Logica Universalis

, Volume 6, Issue 1–2, pp 109–118 | Cite as

Approaching the Alethic Modal Hexagon of Opposition

  • Peter SimonsEmail author


Modal logic like many others sustains a hexagon of opposition, with the two “additional” vertices expressing contingency and non-contingency. We first illustrate hexagons of opposition generally by treating them as cut-down entailment lattices with order distinctions among multiple arguments suppressed. We then approach the modal case by treating it heuristically as a particular case of the hexagon for quantified propositions. Historically, possibility and contingency were sometimes confused: we show using the notion of duality that contingency, as negation-symmetric, is logically less interesting than possibility.

Mathematics Subject Classification (2010)

03B45 03A05 


Modal logic hexagon of opposition duality 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of PhilosophyTrinity College DublinDublin 2Ireland

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