An axiomatic approach to theodicy via formal applied systems

Edward Nieznański developed two logical systems in order to deal with a version of the problem of evil associated with two formulations of religious determinism. The aim of this research was to revisit these systems, providing them with a more appropriate formalization. The new resulting systems, namely, N1 and N2, were reformulated in first-order modal logic; they retain much of their original basic structures, but some additional results were obtained. Furthermore, our research found that an underlying minimal set of axioms is enough to settle the questions proposed. Thus, we developed a minimal system, called N3, that solves the same issues tackled by N1 and N2, but with less assumptions than these systems. All of the systems developed here are proposed as solutions to the logical problem of evil through the refutation of two versions of religious determinism, showing that the attributes of God in Classical Theism, namely, those of omniscience, omnipotence, infallibility, and omnibenevolence, when formalized, are consistent with the existence of evil, providing one more response to this traditional issue.