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


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.


Modals Counterfactuals Incomparability Ordering semantics Premise semantics 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MichiganAnn ArborUSA

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