Squaring and Hexagonizing Logical Relations Among Three Different Kinds of Deontic Modality “Obligatory”: A Model for Logically Formalized Axiomatic Epistemology Theory

In contrast and complement to the logical square and hexagon by G. Kalinowski modeling logic of norms, in this paper such logical square and hexagon of conceptual opposition are submitted which model logical interconnections among three different kinds of deontic modality “obligatory”. The qualitative differentiation among the three is in accordance with a logically formalized axiomatic epistemology theory. It is proved that the axiomatic theory is consistent and implies substantial difference between a-priori knowledge of obligatory-ness and a-posteriori one. The paper submits a formal inference (in that axiomatic theory) of the logic equivalence of modalities “necessary” and “obligatory” from the assumption that the relevant knowledge is a-priori one. Formal proving that theorem means the conditional equivalence of corresponding deontic and alethic modalities. This is a significant explication and correction of the modality views which many philosophers are used to. Squaring and hexagonizing logical relations among the three different kinds of deontic modality “obligatory” helps to grasp the novel idea effectively.