Journal of Philosophical Logic

, Volume 36, Issue 1, pp 1–32 | Cite as

Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness

  • Lloyd Humberstone


The logic of ‘elsewhere,’ i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions (explaining the use of the word ‘elsewhere’), as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers un-der the name ‘modal agnosticism.’ In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position – its neutrality as between modal realism and modal anti-realism.

Key words

Halldén completeness modal logic possible worlds 


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© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Monash UniversityVictoriaAustralia

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