Which Modal Models are the Right Ones (for Logical Necessity)?

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THEORIA. An International Journal for Theory, History and Foundations of Science, ISSN: 2171-679X, Vol: 18, Issue: 2, Page: 145-158

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John P. Burgess
Euskal Herriko Unibertsitatea / Universidad del País Vasco
article description
Recently it has become almost the received wisdom in certain quarters that Kripke models are appropriate only for something like metaphysical modalities, and not for logical modalities. Here the line of thought leading to Kripke models, and reasons why they are no less appropriate for logical than for other modalities, are explained. It is also indicated where the fallacy in the argument leading to the contrary conclusion lies. The lessons learned are then applied to the question of the status of the formula ¯$x$y (x ¹ y).