Abstract
An agent’s belief in a proposition, E0, is justified by an infinite regress of deferred justification just in case the belief that E0 is justified, and the justification for believing E0 proceeds from an infinite sequence of propositions, E0, E1, E2, etc., where, for all n ≥ 0, E n+1 serves as the justification for E n . In a number of recent articles, Atkinson and Peijnenburg claim to give examples where a belief is justified by an infinite regress of deferred justification. I argue here that there is no reason to regard Atkinson and Peijnenburg’s examples as cases where a belief is so justified. My argument is supported by careful consideration of the grounds upon which relevant beliefs are held within Atkinson and Peijnenburg’s examples.
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Notes
Whether infinitism and foundationalism are formally inconsistent depends on the exact conception of the two doctrines. I would opt for a conception of foundationalism such that justification cannot proceed from an infinite regress of propositions, while at the same time originating from basic beliefs (but see Aikin 2008, where mutually consistent versions of the two views are described). I take it that a version of foundationalism of the sort I prefer is consistent with there being cases, as proposed by Turri (2009, 162-3), where (i) an agent has access to an infinite sequence of reasons, E0, E2, E3, etc., each of which is entailed by its successor, and (ii) the agent is justified in believing the first element of the sequence, E0.
Contrary to the latter claim, A&P maintain that foundationalism is in tension with the claim that an unconditional probability could be justified by an infinite number of conditional probabilities (Peijnenburg and Atkinson 2014a). In advancing the preceding point, A&P are correct in observing that conditional probabilities are not the sort of entities that foundationalists have typically embraced as a sort of basic belief. However, in accepting that an unconditional probability could be justified by an infinite number of conditional probabilities, a foundationalist need not take the conditional probabilities as foundational. Rather a foundationalist may happily maintain that an unconditional probability could be justified by an infinite number of conditional probabilities, in a case where the conditional probabilities (or their adoption) were, in turn, justified by the agent’s basic beliefs.
To be precise, it follows from P(E0) = β + β(α − β) + β(α − β)2 + … + β(α − β)n + (α − β)n+1P(E n+1), for all n ≥ 3, that lim n→∞ P(E0) = lim n→∞ (β + β(α − β) + β(α − β)2 + … + β(α − β)n + (α − β)n+1P(E n+1)). But lim n→∞ P(E0) = P(E0), and lim n→∞ (β + β(α − β) + β(α − β)2 + … + β(α − β)n + (α − β)n+1P(E n+1)) = lim n→∞ (β + β(α − β) + β(α − β)2 + … + β(α − β)n) + lim n→∞ (α − β)n+1P(E n+1) [by the Sum Rule] = lim n→∞ (β + β(α − β) + β(α − β)2 + … + β(α − β)n) [since lim n→∞ (α − β)n+1P(E n+1) = 0] = \( \sum_{n=0}^{\mathit{\infty}}\upbeta {\left(\upalpha -\upbeta \right)}^n \). So P(E0) = \( \sum_{n=0}^{\mathit{\infty}}\upbeta {\left(\upalpha -\upbeta \right)}^n \).
For evidence that this is what A&P actually think, see (for example) the final paragraph of page 553 of (Peijnenburg and Atkinson 2013).
While A&P are uncommitted on the question of whether their examples concern doxastic or propositional justification (Peijnenburg and Atkinson 2013, 546, 555), I here proceed as if the key issue is of the doxastic justification for belief in E0. My approach to the example simplifies matters, without loss of generality. There is no loss of generality, since it is correct to hold that E0 is propositionally justified by an infinite regress of deferred justification, for the agent of A&P’s example, just in case there is some reading/elaboration of A&P’s example (concerning the grounds upon which relevant beliefs are held) such that the agent’s belief that E0 is doxastically justified by an infinite regress, within that reading/elaboration (cf. Turri 2010).
The assumption granted is a big one. Indeed, the claim that E n+1 probabilistically supports E n , taken together with P(E n+1) = 1, does not imply that P(E n ) > 0.5 (nor even that P(E n ) > ε, for any ε > 0).
It goes without saying that justified belief in a set of propositions that entails another proposition, E, is insufficient to justify belief in E (otherwise every belief whose content was a logical truth would automatically be justified for every agent who held the belief).
A&P argue that their examples provide a model of how it is that justification may emerge from a regress of reasons (Peijnenburg and Atkinson 2013, 549). If we had reason to think that this model was correct, then the model could be used to address worries concerning the justificatory capacity of regresses. However, A&P’s claim to have provided a model of how justification emerges within regresses depends crucially on the claim that their examples exemplify cases where a belief is justified by a regress. So A&P cannot appeal to their model in order to address worries about their examples, without reasoning in a circle.
Notice that at each step n, the proposition for which justification is deferred is equivalent to the claim that P(E n ) = 2/3. In this sense, each step corresponds to an appeal to the claim that E n is probable.
References
Aikin, S. (2008). Meta-epistemology and the varieties of epistemic infinitism. Synthese, 163(2), 175–185.
Aikin, S. (2011). Epistemology and the regress problem. Abingdon: Routledge.
Atkinson, D., & Peijnenburg, J. (2009). Justification by an infinity of conditional probabilities. Notre Dame Journal of Formal Logic, 50, 183–193.
Dancy, J. (1985). Introduction to contemporary epistemology. Oxford: Blackwell.
Gillett, C. (2003). Infinitism Redux? Philosophy and Phenomenological Research, 66, 709–717.
Klein, P. (1998). Foundationalism and the infinite regress of reasons. Philosophy and Phenomenological Research, 58, 919–925.
Klein, P. (2007). Human knowledge and the infinite progress of reasoning. Philosophical Studies, 134, 1–17.
Moser, P. (1985). Whither infinite regresses of justification? Southern Journal of Philosophy, 23, 65–74.
Peijnenburg, J., & Atkinson, D. (2013). The emergence of justification. The Philosophical Quarterly, 63(252), 546–564.
Peijnenburg, J., & Atkinson, D. (2014a). Can an infinite regress justify everything? In J. Turri & P. Klein (Eds.), Ad infinitum: new essays on epistemological infinitism (pp. 162–178). Oxford: Oxford University Press.
Peijnenburg, J., & Atkinson, D. (2014b). The need for justification. Metaphilosophy, 45(2), 201–210.
Post, J. (1980). Infinite regresses of justification and of explanation. Philosophical Studies, 38(1), 31–52.
Turri, J. (2009). On the regress argument for infinitism. Synthese, 166(1), 157–163.
Turri, J. (2010). On the relationship between propositional and doxastic justification. Philosophy and Phenomenological Research, 80(2), 312–326.
Acknowledgements
Work on this article was supported by DFG Grant SCHU1566/9-1 as part of the priority programme “New Frameworks of Rationality” (SPP 1516). For helpful comments on an earlier presentation of this paper, I thank an audience at University of Düsseldorf. I also thank Ludwig Fahrbach, David Atkinson, Jeanne Peijnenburg, Ionannis Votsis, and an anonymous referee for Philosophia, for helpful comments on earlier drafts of this paper.
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Thorn, P.D. A Note Concerning Infinite Regresses of Deferred Justification. Philosophia 45, 349–357 (2017). https://doi.org/10.1007/s11406-016-9751-6
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DOI: https://doi.org/10.1007/s11406-016-9751-6