No Match Point for the Permissibility Account


In the literature, one finds two accounts of the normative status of rational belief: the ought account and the permissibility account. Both accounts have their advantages and shortcomings, making it difficult to favour one over the other. Imagine that there were two principles of rational belief or rational degrees of belief commonly considered plausible, but which, however, yielded a paradox together with one account, but not with the other. One of the accounts therefore requires us to give up one of the plausible principles; whereas the other allows us to save them both. The fact that it allows us to save both of the plausible principles might well be considered a strong reason in favour of the relevant account. The permissibility-account-based resolution of the lottery paradox suggests that the permissibility account is a candidate for being supported in this way, since the account seems to save two plausible principles of rational belief and rational degrees of belief. I argue that even if the permissibility account were supported in this way the support would be defeated, since one cannot provide an analogous resolution of the preface paradox. The principles remain unsaved by the permissibility account.

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  1. 1.

    In epistemology the terms ‘rational’ and ‘justified’ are often used synonymously. I will adopt this usage, and will pretend that the authors I discuss do likewise. Furthermore, in this paper I am concerned with propositional rationality, or justification—as understood by Moretti, who characterises it as follows:

    A subject has propositional justification for a proposition \(P\) just in case \(P\) is epistemically worthy of being believed by her whether or not she believes \(P\) for the right reason or at all. (Moretti 2014: Fn. 1)

    For the sake of simplicity, phrases of the form ‘one is rational to believe that \(p\)’ are used synonymously with phrases of the form ‘one is rational in believing that \(p\)’, and even with ‘one’s belief in \(p\) is rational’.

  2. 2.

    See Brössel et al. (2013) and Kelly (2003, 2007) for the consequentialism vs. non-consequentialism debate. See Goldman (1980) and Pollock (1987) for the internalism vs. externalism debate. See White (2005, 2014) and Kelly (2014) for the debate on rational disagreement. In the present paper I presuppose a deontic conception of the normative status of rational belief: the normative status of rational belief is stated in terms of obligations or permissions. However, this is not to say that I think that this conception of normative status is always adequate. In Eder 2015 I argue for a pluralistic account of the adequate normative status of rational belief. Depending on the purpose for which the respective theory of rational belief is being proposed, the normative status may be an evaluative status (stated in evaluative terms such as in terms of goodness or badness) or a deontic status (stated in deontic terms such as in terms of obligations or permissions). It is beyond the scope of this paper to give the details here.

  3. 3.

    For the sake of simplicity, in this paper it is presupposed that ‘ought’, ‘must’, and ‘is obliged’ are synonymous. Nothing I shall argue for hangs on the exact reading of these expressions. What is relevant is that ‘ought’—as understood here—has a deontic and not an evaluative reading. It is often not clear whether proponents of the ought account share this latter presupposition.

  4. 4.

    Kroedel presents his resolution of the lottery paradox in terms of justified belief. However, he claims that it can be employed just as well if one refers to rational belief instead (2012: 59). The lottery paradox, the preface paradox, and the mentioned principles were originally presented in terms of rational belief (see Makinson 1965: 205; Foley 1992: 111; Kyburg 1961: 197; the latter refers to rational acceptance, seemingly meaning rational belief). Moreover, ‘justified belief’ and ‘rational belief’ are often used synonymously. Thus, I refer only to rational belief, and will pretend Kroedel does likewise.

  5. 5.

    The lottery paradox was first presented by Kyburg (1961). The preface paradox is due to Makinson (1965).

  6. 6.

    It is noteworthy that this does not imply that one is permitted to believe and disbelieve the same proposition at the same time. Permissibility does not agglomerate; we will come back to this shortly.

  7. 7.

    Nelson, for example, claims something in this line: “Given th[e] same visual evidence, which propositions should I not believe? On the permissive view [which Nelson endorses], the answer is simple: other things being equal, I should believe nothing that is clearly incompatible with any beliefs that are on balance licensed for me” (Nelson 2010: 87).

  8. 8.

    See also Kroedel (2012): 58. The paradox’s premises are made more explicit here. This helps to better compare the lottery and the preface paradox and to clarify how far both paradoxes rest on both principles.

  9. 9.

    To be more precise, in order to replace ‘rational’ by ‘permitted’ in a context which concerns degrees of belief, we require the following principle:


    For each proposition, one is rational to believe it to a high degree iff one is permitted to have a high degree of belief in it.

    I think that if one accepts PERMISSIBILITY, one is also committed to accepting PERMISSIBILITY*. However, my objections against the permissibility resolution do not depend on this.

  10. 10.

    It is noteworthy that one may object right from the outset that the sentence ‘For each ticket, one is permitted to believe that it will lose’ is not ambiguous and that the narrow scope reading of ‘permitted’ is the correct one (Wolfgang Spohn in conversation), and thus that CLOSURE, or CLOSURE*, is false and CLOSURE** is correct. However, what is decisive is that permissibility does not agglomerate. By contrast, if one adopted the ought account and replaced ‘permitted’ by ‘ought’, the respective proposal would not work since oughts do agglomerate.

  11. 11.

    This example furthermore shows very well that permissibility does not agglomerate in practical cases. While Littlejohn agrees that permission does not agglomerate in practical cases, he considers it to be plausible that it agglomerates in epistemic cases. He presents possible ways to argue in defence of agglomeration in epistemic cases (2013: 236–238). In this paper I assume—with Kroedel—that epistemic permission does not agglomerate. For lack of space I cannot discuss the issue here, and for the purposes of the present paper such a discussion is not necessary. It is not an aim of the paper to show that Kroedel is wrong with respect to the lottery paradox.

  12. 12.

    I am grateful to an anonymous reviewer for making me aware of the need to expand my remarks on this strategy.

  13. 13.

    That one knows that at least one assertion in the book is not true is stated in the book’s preface; thus the label ‘preface paradox’.

  14. 14.

    As Hannes Leitgeb pointed out to me in conversation, the falsity of C*\(^P\) may not be as obvious as the falsity of C*\(^L\). However, it follows from (i) PREFACE and (ii) if one knows a proposition, then one ought not to disbelieve it.

  15. 15.

    Relevant aspects might include whether the proposition gets evidential support and if so how much, the proposition’s relationship to other propositions, and background assumptions of the agent.

  16. 16.

    Note that although the PRINCIPLE OF FACTUAL DETACHMENT is not acceptable, this does not imply that there is no instance of it that is acceptable.


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Thanks to Peter Brössel, Thomas Kroedel, Hannes Leitgeb, Wolfgang Spohn, Raphael van Riel, and Ben Young for insightful suggestions and comments on previous versions of this paper. I am also grateful to three anonymous referees for providing very helpful remarks. My research was funded by the Volkswagenstiftung (Dilthey Program) through the research project A Study in Explanatory Power at the University of Duisburg-Essen as well as by a fellowship (Stipendium nach dem Landesgraduiertenförderungsgesetz) sponsored by the State of Baden-Württemberg (Germany).

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Correspondence to Anna-Maria Asunta Eder.

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Eder, AM.A. No Match Point for the Permissibility Account. Erkenn 80, 657–673 (2015).

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  • Strong Reason
  • Rational Belief
  • Epistemic Justification
  • Ticket Lottery
  • Total Evidence