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On the Ternary Relation and Conditionality

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Abstract

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley–Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

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Author information

Authors and Affiliations

  1. University of Connecticut, Storrs, CT, 06269-2054, USA

    Jc Beall

  2. University of Otago, Otago, New Zealand

    Jc Beall

  3. La Trobe University, Melbourne, VIC 3086, Australia

    Ross Brady

  4. Indiana University, Bloomington, IN, 47405, USA

    J. Michael Dunn

  5. University of Alberta, Alberta, Canada

    A. P. Hazen

  6. University of Melbourne, Parkville, VIC 3010, Australia

    A. P. Hazen, Graham Priest, Greg Restall & David Ripley

  7. Victoria University of Wellington, Wellington, 6140, New Zealand

    Edwin Mares

  8. Australian National University, Canberra, ACT 0200, Australia

    Robert K. Meyer, John Slaney & Richard Sylvan

  9. Graduate Center, City University of New York, New York, NY, 10016, USA

    Graham Priest

  10. University of St Andrews, St Andrews, Fife, KY16 9AL, UK

    Graham Priest

Authors
  1. Jc Beall
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  2. Ross Brady
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  3. J. Michael Dunn
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  4. A. P. Hazen
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  5. Edwin Mares
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  6. Robert K. Meyer
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  7. Graham Priest
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  8. Greg Restall
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  9. David Ripley
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  10. John Slaney
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  11. Richard Sylvan
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Corresponding author

Correspondence to Jc Beall.

Additional information

This paper emerged from some working sessions at the University of Melbourne in 2009. Beall, Brady, Hazen, Priest, Restall, Ripley, and Slaney were involved on the ground. The work of Dunn and Mares kept coming up during the sessions, and the paper greatly benefited from their joining the effort after the event. Looming even larger in the initial discussions were two others: despite their deaths, much of the early work of Sylvan and Meyer was heavily represented. While we can’t speak for the current views of Bob (Meyer) or Richard (Sylvan), we wanted to honor them for their starting this ternary-relation idea in the first place. Hence, we include them as authors. While not all of us (authors) agree on all ideas herein, we do agree with the main thrust of this paper: namely, that, despite first appearances, the ternary-relation approach to conditionality is very much philosophically plausible as capturing an important aspect of conditionality.

R. K. Meyer and R. Sylvan (formerly Routley), both deceased.

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Beall, J., Brady, R., Dunn, J.M. et al. On the Ternary Relation and Conditionality. J Philos Logic 41, 595–612 (2012). https://doi.org/10.1007/s10992-011-9191-5

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