A Compositional Semantics for ‘Even If’ Conditionals

Mathieu Vidal

DOI: http://dx.doi.org/10.12775/LLP.2016.031


This paper presents the first possible world semantics for concessive conditionals (i.e., even if A, C conditionals) constructed in a compositional way. First, the meaning of if is formalized through a semantics that builds on the proposal given by Stalnaker [1968]. A major difference from Stalnaker’s approach is that irrelevant conditionals (i.e., conditionals where the antecedent and the consequent have no connection) are false in this new setting. Second, the meaning of even is analyzed through a formal semantics based on the notion of scale. This analysis overcomes the problems arising in standard approaches, in which even is analyzed with the help of pragmatic presuppositions. Finally, the two particles are combined in order to provide a formal analysis of even if. This theory predicts the major phenomena concerning the behavior of concessive conditionals and without any call to pragmatic explanations. More generally, this approach creates the possibility of a compositional analysis of other conditionals such as if then or only if forms.


Conditional logic; even; if; even if

Full Text:



Adams, E.W., The Logic of Conditionals, D. Reidel Publishing Co., Dordrecht, 1975. DOI: 10.1007/978-94-015-7622-2

Barker, S.J., “Even, still and counterfactuals”, Linguistics and Philosophy, 14, 1 (1991): 1–38. DOI: 10.1007/BF00628303

Barker, S.J., “The consequent-entailment problem for even if”, Linguistics and Philosophy, 17 (1994): 248–260.

Bennett, J., “Even if”, Linguistics and Philosophy, 5, 2 (1982): 403–418. DOI: 10.1007/BF00351461

Bennett, J., A Philosophical Guide to Conditionals, Clarendon Press, Oxford, 2003. DOI: 10.1093/0199258872.003.0017

Chellas, B., “Basic conditional logic”, Journal of Philosophical Logic, 4, 2 (1975): 133–154. DOI: 10.1007/BF00693270

Douven, I., “How to account for the oddness of missing-link conditionals”, Synthese (2015). DOI: 10.1007/s11229-015-0756-7

Ducrot, O., La Preuve et le Dire, Mame, Paris, 1973.

Fauconnier, G., “Pragmatic scales and logical structure”, Linguistic Inquiry, 4 (1975): 353–375.

Giannakidou, A., “The landscape of even”, Natural Language and Linguistic Theory, 25, 1 (2007): 39–81. DOI: 10.1007/s11049-006-9006-5

Gillies, A.S., “Counterfactual scorekeeping”, Linguistics and Philosophy, 30, 3 (2007): 329–360. DOI: 10.1007/s10988-007-9018-6

Grice, H.P., “Logic and conversation”, pages 64–75 in P. Cole and J. Morgan (eds.), Syntax and Semantics 3: Speech Acts, Academic Press, New York, 1975.

Guerzoni, E., “Even-npis in yes/no questions”, Natural Language Semantics, 12, 4 (2004): 319–343. DOI: 10.1007/s11050-004-8739-0

Horn, L.R., “On the semantic properties of logical operators in English”, Ph.D. dissertation, UCLA, 1972.

Iten, C., “Even if and even: The case for an inferential scalar account”, UCL Working Papers in Linguistics, 14 (2002): 119–156.

Karttunen, L., and S. Peters, “Conventional implicature”, pages 1–56 in C. Oh and D. Dineen (eds.), Syntax and Semantics 11: Presuppositions, Academic Press, NY, 1979.

Kay, P., “Even”, Linguistics and Philosophy, 13, 1 (1990): 59–111. DOI: 10.1007/BF00630517

Krzyżanowska, K., S. Wenmackers, and I. Douven, “Rethinking Gibbard’s riverboat argument”, Studia Logica, 102, 4 (2014): 771–792, DOI: 10.1007/s11225-013-9507-2

Lahiri, U., “Focus and negative polarity in hindi”, Natural Language Semantics, 6 (1998): 57–123.

Lewis, D.K., Counterfactuals, Harvard University Press, Cambridge, Massachusetts, 1973.

Lycan, W.G., “Even and Even If”, Linguistics and Philosophy, 14, 2 (1991): 115–150. DOI: 10.1007/BF00627400

Lycan, W.G., Real Conditionals, Oxford University Press, Oxford, 2001.

Moreno-Ríos, S., J.A. Garcia-Madruga, and R.M.J. Byrne, “Inferences from semifactual ‘even if’ conditionals”, Acta Psychologica, 128, 2 (2008): 197–209. DOI: 10.1016/j.actpsy.2007.12.008

Moss, S., “On the pragmatics of counterfactuals”, Noûs, 46, 3 (2012): 561–586. DOI: 10.1111/j.1468-0068.2010.00798.x

Nakanishi, K., “ ‘Even’, ‘only’, and negative polarity in Japanese”, pages 138–156 in M. Gibson and J. Howell (eds.), SALT XVI, Ithaca, NY: Cornell University, 2006.

Nute, D., Topics in Conditional Logic, Reidel, Dordrecht, 1980. DOI: 10.1007/978-94-009-8966-5

Pollock, J.L., Subjunctive Reasoning, D. Reidel Publishing Co., Dordrecht, 1976. DOI: 10.1007/978-94-010-1500-4

Priest, G., An Introduction to Non-classical Logic: From If to Is, Cambridge University Press, 2008. DOI: 10.1017/CBO9780511801174

Ramsey, F., “Law and causality”, pages 140–163 in D.H. Mellor (ed.), Philosophical Papers, Cambridge University Press, 1990.

Rooth, M., “Association with focus”, Ph.D. dissertation, University of Massachusetts at Amherst, 1985.

Ruiz-Ballesteros, J.A., and S. Moreno-Ríos, “Even if after if then conditionals”, Technical report, University of Grenada, Spain, 2013. https://mindmodeling.org/cogsci2013/papers/0592/paper0592.pdf

Rullmann, H., “Even, polarity and scope”, pages 40–64 in M. Gibson, G. Wiebe, and G. Libben (eds.), Papers in Experimental and Theoretical Linguistics, volume 4, Department of Linguistics, University of Alberta, 1997.

Santamaría, C., O. Espino, and R.M.J. Byrne, “Counterfactual and semifactual conditionals prime alternative possibilities”, Journal of ExperimentalPsychology: Learning, Memory, and Cognition, 31, 5 (2005): 1149–1154. DOI: 10.1037/0278-7393.31.5.1149

Schwarz, B., “Scalar additive particles in negative contexts”, Natural Language Semantics, 13, 2 (2005): 125–168. DOI: 10.1007/s11050-004-2441-0

Stalnaker, R.C., “A theory of conditionals”, pages 98–112 in N. Rescher (ed.), Studies in Logical Theory, Basil Blackwell Publishers, Oxford, 1968. DOI: 10.1007/978-94-009-9117-0_2

Vidal, M., “Conditionnels et connexions”, Ph.D. dissertation, Institut Jean Nicod, E.H.E.S.S., Paris, 2012.

von Fintel, K., “Counterfactuals in a dynamic context”, pages 123–152 in M. Kenstowicz (ed.), Ken Hale: A Life in Language, The MIT Press, Cambridge, Massachusetts, 2001.

Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism