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On the Treatment of Incomparability in Ordering Semantics and Premise Semantics

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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.

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  1. Department of Philosophy, University of Michigan, Ann Arbor, MI, USA

    Eric Swanson

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Swanson, E. On the Treatment of Incomparability in Ordering Semantics and Premise Semantics. J Philos Logic 40, 693–713 (2011). https://doi.org/10.1007/s10992-010-9157-z

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