Skip to main content


  • ERIC RAIDL (a1)

Standard conditionals $\varphi > \psi$ , by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$ , in that ID ( $\varphi > \varphi$ ) or even CN ( $\varphi > \top$ ) are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries.

Corresponding author
Hide All
Alchourrón, C. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50, 510530.
Berto, F., French, R., Priest, G., & Ripley, D. (2018). Williamson on counterpossibles. Journal of Philosophical Logic, 47(4), 693713.
Burgess, J. (1981). Quick completeness proofs for some logics of conditionals. Notre Dame Journal of Formal Logic, 22, 7684.
Bjerring, J. C. (2014). On counterpossibles. Philosophical Studies, 168, 327353.
Brogaard, B. & Salerno, J. (2013). Remarks on counterpossibles. Synthese, 190, 639660.
Chellas, B. F. (1975). Basic conditional logic. Journal of Philosophical Logic, 4, 133153.
Darwiche, A. & Pearl, J. (1997). On the logic of iterated belief revision. Artificial Intelligence, 89(1–2), 129.
Fine, K. (1975). Review of counterfactuals. Mind, 84, 451458.
Friedman, N. & Halpern, J. (2001). Plausibility measures and default reasoning. Journal of the Association for Computing Machinery, 48(4), 648685.
Gärdenfors, P. (1982). Imaging and conditionalization. The Journal of Philosophy, 79(12), 747760.
Goldszmidt, M. & Pearl, J. (1996). Qualitative probabilities for default reasoning, belief revision, and causal modelling. Artificial Intelligence, 84, 57112.
Halpern, J. (2003). Reasoning About Uncertainty. Cambridge, MA: MIT Press.
Huber, F. (2006). Ranking functions and rankings on languages. Artificial Intelligence, 170, 462471.
Huber, F. (2007a). The logic of theory assessment. Journal of Philosophical Logic, 36, 511538.
Huber, F. (2007b). The consistency argument for ranking functions. Studia Logica, 86(2), 299329.
Huber, F. (2014). New foundations for counterfactuals. Synthese, 91, 21672193.
Huber, F. (2015). What should I believe about what would have been the case? Journal of Philosophical Logic, 44, 81110.
Huber, F. (2017). Why follow the royal rule? Synthese, 194(5), 15651590.
Kment, B. (2014). Modality and Explanatory Reasoning. Oxford: Oxford University Press.
Lauer, S. (2017). ‘I believe’ in a ranking-theoretic analysis of ‘believe’. In van Gessel, T. and Roelofsen, F., editors. Proceedings of the 21st Amsterdam Colloquium. Amsterdam: ILLC, pp. 335344.
Lewis, D. (1971). Completeness and decidability of three logics of counterfactual conditionals. Theoria, 37(1), 7485.
Lewis, D. (1973). Counterfactuals and comparative possibility. Journal of Philosophical Logic, 2, 418446.
Loewer, B. M. (1979). Cotenability and counterfactual logics. Journal of Philosophical Logic, 8(1), 99115.
Mares, E. D. & Fuhrmann, A. (1995). A relevant theory of conditionals. Journal of Philosophical Logic, 24, 645665.
Mayer, J. C. (1981). A misplaced thesis of conditional logic. Journal of Philosophical Logic, 10(2), 235238.
Nolan, D. (1997). Impossible worlds: A modest approach. Notre Dame Journal of Formal Logic, 38, 535572.
Raidl, E. (2018). Ranking semantics for doxastic necessities and conditionals. In Pavel, A. & Lávička, T., editors. Logica Yearbook 2017. London: College Publications, pp. 223238.
Raidl, E. & Skovgaard-Olsen, N. (2017). Simulating Lewis/Stalnaker Conditionals in Ranking Theory. Unpublished manuscript.
Spohn, W. (1988). Ordinal conditional functions. A dynamic theory of epistemic states. In Harper, W. L. and Skyrms, B. editors. Causation in Decision, Belief Change, and Statistics, Vol. 2. Dordrecht: Kluwer, pp. 105134.
Spohn, W. (2012). The Laws of Belief: Ranking Theory and its Philosophical Applications. Oxford: Oxford University Press.
Spohn, W. (2015). Conditionals: A unifying ranking-theoretic perspective. Philosopher’s Imprint, 15(1), 130.
Unterhuber, M. (2016). Beyond system P – Hilbert-Style convergence results for conditional logics with a connexive twist. IFCoLog Journal of Logics and their Application, 3(3), 376412.
Williamson, T. (2007). The philosophy of philosophy. Oxford: Oxford University Press.
Williamson, T. (2018). Counterpossibles. Topoi, 37(3), 357368.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed