On the Treatment of Incomparability in Ordering Semantics and Premise Semantics

Journal of Philosophical Logic 40 (6):693-713 (2011)
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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References found in this work BETA
Niko Kolodny & John MacFarlane (2010). Ifs and Oughts. Journal of Philosophy 107 (3):115-143.
Angelika Kratzer (1979). Conditional Necessity and Possibility. In. In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds.), Semantics From Different Points of View. Springer-Verlag. 117--147.

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