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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DOI 10.1007/s10992-010-9157-z
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References found in this work BETA
Counterfactuals.David K. Lewis - 1973 - Blackwell.
Ifs and Oughts.Niko Kolodny & John MacFarlane - 2010 - Journal of Philosophy 107 (3):115-143.
Most Counterfactuals Are False.Alan Hájek - 2014 - Http://Philrsss.Anu.Edu.Au/People-Defaults/Alanh/Papers/Mcf.Pdf, Accessed June 12, 2014.
What 'Must' and 'Can' Must and Can Mean.Angelika Kratzer - 1977 - Linguistics and Philosophy 1 (3):337--355.
Ifs. Conditionals, Belief, Decision, Chance, and Time.W. Harper, R. Stalnaker & G. Pearce - 1984 - Tijdschrift Voor Filosofie 46 (1):181-182.

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Citations of this work BETA
What We Know and What to Do.Nate Charlow - 2013 - Synthese 190 (12):2291-2323.
Modality, Weights and Inconsistent Premise Sets.Alex Silk - 2017 - Journal of Semantics 34 (4):683-707.
Evidence Sensitivity in Weak Necessity Deontic Modals.Alex Silk - 2014 - Journal of Philosophical Logic 43 (4):691-723.

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Remarks on Counterpossibles.Berit Brogaard & Joe Salerno - 2013 - Synthese 190 (4):639-660.
What We Know and What to Do.Nate Charlow - 2013 - Synthese 190 (12):2291-2323.
Situations in Natural Language Semantics.Angelika Kratzer - 2008 - Stanford Encyclopedia of Philosophy.
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