I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: (i) that a conditional is logically independent from its antecedent; (ii) that a sequence of antecedents behaves like a single conjunctive antecedent (the import-export equivalence); and (iii) that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Adams, E. (1965). The logic of conditionals. Inquiry, 8(1-4), 166–197.
Adams, E. (1970). Subjunctive and indicative conditionals. Foundations of Language, 6(1), 89–94.
Adams, E. (1975). The logic of conditionals: an application of probability to deductive logic Vol. 86. Berlin: Springer Science & Business Media.
Alchourrón, C., Gärdenfors, P., Makinson, D. (1985). On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 50(02), 510–530.
Alonso-Ovalle, L. (2009). Counterfactuals, correlatives, and disjunction. Linguistics and Philosophy, 32, 207–244.
Arló-Costa, H. (1997). Belief revision conditionals: models of suppositional reasoning. Technical Report, Carnegie Mellon University.
Arló-Costa, H., & Levi, I. (1996). Two notions of epistemic validity. Synthese, 109(2), 217–262.
Baltag, A., & Smets, S. (2006). Dynamic belief revision over multi-agent plausibility models. In Proceedings of LOFT.
Bledin, J. (2014). Logic informed. Mind, 123(490), 277–316.
Bledin, J. (2015). Modus ponens defended. The Journal of Philosophy, 112 (2), 57–83.
Bledin, J. (2018). Fatalism and the logic of unconditionals. Noûs.
Bledin, J., & Lando, T. (2018). Closure and epistemic modals. Philosophy and Phenomenological Research, 97(1), 3–22.
Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49(1), 49–80.
Briggs, R. (2012). Interventionist counterfactuals. Philosophical Studies, 160 (1), 139–166.
Cantwell, J. (2008). Changing the modal context. Theoria, 74(4), 331–351.
Ciardelli, I. (2016). Lifting conditionals to inquisitive semantics. In M. Moroney, C.-R. Little, J. Collard, D. Burgdorf (Eds.), Semantics and linguistic theory (SALT) 26. Ithaca: LSA and CLC Publications.
Dekker, P. (1993). Transsentential meditations. Ups and downs in dynamic semantics. Ph.D thesis, ILLC, University of Amsterdam.
Edgington, D. (1986). Do conditionals have truth conditions? Crítica: Revista Hispanoamericana de Filosofía, 18(52), 3–39.
Edgington, D. (1995). On conditionals. Mind, 104, 235–329.
Egré, P., & Politzer, G. (2013). On the negation of indicative conditionals. In M. Aloni, M. Franke, F. Roelofsen (Eds.), Proceedings of the nineteenth Amsterdam Colloquium (pp. 10–18).
Fine, K. (2017). Truthmaker semantics. In B. Hale, C. Wright, A. Miller (Eds.), A companion to the philosophy of language (pp. 556–577). Wiley.
Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of the epistemic states. Cambridge: MIT press.
Gibbard, A. (1980). Two recent theories of conditionals. In Ifs: Conditionals, beliefs, decision, chance, time (pp. 211–247). Dordrecht: Reidel.
Gillies, A. (2004). Epistemic conditionals and conditional epistemics. Noûs, 38(4), 585–616.
Gillies, A. (2009). On truth-conditions for if (but not quite only if ). Philosophical Review, 118(3), 325–349.
Gillies, A.S. (2007). Counterfactual scorekeeping. Linguistics and Philosophy, 30(3), 329–360.
Gillies, A.S. (2010). Iffiness. Semantics and Pragmatics, 3, 4–1.
Gillies, A.S. (2018). Updating data semantics. Mind.
Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17(2), 157–170.
Herzberger, H.G. (1979). Counterfactuals and consistency. The Journal of Philosophy, 76(2), 83–88.
Higginbotham, J. (1986). Linguistic theory and Davidson’s program in semantics. In E. Lepore (Ed.), Truth and interpretation: perspectives on the philosophy of Donald Davidson (pp. 29–48). Basil Blackwell.
Khoo, J. (2018). Disjunctive antecedent conditionals. Synthese.
Klinedinst, N. (2010). Quantified conditionals and conditional excluded middle. Journal of Semantics, 28(1), 149–170.
Kolodny, N., & MacFarlane, J. (2010). Ifs and oughts. The Journal of Philosophy, 107(3), 115–143.
Kratzer, A. (1981). The notional category of modality. In H. Eikmeyer, & H. Rieser (Eds.), Words, worlds, and contexts: new approaches in word semantics (pp. 38–74). Berlin: Walter de Gruyter.
Kratzer, A. (1986). Conditionals. Chicago Linguistics Society, 22(2), 1–15.
Kraus, S., Lehmann, D., Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1-2), 167–207.
Leitgeb, H. (2010). On the Ramsey test without triviality. Notre Dame Journal of Formal Logic, 51(1), 21–54.
Levi, I. (1988). Iteration of conditionals and the Ramsey test. Synthese, 76(1), 49–81.
Lewis, D. (1973). Counterfactuals. Basil Blackwell.
McGee, V. (1985). A counterexample to modus ponens. The Journal of Philosophy, 82(9), 462–471.
Pearl, J. (2000). Causality: models, reasoning and inference Vol. 29. Berlin: Springer.
Price, H. (1983). Does “probably” modify sense? Australasian Journal of Philosophy, 61(4), 396–408.
Ramsey, F.P. (1929). General propositions and causality. In D. H. Mellor (Ed.), F.P. Ramsey: philosophical papers. Cambridge University Press.
Rott, H. (1989). Conditionals and theory change: revisions, expansions, and additions. Synthese, 81(1), 91–113.
Santorio, P. (2017). Conditional excluded middle in informational semantics. In T. V. G. Alexandre Cremers, & F. Roelofsen (Eds.), Proceedings of the 21st Amsterdam Colloquium (pp. 385–394).
Santorio, P. (2018). Alternatives and truthmakers in conditional semantics. The Journal of Philosophy, 115(10), 513–549.
Schulz, K. (2011). If you’d wiggled a, then b would’ve changed. Synthese, 179 (2), 239–251.
Schulz, M. (2010). Epistemic modals and informational consequence. Synthese, 174(3), 385–395.
Schulz, M. (2018). Modus ponens under the restrictor view. Journal of Philosophical Logic, 47(6), 1001–1028.
Segerberg, K. (1998). Irrevocable belief revision in dynamic doxastic logic. Notre Dame Journal of Formal Logic, 39(3), 287–306.
Stalnaker, R. (1968). A theory of conditionals. In N. Rescher (Ed.), Studies in Logical Theory. Oxford: Blackwell.
Stalnaker, R. (1976). Indicative conditionals. In Ifs (pp. 193–210). Reidel.
Starr, W. (2014). A uniform theory of conditionals. Journal of Philosophical Logic, 43(6), 1019–1064.
Veltman, F. (1981). Data semantics. In J. Groenendijk, T. Janssen, M. Stokhof (Eds.), Formal Methods in the Study of Language. Mathematical Centre.
Veltman, F. (1985). Logics for conditionals. Ph.D. thesis, University of Amsterdam.
Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic, 25(3), 221–261.
von Fintel, K. (1997). Bare plurals, bare conditionals, and only. Journal of Semantics, 14(1), 1–56.
von Fintel, K. (1998). The presupposition of subjunctive conditionals. The Interpretive Tract, 25, 29–44.
von Fintel, K., & Gillies, A. (2010). Might made right. In A. Egan, & B. Weatherson (Eds.), Epistemic Modality. Oxford: Oxford University Press.
Willer, M. (2014). Dynamic thoughts on ifs and oughts. Philosophers’ Imprint, 14(28), 1–30.
Willer, M. (2017). Lessons from Sobel sequences. Semantics and Pragmatics, 10, Article 4.
Willer, M. (2018). Simplifying with free choice. Topoi, 37(3), 379–392.
Yalcin, S. (2007). Epistemic modals. Mind, 116(464), 983–1026.
Yalcin, S. (2011). Nonfactualism about epistemic modality. In A. Egan, & B. Weatherson (Eds.), Epistemic Modality. Oxford University Press.
Yalcin, S. (2012). A counterexample to modus tollens. Journal of Philosophical Logic, 41(6), 1001–1024.
Yalcin, S. (2015). Epistemic modality de re. Ergo, 19(2), 475–527.
For inspiring discussions and/or useful feedback on earlier drafts, I am grateful to Maria Aloni, Justin Bledin, Bruno Jacinto, Hannes Leitgeb, Vít Punčochár, Floris Roelofsen, Lorenzo Rossi, Katrin Schulz, Frank Veltman, Malte Willer, Seth Yalcin, and two anonymous reviewers.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Ciardelli, I. Indicative Conditionals and Graded Information. J Philos Logic 49, 509–549 (2020). https://doi.org/10.1007/s10992-019-09528-6
- Indicative conditionals
- Information semantics
- Epistemic modals
- Non-monotonic reasoning
- Modus ponens
- Modus tollens