Approaching the Alethic Modal Hexagon of Opposition
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- Simons, P. Log. Univers. (2012) 6: 109. doi:10.1007/s11787-012-0042-0
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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.