Abstract
For over a decade now epistemologists have been thinking about the peer disagreement problem of whether a person is reasonable in not lowering her confidence in her belief P when she comes to accept that she has an epistemic peer on P who disbelieves P. However, epistemologists have overlooked a key realistic way how epistemic peers can, or even have to, differ epistemically—a way that reveals the inadequacy of both conformist and non-conformist views on peer disagreement by uncovering how the causes of peer disagreement bear on the debate’s core philosophical issue. Part of our argument for this thesis will involve giving a thorough yet entirely informal presentation of mathematical theorems in economics by Robert Aumann (Ann Stat 4(6):1236–1239,1976) and Polemarchakis and Geneakoplos (J Econ Theory 26:363–390,1982) which represent a formally precise description of how two rational agents must deal with disagreement under certain epistemically interesting circumstances.
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Notes
This term comes from Feldman (2006).
We borrow these terms from Lackey (2010).
Examples of condition (a) include Christensen (2009), Elgin (2010), Matheson (2009), King (2012), and Kelly (2010). Examples of condition (b) include Lackey (2010), Kelly (2005), and Kelly (2010). Examples of (c) include Christensen (2009), Elgin (2010), Matheson (2009), King (2012), Kelly (2005), Kelly (2010), and Goldberg (2013).
For the purposes of this article, ‘disagree over P’ is stipulated to have the meaning of the expression in the parenthetical clause.
This point has been made, among others, in Frances (2010) and King (2012). The latter notices how the conditions for epistemic peerhood are very seldom met in real life and that, if the debate focuses on the disagreement cases in which the agents have reasons for believing that they are epistemic peers, then the epistemic implications of the disagreement don’t have as wide a scope as the literature usually takes them to have. We agree with him and, in order to restore the wider scope that the peer disagreement is assumed to have, in what follows we endorse what King calls a `lenient, less draconian’ standard of peerhood.
King (2012) points out that this is one of the main worries for any lenient, less draconian account of peerhood.
Notice that neither of these definitions say the agents disagree on P: equal-position peers can have the same credence in P and the agents in an equal-position case can have the same credence in P.
In the theorem, there is nothing that would prevent the prior distribution from being an objective distribution to which the agents conform via, for example, the Principal Principle. In other words, nothing in the theorem prevents the priors from indeed being objective probabilities. Yet, even upon the assumption that such an objective probability distribution exists, it is implausible to stipulate that the agents get access to it. On these grounds, in our story we will be content with considering the priors a subjective probability distribution whose common source is, for example, reliable.
Common knowledge of equal priors is not explicitly listed among the requirements with which the agents have to comply, but it is essential for the dynamic version of the result (Polemarchakis and Geneakoplos 1982) to hold.
More precisely, the theorem to which we refer here (Polemarchakis and Geneakoplos 1982) proves that the convergence to a common credence will be reached in a finite number of steps, if the agents keep sharing back and forth their posteriors. That Ann and Belle will reach the agreement upon sharing their posteriors only once is only a particular instance of the theorem. Thank you to Reviewer 1 for this comment.
As mentioned earlier, we might well replace the same-evidence condition with a same-degree-of-support condition, by claiming that peers do not have to obtain literally the same evidence as long as their differing bodies of evidence support P to the same degree. Our argument wouldn’t be affected by any change of this kind.
One might go so far as to say that if X has excellent overall evidence that Y is her disagreeing peer on P, then even if X thinks that Y isn’t her peer but inferior on P, the intuitions that make the debate over conformism interesting are fully engaged. We need not take a stand on that issue.
The agents come to entertain thee credences by conditionalizing on the different information that they gather in each of the possible states of the world and that we listed in Table 1.
The question whether the theorem can be interpreted as vindicating or supporting the right reasons view rather than the conciliatory view as a paradigm of the conformist reply in some case doesn’t fall within the purpose of the present paper.
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Funding
This study was funded by Mobilitas Pluss (Grant No. MOBTT45) and by the European Regional Development Fund (Grant No. IUT20-5).
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Cocchiaro, M.Z., Frances, B. Epistemically Different Epistemic Peers. Topoi 40, 1063–1073 (2021). https://doi.org/10.1007/s11245-019-09678-x
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DOI: https://doi.org/10.1007/s11245-019-09678-x