The search for symmetry in Hohfeldian modalities

In Amrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo & Petrucio Viana (eds.), Diagrammatic Representation and Inference. 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings. Springer. pp. 87-102 (2021)
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Abstract

In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition and exploit the notions of contingency and absoluteness in order to restore the symmetry of Hohfeldian modalities in accordance to the diagrams presented by Hohfeld. Interestingly, the investigation unveils three potestative squares defined at different levels of granularity (force, outcome and change) and allows us to further elaborate on the connections between deontic and potestative relations.

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Matteo Pascucci
Slovak Academy of Sciences

References found in this work

The power of the hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Voluntary Obligations and Normative Powers.Neil MacCormick & Joseph Raz - 1972 - Aristotelian Society Supplementary Volume 46 (1):59 - 102.
Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.
On the formal representation of rights relations.David Makinson - 1986 - Journal of Philosophical Logic 15 (4):403 - 425.

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