Logica Universalis

, Volume 6, Issue 1–2, pp 109–118

Approaching the Alethic Modal Hexagon of Opposition

Article
  • 125 Downloads

Abstract

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 

Keywords

Modal logic hexagon of opposition duality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of PhilosophyTrinity College DublinDublin 2Ireland

Personalised recommendations