Breaking de Morgan's law in counterfactual antecedents

Abstract

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal.

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References found in this work

Semantics in generative grammar.Irene Heim & Angelika Kratzer - 1998 - Malden, MA: Blackwell. Edited by Angelika Kratzer.
A Theory of Conditionals.Robert Stalnaker - 1968 - In Nicholas Rescher (ed.), Studies in Logical Theory. Oxford,: Blackwell. pp. 98-112.
Counterfactuals.David Lewis - 1973 - Tijdschrift Voor Filosofie 36 (3):602-605.
Counterfactuals.David Lewis - 1973 - Foundations of Language 13 (1):145-151.
Causality: Models, Reasoning and Inference.Judea Pearl - 2000 - Tijdschrift Voor Filosofie 64 (1):201-202.

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