M. Duží, B. Jespersen and P. Materna rejected a revolution in analytic philosophy brought about by S. Kripke and H. Putnam. The revolution championed new views on meaning, modalities and essences based on extensional essentialism, semantic externalism, and metaphysical necessity. Duží, Jespersen and Materna offer an opposite approach: semantic internalism, priority of logical necessity, and essentialism related only to concepts. Despite their disagreements, both sides prefer modal monism based on one fundamental source of modality. The aim of the paper is to show that modal monism is not adequate and should be replaced by a dualistic view as it is found, for instance, in two-dimensional semantics. Two-dimensional semantics enables Duží, Jespersen and Materna to maintain their views but avoid problems that stem from their rationalistic modal monism.