Breaking de Morgan's law in counterfactual antecedents

Lucas Champollion, Ivano Ciardelli, Linmin Zhang


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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Alonso-Ovalle, Luis. 2006. Disjunction in alternative semantics. Amherst, MA: University of Massachusetts dissertation. dissertations/AAI3242324/.

Alonso-Ovalle, Luis. 2009. Counterfactuals, correlatives, and disjunction. Linguistics and Philosophy 32(2). 207–244. doi:10.1007/s10988-009-9059-0.

Ciardelli, Ivano. 2016. Lifting conditionals to inquisitive semantics. In Mary Moroney, Carol-Rose Little, Jacob Collard & Dan Burgdorf (eds.), Semantics and Linguistic Theory (SALT) 26, Ithaca, NY: LSA and CLC Publications.

Ciardelli, Ivano, Jeroen Groenendijk & Floris Roelofsen. 2013. Inquisitive semantics: A new notion of meaning. Language and Linguistics Compass 7(9). 459–476. doi:10.1111/lnc3.12037.

Erlewine, Michael Yoshitaka & Hadas Kotek. 2016. A streamlined approach to online linguistic surveys. Natural Language and Linguistic Theory 34(2). 481–495. doi:10.1007/s11049-015-9305-9.

Fine, Kit. 2012. Counterfactuals without possible worlds. The Journal of Philosophy 109(3). 221–246. doi:10.5840/jphil201210938.

Fine, Kit. 2014. Truth-maker semantics for intuitionistic logic. Journal of Philosophical Logic 43(2-3). 549–577. doi:10.1007/s10992-013-9281-7.

Fox, Danny. 2007. Free choice and the theory of scalar implicatures. In Uli Sauerland & Penka Stateva (eds.), Presupposition and implicature in compositional semantics, 71–120. London, UK: Palgrave Macmillan. doi:10.1057/9780230210752.

Heim, Irene & Angelika Kratzer. 1998. Semantics in Generative Grammar. Oxford, UK: Blackwell Publishing.

Horn, Laurence. 1972. On the semantic properties of logical operators in English. Los Angeles, CA: University of California dissertation.

Kratzer, Angelika. 1981. Partition and revision: The semantics of counterfactuals. Journal of Philosophical Logic 10(2). 201–216. doi:10.1007/bf00248849.

Lewis, David. 1973. Counterfactuals. Oxford, UK: Blackwell.

Lifschitz, Vladimir. 1990. Frames in the space of situations. Artificial Intelligence 46(3). 365–376. doi:10.1016/0004-3702(90)90021-q.

Pearl, Judea. 2000. Causality: Models, reasoning, and inference. Cambridge, UK: Cambridge University Press. doi:10.1017/cbo9780511803161.

Roelofsen, Floris. 2013. Algebraic foundations for the semantic treatment of inquisitive content. Synthese 190(1). 79–102. doi:10.1007/s11229-013-0282-4. van Rooij, Robert. 2006. Free choice counterfactual donkeys. Journal of Semantics 23(4). 383–402. doi:10.1093/jos/ffl004.

Rooth, Mats. 1985. Association with focus. Amherst, MA: University of Massachusetts dissertation. AAI8509599/.

Schlenker, Philippe. to appear. The semantics/pragmatics interface. In Paul Dekker & Maria Aloni (eds.), Cambridge handbook of formal semantics, Cambridge, UK: Cambridge University Press.

Schulz, Katrin. 2007. Minimal models in semantics and pragmatics: Free choice, exhaustivity, and conditionals. Amsterdam, Netherlands: University of Amsterdam dissertation.

Spector, Benjamin. 2007. Aspects of the pragmatics of plural morphology: On higher-order implicatures. In Uli Sauerland & Penka Stateva (eds.), Presuppositions and implicature in compositional semantics, 243–281. London, UK: Palgrave. doi:10.1057/9780230210752.

Stalnaker, Robert C. 1968. A theory of conditionals. In Nicholas Rescher (ed.), Studies in logical theory, 98–113. Oxford, UK: Blackwell. doi:10.1007/978-94009-9117-0_2.


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