The epistemology of Mario Bunge draws conclusions from the postulate that it is in theory possible to axiomatize any scientific discipline. But axiomatization is an effort of reorganization which comes with the aftermath—even after a crisis—in the goal of examining the validity of a theory and the formalization of its relations to other theories which, in any event, has known limits (Godel). It is more a theoretical instrument than a theoretical project of the foundation of science.