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Identity and Harmony and Modality

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Abstract

Stephen Read presented harmonious inference rules for identity in classical predicate logic. I demonstrate here how this approach can be generalised to a setting where predicate logic has been extended with epistemic modals. In such a setting, identity has two uses. A rigid one, where the identity of two referents is preserved under epistemic possibility, and a non-rigid one where two identical referents may differ under epistemic modality. I give rules for both uses. Formally, I extend Quantified Epistemic Multilateral Logic with two identity signs. I argue that a uniform meaning for identity tout court can be given by adopting Maria Aloni’s account of reference using conceptual covers. We obtain a harmonious set of rules for identity that is sound and complete for Aloni’s model theory.

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Acknowledgements

I thank Maria Aloni and Luca Incurvati, as well as two referees for this journal, for helpful discussions on earlier versions of this work.

Funding

This work has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 758540) within the project From the Expression of Disagreement to New Foundations for Expressivist Semantics.

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  1. Philosophy Department, University of Connecticut, Storrs, Mansfield, CT, USA

    Julian J. Schlöder

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  1. Julian J. Schlöder
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Schlöder, J.J. Identity and Harmony and Modality. J Philos Logic 52, 1269–1294 (2023). https://doi.org/10.1007/s10992-023-09705-8

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