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Extended Modal Dimensionalism is a metaphysical theory that is realism about spaces, times, and worlds. It is proposed by Martin Vacek. The theory involves an analysis of the nature of mathematical modality and its applications to unrestricted quantification and absolute decidability. It goes beyond two-dimensional hyperintensional formalizations of the modal logic of Zermelo–Fraenkel set theory, Large cardinal, Omega-logic, and the Epistemic modal logic.

The ambitious modal epistemology involves an inconsistent triad composed of Model monism, Two-dimensionalism, and what I call “Metaphysical Kripkeanism”. There is a fundamental incompatibility between Chalmers’ Modal Rationalism and Kripke’s modal Metaphysics. Specifically, Chalmers’ conceivability entails possibilities that a Kripkean rejects as genuinely metaphysical. However, three positive stances in modal epistemology emerge from the combinations that the triad allows. One of those offers a promising way forward for 2D modal epistemologies.

Background
Modal dimensionalism (MD) is realism about spaces, times, and worlds-metaphysical indices that make objects spatial, temporal, and modal, respectively, and that play the role of alethic relativizers, i.e. items to which matters of truth are relativized. If Four-dimensional space is an ontological, rather than conceptual or ordinary-language, thesis, some traditional objections are misguided. It then does not require any particular semantics for tensed claims, does not imply any conceptual or epistemic priority of stage-talk, and does not preclude a distinction in ordinary thought between processes and things. A more metaphysical traditional objection is that Four-dimensionalism precludes genuine change, but there is no good reason to regard the four-dimensionalist's position as committed to this claim.