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Prioritised ceteris paribus logic for counterfactual reasoning

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Abstract

The semantics for counterfactuals due to David Lewis has been challenged by appealing to miracles. Miracles may skew a given similarity order in favour of those possible worlds which exhibit them. Lewis responded with a system of priorities that mitigates the significance of miracles when constructing similarity relations. We propose a prioritised ceteris paribus analysis of counterfactuals inspired by Lewis’ system of priorities. By analysing the couterfactuals with a ceteris paribus clause one forces out, in a natural manner, those possible worlds which do not satisfy the requirements of the clause, thus excluding miracles. If no world can satisfy the ceteris paribus clause in its entirety, then prioritisation is triggered to select worlds that maximise agreement on those things which are favoured most.

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Notes

  1. See Schurz (2002) on comparative ceteris paribus laws.

  2. The choice of \(\varGamma \) finite is largely technical. We will mention some possibilities and difficulties regarding the case where the ceteris paribus set \(\varGamma \) may be infinite in Sect. 7.

  3. We redefine the language more precisely as Definition 6 in the appendix, particularly avoiding non-well-founded sets \(\varGamma \). For simplicity we work with the one now stated.

  4. Though the set \(\mathsf {Prop}\setminus (\mathsf {UD}(\varphi ) \cup \mathsf {UD}(\psi ))\) is an infinite set when \(\mathsf {Prop}\) is, it is not as ambitious as the previous infinite sets we’ve considered, because it is a co-finite set. Co-finite sets are a special cases of flexible sets as defined and axiomatised in Seligman and Girard (2011). To keep focus, we will stick with finite \(\mathsf {CP}\)-sets in this paper, and leave an exploration of the flexibility approach to infinite sets in conditional logic for future research.

  5. It could be that neither \(A_\varGamma ^\mathcal {M}(v,w) \unlhd A_\varGamma ^\mathcal {M}(u,w)\) nor \(A_\varGamma ^\mathcal {M}(u,w) \unlhd A_\varGamma ^\mathcal {M}(v,w)\), as \(\unlhd \) is a preorder.

  6. We provide an example of a prioritisation order that allows for incomparability in Sect. 5.2.2.

  7. In \([\varphi ,\varGamma ,\le ]\), we use \(\le \) instead of \(\unlhd \) to indicate that the modality is based on the specific ceteris prioritisation given by naïve counting. We will use notation in a similar fashion below.

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Acknowledgements

We wish to thank the participants at the Australasian Association of Logic and the Analysis, Randomness and Applications meetings held in New Zealand in 2014. A preliminary version of this paper was presented at TARK XV and we wish to thank the participants for helpful suggestions on improving the paper. We also wish to thank Sam Baron, Andrew Withy, Balder ten Cate and the anonymous referees for valuable comments.

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Authors and Affiliations

  1. Department of Philosophy, University of Auckland, Auckland, New Zealand

    Patrick Girard

  2. University of Auckland, Auckland, New Zealand

    Marcus A. Triplett

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  1. Patrick Girard
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  2. Marcus A. Triplett
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Correspondence to Patrick Girard.

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Girard, P., Triplett, M.A. Prioritised ceteris paribus logic for counterfactual reasoning. Synthese 195, 1681–1703 (2018). https://doi.org/10.1007/s11229-016-1296-5

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