Abstract

The paper investigates the formal distinction between logical necessity and metaphysical necessity. After K. Fines terminology, we differentiate between ‘logical necessity’ (or ‘absolute necessity’) and ’metaphysical necessity’ in the debate between modal monists, who believe these modalities are reducible to one another, and pluralists, who argue for their irreducibility. This is one of the key and long-discussed issues in modal metaphysics, examined through the works of notable philosophers and logicians such as D. Chalmers, P. Van Inwagen, S. Kripke, D. Lewis, G. Rosen, R. Stalnaker, and, of course, Fine. We adopt a formal approach to model these modalities using Kripke structures. We argue that metaphysical necessity, constrained by the formal strength of at most $$\textsf {S5}$$ S 5, cannot be considered as absolute as the formal strength of absolute necessity in a proper extension of modal logic $$\textsf {S5}$$ S 5. This is because in all models, absolute necessary truths are logical truths, and there are no additional accidental or possible truths in this sense. This does not hold even for necessity in modal logic $$\textsf {S5}$$ S 5. The paper is organized as follows: we begin by outlining pre-theoretical intuitions. Next we present the semantics of non-accidental Kripke models for metaphysical and absolute necessity. The first one will be considered as a modality dependent on the accessibility relation between possible worlds, while the second will be independent of it and forces truth in all possible worlds across all models. We prove that our absolute necessity, contrary to metaphysical necessity, always captures only logically valid formulas. Finally we develop a formal system, prove its completeness and discuss the implications and limitations of the approach. We aim to provide new insights into the ongoing debate between modal monists and pluralists, which turns out to be connected with R. Carnap’s old idea of logical necessity, expressed in terms of possible worlds semantics.