Advertisement

Indicative Conditionals and Graded Information

  • Ivano CiardelliEmail author
Article

Abstract

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.

Keywords

Indicative conditionals Information semantics Import-export Epistemic modals Non-monotonic reasoning Modus ponens Modus tollens 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

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.

References

  1. 1.
    Adams, E. (1965). The logic of conditionals. Inquiry, 8(1-4), 166–197.CrossRefGoogle Scholar
  2. 2.
    Adams, E. (1970). Subjunctive and indicative conditionals. Foundations of Language, 6(1), 89–94.Google Scholar
  3. 3.
    Adams, E. (1975). The logic of conditionals: an application of probability to deductive logic Vol. 86. Berlin: Springer Science & Business Media.CrossRefGoogle Scholar
  4. 4.
    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.CrossRefGoogle Scholar
  5. 5.
    Alonso-Ovalle, L. (2009). Counterfactuals, correlatives, and disjunction. Linguistics and Philosophy, 32, 207–244.CrossRefGoogle Scholar
  6. 6.
    Arló-Costa, H. (1997). Belief revision conditionals: models of suppositional reasoning. Technical Report, Carnegie Mellon University.Google Scholar
  7. 7.
    Arló-Costa, H., & Levi, I. (1996). Two notions of epistemic validity. Synthese, 109(2), 217–262.CrossRefGoogle Scholar
  8. 8.
    Baltag, A., & Smets, S. (2006). Dynamic belief revision over multi-agent plausibility models. In Proceedings of LOFT.Google Scholar
  9. 9.
    Bledin, J. (2014). Logic informed. Mind, 123(490), 277–316.CrossRefGoogle Scholar
  10. 10.
    Bledin, J. (2015). Modus ponens defended. The Journal of Philosophy, 112 (2), 57–83.CrossRefGoogle Scholar
  11. 11.
    Bledin, J. (2018). Fatalism and the logic of unconditionals. Noûs.Google Scholar
  12. 12.
    Bledin, J., & Lando, T. (2018). Closure and epistemic modals. Philosophy and Phenomenological Research, 97(1), 3–22.CrossRefGoogle Scholar
  13. 13.
    Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49(1), 49–80.CrossRefGoogle Scholar
  14. 14.
    Briggs, R. (2012). Interventionist counterfactuals. Philosophical Studies, 160 (1), 139–166.CrossRefGoogle Scholar
  15. 15.
    Cantwell, J. (2008). Changing the modal context. Theoria, 74(4), 331–351.CrossRefGoogle Scholar
  16. 16.
    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.Google Scholar
  17. 17.
    Dekker, P. (1993). Transsentential meditations. Ups and downs in dynamic semantics. Ph.D thesis, ILLC, University of Amsterdam.Google Scholar
  18. 18.
    Edgington, D. (1986). Do conditionals have truth conditions? Crítica: Revista Hispanoamericana de Filosofía, 18(52), 3–39.Google Scholar
  19. 19.
    Edgington, D. (1995). On conditionals. Mind, 104, 235–329.CrossRefGoogle Scholar
  20. 20.
    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).Google Scholar
  21. 21.
    Fine, K. (2017). Truthmaker semantics. In B. Hale, C. Wright, A. Miller (Eds.), A companion to the philosophy of language (pp. 556–577). Wiley.Google Scholar
  22. 22.
    Gärdenfors, P. (1988). Knowledge in flux: Modeling the dynamics of the epistemic states. Cambridge: MIT press.Google Scholar
  23. 23.
    Gibbard, A. (1980). Two recent theories of conditionals. In Ifs: Conditionals, beliefs, decision, chance, time (pp. 211–247). Dordrecht: Reidel.Google Scholar
  24. 24.
    Gillies, A. (2004). Epistemic conditionals and conditional epistemics. Noûs, 38(4), 585–616.CrossRefGoogle Scholar
  25. 25.
    Gillies, A. (2009). On truth-conditions for if (but not quite only if ). Philosophical Review, 118(3), 325–349.CrossRefGoogle Scholar
  26. 26.
    Gillies, A.S. (2007). Counterfactual scorekeeping. Linguistics and Philosophy, 30(3), 329–360.CrossRefGoogle Scholar
  27. 27.
    Gillies, A.S. (2010). Iffiness. Semantics and Pragmatics, 3, 4–1.CrossRefGoogle Scholar
  28. 28.
    Gillies, A.S. (2018). Updating data semantics. Mind.Google Scholar
  29. 29.
    Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17(2), 157–170.CrossRefGoogle Scholar
  30. 30.
    Herzberger, H.G. (1979). Counterfactuals and consistency. The Journal of Philosophy, 76(2), 83–88.CrossRefGoogle Scholar
  31. 31.
    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.Google Scholar
  32. 32.
    Khoo, J. (2018). Disjunctive antecedent conditionals. Synthese.Google Scholar
  33. 33.
    Klinedinst, N. (2010). Quantified conditionals and conditional excluded middle. Journal of Semantics, 28(1), 149–170.CrossRefGoogle Scholar
  34. 34.
    Kolodny, N., & MacFarlane, J. (2010). Ifs and oughts. The Journal of Philosophy, 107(3), 115–143.CrossRefGoogle Scholar
  35. 35.
    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.Google Scholar
  36. 36.
    Kratzer, A. (1986). Conditionals. Chicago Linguistics Society, 22(2), 1–15.Google Scholar
  37. 37.
    Kraus, S., Lehmann, D., Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1-2), 167–207.CrossRefGoogle Scholar
  38. 38.
    Leitgeb, H. (2010). On the Ramsey test without triviality. Notre Dame Journal of Formal Logic, 51(1), 21–54.CrossRefGoogle Scholar
  39. 39.
    Levi, I. (1988). Iteration of conditionals and the Ramsey test. Synthese, 76(1), 49–81.CrossRefGoogle Scholar
  40. 40.
    Lewis, D. (1973). Counterfactuals. Basil Blackwell.Google Scholar
  41. 41.
    McGee, V. (1985). A counterexample to modus ponens. The Journal of Philosophy, 82(9), 462–471.CrossRefGoogle Scholar
  42. 42.
    Pearl, J. (2000). Causality: models, reasoning and inference Vol. 29. Berlin: Springer.Google Scholar
  43. 43.
    Price, H. (1983). Does “probably” modify sense? Australasian Journal of Philosophy, 61(4), 396–408.CrossRefGoogle Scholar
  44. 44.
    Ramsey, F.P. (1929). General propositions and causality. In D. H. Mellor (Ed.), F.P. Ramsey: philosophical papers. Cambridge University Press.Google Scholar
  45. 45.
    Rott, H. (1989). Conditionals and theory change: revisions, expansions, and additions. Synthese, 81(1), 91–113.CrossRefGoogle Scholar
  46. 46.
    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).Google Scholar
  47. 47.
    Santorio, P. (2018). Alternatives and truthmakers in conditional semantics. The Journal of Philosophy, 115(10), 513–549.CrossRefGoogle Scholar
  48. 48.
    Schulz, K. (2011). If you’d wiggled a, then b would’ve changed. Synthese, 179 (2), 239–251.CrossRefGoogle Scholar
  49. 49.
    Schulz, M. (2010). Epistemic modals and informational consequence. Synthese, 174(3), 385–395.CrossRefGoogle Scholar
  50. 50.
    Schulz, M. (2018). Modus ponens under the restrictor view. Journal of Philosophical Logic, 47(6), 1001–1028.CrossRefGoogle Scholar
  51. 51.
    Segerberg, K. (1998). Irrevocable belief revision in dynamic doxastic logic. Notre Dame Journal of Formal Logic, 39(3), 287–306.CrossRefGoogle Scholar
  52. 52.
    Stalnaker, R. (1968). A theory of conditionals. In N. Rescher (Ed.), Studies in Logical Theory. Oxford: Blackwell.Google Scholar
  53. 53.
    Stalnaker, R. (1976). Indicative conditionals. In Ifs (pp. 193–210). Reidel.Google Scholar
  54. 54.
    Starr, W. (2014). A uniform theory of conditionals. Journal of Philosophical Logic, 43(6), 1019–1064.CrossRefGoogle Scholar
  55. 55.
    Veltman, F. (1981). Data semantics. In J. Groenendijk, T. Janssen, M. Stokhof (Eds.), Formal Methods in the Study of Language. Mathematical Centre.Google Scholar
  56. 56.
    Veltman, F. (1985). Logics for conditionals. Ph.D. thesis, University of Amsterdam.Google Scholar
  57. 57.
    Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic, 25(3), 221–261.CrossRefGoogle Scholar
  58. 58.
    von Fintel, K. (1997). Bare plurals, bare conditionals, and only. Journal of Semantics, 14(1), 1–56.CrossRefGoogle Scholar
  59. 59.
    von Fintel, K. (1998). The presupposition of subjunctive conditionals. The Interpretive Tract, 25, 29–44.Google Scholar
  60. 60.
    von Fintel, K., & Gillies, A. (2010). Might made right. In A. Egan, & B. Weatherson (Eds.), Epistemic Modality. Oxford: Oxford University Press.Google Scholar
  61. 61.
    Willer, M. (2014). Dynamic thoughts on ifs and oughts. Philosophers’ Imprint, 14(28), 1–30.Google Scholar
  62. 62.
    Willer, M. (2017). Lessons from Sobel sequences. Semantics and Pragmatics, 10, Article 4.Google Scholar
  63. 63.
    Willer, M. (2018). Simplifying with free choice. Topoi, 37(3), 379–392.CrossRefGoogle Scholar
  64. 64.
    Yalcin, S. (2007). Epistemic modals. Mind, 116(464), 983–1026.CrossRefGoogle Scholar
  65. 65.
    Yalcin, S. (2011). Nonfactualism about epistemic modality. In A. Egan, & B. Weatherson (Eds.), Epistemic Modality. Oxford University Press.Google Scholar
  66. 66.
    Yalcin, S. (2012). A counterexample to modus tollens. Journal of Philosophical Logic, 41(6), 1001–1024.CrossRefGoogle Scholar
  67. 67.
    Yalcin, S. (2015). Epistemic modality de re. Ergo, 19(2), 475–527.Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Munich Center for Mathematical PhilosophyLMUMunichGermany

Personalised recommendations