Skip to main content
Article thumbnail
Location of Repository

An alternative rule of disjunction in modal logic

By Timothy Williamson


Lemmon and Scott introduced the notion of a modal system's providing the rule of disjunction. No consistent normal extension of KB provides this rule. An alternative rule is defined, which KDB, KTB, and other systems are shown to provide, while K and other systems provide the Lemmon-Scott rule but not the alternative rule. If S provides the alternative rule then either —A is a theorem of S or A is whenever A -> ΠA is a theorem; the converse fails. It is suggested that systems with this property are appropriate for handling sorites paradoxes, where D is read as 'clearly*. The S4 axiom fails in such systems

Topics: Philosophy, Logic, logic
Year: 1992
DOI identifier: 10.1305/ndjfl
OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.