ON CONSTRUCTIVE AXIOMATIC METHOD

Abstract. Formal axiomatic method popularized by Hilbert and recently defended by Hintikka (in its semantic version) is not fully adequate to the recent practice of axiom-atizing mathematical theories. The axiomatic architecture of (elementary) Topos theory and Homotopy type theory do not fit the pattern of formal axiomatic theory in the stan-dard sense of the word. However these theories fall under a more traditional and more general notion of axiomatic theory, which Hilbert calls constructive. A modern version of constructive axiomatic method can be more suitable for building physical and some other scientific theories than the standard formal axiomatic method. 1