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A Theory of Necessities

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Abstract

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of being a necessity, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic.

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Authors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Andrew Bacon & Jin Zeng

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  1. Andrew Bacon
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  2. Jin Zeng
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Correspondence to Andrew Bacon or Jin Zeng.

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Thanks are due to Cian Dorr and an anonymous referee for making several helpful suggestions. Both authors contributed equally to this paper.

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Bacon, A., Zeng, J. A Theory of Necessities. J Philos Logic 51, 151–199 (2022). https://doi.org/10.1007/s10992-021-09617-5

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  • DOI: https://doi.org/10.1007/s10992-021-09617-5

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