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

Lloyd Humberstone
Journal of Philosophical Logic
Vol. 36, No. 1 (Feb., 2007), pp. 1-32
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226885
Page Count: 32
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Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness
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Abstract

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 under 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.

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