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Journal of Philosophical Logic

, Volume 40, Issue 6, pp 693–713 | Cite as

On the Treatment of Incomparability in Ordering Semantics and Premise Semantics

  • Eric Swanson
Article

Abstract

In his original semantics for counterfactuals, David Lewis presupposed that the ordering of worlds relevant to the evaluation of a counterfactual admitted no incomparability between worlds. He later came to abandon this assumption. But the approach to incomparability he endorsed makes counterintuitive predictions about a class of examples circumscribed in this paper. The same underlying problem is present in the theories of modals and conditionals developed by Bas van Fraassen, Frank Veltman, and Angelika Kratzer. I show how to reformulate all these theories in terms of lower bounds on partial preorders, conceived of as maximal antichains, and I show that treating lower bounds as cutsets does strictly better at capturing our intuitions about the semantics of modals, counterfactuals, and deontic conditionals.

Keywords

Modals Counterfactuals Incomparability Ordering semantics Premise semantics 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MichiganAnn ArborUSA

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