Disagreement, equal weight and commutativity


How should we respond to cases of disagreement where two epistemic agents have the same evidence but come to different conclusions? Adam Elga has provided a Bayesian framework for addressing this question. In this paper, I shall highlight two unfortunate consequences of this framework, which Elga does not anticipate. Both problems derive from a failure of commutativity between application of the equal weight view and updating in the light of other evidence.

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  1. 1.

    Elga does specify a coarse-graining constraint on circumstances of disagreement, but this won’t be relevant to my discussion.

  2. 2.

    In the relevant sense, two agents disagree about more than one thing if there are two families of propositions, logically independent from each other, over which the two agents have different credence distributions. We can’t say that disagreeing about more than one thing is disagreeing about more than one (structured) proposition, since if two agents have different credences in p they will ipso facto have different credences in p&p.

  3. 3.

    One possible response would be to take the average of the credences resulting from applying the processes in different orders. Another would be to insist that one of the two processes should always be applied first. Without independent motivation, such proposals seem unacceptably ad hoc.

  4. 4.

    I have more general concerns about Elga’s proposal, since it applies Bayesian methods, which assume logical infallibility, to scenarios more naturally thought of as involving imperfect reasoning. However, I will not pursue these concerns here.

  5. 5.

    Thanks to an audience at Oxford, and particularly to Frank Arntzenius and John Hawthorne.


  1. Elga, A. (2007). Reflection and disagreement. Noûs, 41(3), 478–502.

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Correspondence to Alastair Wilson.

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Wilson, A. Disagreement, equal weight and commutativity. Philos Stud 149, 321–326 (2010). https://doi.org/10.1007/s11098-009-9362-1

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  • Disagreement
  • Equal weight view
  • Commutativity
  • Averaging
  • Credences
  • Evidence
  • Epistemic peer