Abstract
The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for “Necessarily P” is a state that bans every exact truthmaker for “Not P”, and an exact truthmaker for “Possibly P” is a state that allows an exact truthmaker for P. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of “truth at a possible world” in terms of exact truthmaking.
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Acknowledgements
This paper derives largely from the first and second chapters of my dissertation Necessity, Essence, and Analyticity: Toward an Analytic Essentialist Account of Necessity delivered to the Graduate Faculty in Philosophy at the Graduate Center, City University of New in 2022. I would first like to express my deepest gratitude to Kit Fine, Graham Priest, and Melvin Fitting for their insightful and often incisive feedback on multiple drafts of this paper and for engaging in many enlightening discussions. My gratitude also goes to the other members of my dissertation committee, Michael Devitt and David Papineau, for their helpful comments. This work was presented at various venues, including the Logic and Metaphysics Workshop at the CUNY Graduate Center in 2019, the Monthly Workshop of the Korean Association for Logic at Jeonbuk National University in 2021, the Second and Third Korea Logic Days at Yonsei Univerisity in 2022 and 2024. I am thankful for the questions and comments from participants of these meetings. Finally, I extend my sincerest thanks to three anonymous reviewers from this journal; their extensive and constructive feedback was crucial both in refining the presentation and in clarifying several of the key ideas in this work.
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Kim, D. Exact Truthmaker Semantics for Modal Logics. J Philos Logic 53, 789–829 (2024). https://doi.org/10.1007/s10992-024-09752-9
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DOI: https://doi.org/10.1007/s10992-024-09752-9