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Deontic Conflicts and Multiple Violations

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Book cover Logic, Language, and Computation (TbiLLC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8984))

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Abstract

This paper presents a novel semantics for deontic modals which provides a uniform solution to prominent puzzles in the literature. The paper focuses on deontic conflicts, discussing them using the Dr. Procrastinate puzzle as an example. The focus lies on the Dr. Procrastinate puzzle as it combines an upward monotonicity puzzle with a conflict of obligations, allowing an explanation of the solutions to both types of puzzle in detail.

The semantics is an extension of radical inquisitive semantics, and it modifies Andersonian deontic modals as it introduces quantification over alternatives. The solution to deontic conflicts is made possible by the semantics allowing permission and prohibition statements to introduce multiple violations. Each rule is assigned a different violation, allowing for reasoning with rules also in cases where it is impossible to avoid violating all rules.

I am grateful to Jeroen Groenendijk, Stefan Hinterwimmer, Floris Roelofsen, Mandy Simons, Carla Umbach, and Matthijs Westera for extensive discussion of the ideas presented here and closely related topics, to two anonymous reviewers for constructive criticism, and to the Estonian Research Council for their support.

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Notes

  1. 1.

    May and must can also receive, among others, epistemic readings. For a related treatment of epistemic modals, see [2].

  2. 2.

    This simple version of a deontic conflict does not pose a problem for Kratzer semantics which also considers an ordering of worlds. See for example Lassiter [25, p. 151] for discussion on deontic conflicts which also cause problems for Kratzer semantics.

  3. 3.

    See [19].

  4. 4.

    See [27].

  5. 5.

    See [20, 30].

  6. 6.

    See [19].

  7. 7.

    In this paper, ought is used interchangeably with must because distinctions between the two do not play a role in the presented treatment.

  8. 8.

    Based on Aher [1, 3, 4].

  9. 9.

    Anderson introduced relevant implication instead of material implication, but a full discussion of this logic is outside of the scope of this paper.

  10. 10.

    The image is taken from the popular online chess site chess.com.

  11. 11.

    A reviewer pointed out that there’s an alternative construal put forward by Frank [18], Kaufmann and Schwager [21] and Cariani, Kaufmann and Kaufmann [12] among others in which there’s always a covert epistemic necessity operator over the consequent of a conditional.

  12. 12.

    The treatment of conditionals will necessarily be brief. The radical framework, developed by Sano [28] and Groenendijk & Roelofsen [16], provides an intuitive basis for this treatment of deontic modals. The details of a suppositional extension can be found in [17].

  13. 13.

    We are constrained to deontic modals. See work in progress on suppositional inquisitive semantics [2] on how to treat epistemic modals in a structurally similar manner.

  14. 14.

    There is a further extension of the system [17] which distinguishes a third relation between states and sentences which concerns a state dismissing a supposition of a sentence. In the semantics presented here, when a state rejects \(p\), it both supports and rejects \(p \rightarrow q\), and \(\Diamond p\). In the suppositional extension such states are characterized as neither supporting nor rejecting them, but as dismissing a supposition of theirs.

  15. 15.

    Equivalence is defined as mutual entailment.

  16. 16.

    The natural language examples are for illustration only. The actual picture of positive and negative responses is naturally more complicated. See for example Brasoveanu et al. [10].

  17. 17.

    If you are reading this in gray-scale, violation worlds are darker and non-violation worlds are lighter.

  18. 18.

    SML treats permission as weaker, so

    figure w

    does not guarantee that when you bring about \(p\), no violation occurs.

  19. 19.

    A comparison of Figs. 9 and 16 also shows that \((p\vee q)\rightarrow r\) and \((p \wedge q)\rightarrow \lnot r\) are consistent with each other. This is also the case in Kratzer semantics if it’s combined with an alternative-based treatment of disjunction. See for example Alonso-Ovalle [6].

  20. 20.

    See [4], especially for discussion on how to also attain disjunctive readings under permission.

  21. 21.

    Stronger is understood through entailment:

    figure al

    .

  22. 22.

    Strengthening the antecedent also doesn’t hold for obligation for the same reason as it does not hold for implication and permission, but we do not have the space to go through the calculations here.

  23. 23.

    This example is a simplification of a World Trade Organization panel report from case DSU 344. For further details see [4, p. 104].

  24. 24.

    This is not to say that further work should not focus on more fine-grained conceptualizations.

  25. 25.

    Such an approach is not to be confused with work on presuppositions which, as far as the author is aware, is an entirely disconnected phenomenon.

  26. 26.

    See [2].

  27. 27.

    More involved scenarios will likely require a more fine-grained approach which compares violations.

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Authors and Affiliations

  1. Tartu University, Tartu, Estonia

    Martin Aher

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  1. Martin Aher
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Editors and Affiliations

  1. University of Tartu, Tartu, Estonia

    Martin Aher

  2. Universität Stuttgart, Stuttgart, Germany

    Daniel Hole

  3. Institute of Mathematics, AS CR, Prague, Czech Republic

    Emil Jeřábek

  4. University of Strathclyde, Glasgow, United Kingdom

    Clemens Kupke

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Aher, M. (2015). Deontic Conflicts and Multiple Violations. In: Aher, M., Hole, D., Jeřábek, E., Kupke, C. (eds) Logic, Language, and Computation. TbiLLC 2013. Lecture Notes in Computer Science(), vol 8984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46906-4_3

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