Secret Mathematics of Agnosticism

Agnosticism usually is classified as an informal philosophical viewpoint or hesitation on theological aspects. However, this paper presents agnosticism as a mathematically optimal state of ignorance represented by the maximal entropy, vacuous probability intervals in the context of Dempster-Shafer theory, and an invariant fixed point during Bayesian belief update. The framework of the empty/epistemic simplex and corresponding entropic dynamics is introduced. Moreover, problems of imprecise probability in the case of radical ignorance and algebraic multi-valued logic are discussed. Finally, open problems and research avenues are suggested for the implementation of mathematical agnosticism in Artificial General Intelligence (AGI) and distributed knowledge management systems.