Operator arguments revisited

  • Peter Fritz
  • John Hawthorne
  • Juhani Yli-Vakkuri


Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how such an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber.


Semantics Modal logic David Kaplan Tense logic Relativism Propositions 



We owe special thanks to Hans Kamp, who provided us with extensive written and oral comments on a draft of this paper, and to Cian Dorr and Timothy Williamson, who did likewise for a draft of a precursor of this paper written by Juhani Yli-Vakkuri. We would also like to thank Berit Brogaard, Vera Flocke, Michael Glanzberg, Jeremy Goodman, Jeff King, Max Kölbel, Øystein Linnebo, Reinhard Muskens, Brian Rabern, Margot Strohminger, Clas Weber, an anonymous referee for Philosophical Studies, and audiences at CSMN at the University of Oslo, the LOGOS Research Group in Analytic Philosophy at the University of Barcelona, the University of Oxford, and Rutgers University for helpful comments and discussions. Juhani Yli-Vakkuri’s work on this paper was supported by the Alexander von Humboldt Foundation and by the University of Tartu ASTRA Project PER ASPERA (European Regional Development Fund).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.University of OsloOsloNorway
  2. 2.University of Southern CaliforniaLos AngelesUSA
  3. 3.University of TartuTartuEstonia

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