Skip to main content
SpringerLink
Log in

Foundationalism with infinite regresses of probabilistic support

  • S.I.: Epistemic Justification
  • Published:
Synthese Aims and scope Submit manuscript

Abstract

There is a long-standing debate in epistemology on the structure of justification. Some recent work in formal epistemology promises to shed some new light on that debate. I have in mind here some recent work by David Atkinson and Jeanne Peijnenburg, hereafter “A&P”, on infinite regresses of probabilistic support. A&P show that there are probability distributions defined over an infinite set of propositions {\(p_{1}, p_{2}, p_{3}, {\ldots }, p_{n}, {\ldots }\}\) such that (i) \(p_{i}\) is probabilistically supported by \(p_{i+1}\) for all i and (ii) \(p_{1}\) has a high probability. Let this result be “APR” (short for “A&P’s Result”). A&P oftentimes write as though they believe that APR runs counter to foundationalism. This makes sense, since there is some prima facie plausibility in the idea that APR runs counter to foundationalism, and since some prominent foundationalists argue for theses inconsistent with APR. I argue, though, that in fact APR does not run counter to foundationalism. I further argue that there is a place in foundationalism for infinite regresses of probabilistic support.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. See Atkinson and Peijnenburg (2006, 2009, 2012), Peijnenburg (2007), and Peijnenburg and Atkinson (2008, 2011, 2013, 2014).

  2. APR concerns non-circular infinite regresses of probabilistic support. A&P also show that there can be high probability by circular infinite regresses of probabilistic support (or “justification by infinite loops”). See Atkinson and Peijnenburg (2010a).

  3. APR concerns one-dimensional infinite regresses of probabilistic support, that is, infinite regresses of probabilistic support where each node is a single proposition. A&P also argue that there can be high probability by many-dimensional infinite regresses of probabilistic support (or “many-dimensional probabilistic networks”). See Atkinson and Peijnenburg (2012).

  4. See Atkinson and Peijnenburg (2006) and Peijnenburg and Atkinson (2011) for helpful discussion of Lewis, along with Bertrand Russell and Hans Reichenbach, on infinite regresses of probabilistic support.

  5. Turri (2009, pp. 162–163) argues for a similar thesis. He argues in particular that there is a place in foundationalism for an infinite and non-repeating series of reasons (available to a subject). He does not address APR or A&P’s work more generally, though, and the infinite regresses he has in mind differ in important respects from the infinite regresses I, following A&P, have in mind. See Peijnenburg and Atkinson (2011, Sects. 5 and 6) for discussion of Turri’s argument. See also Herzberg (2013, Sect. 2).

  6. I am not the first to discuss A&P’s work on infinite regresses of probabilistic support. See Gwiazda (2010), Herzberg (2010), and Podlaskowski and Smith 2014. But my discussion is very different than Gwiazda’s, Herzberg’s, and Podlaskowski and Smith’s discussions. See Peijnenburg (2010) for a response to Gwiazda (2010). See Atkinson and Peijnenburg (2010b) for a response to Herzberg (2010).

  7. For a recent discussion of the distinction between propositional and doxastic justification, and for references, see Silva (2015). See also Korcz (2015) on the basing relation.

  8. The extant literature on the regress problem is vast. See Cling (2008) for references (and for helpful discussion).

  9. See Douven (2011), Roche (2012a, 2015), and Roche and Shogenji (2014).

  10. A&P typically assume IP/IP* in their work on infinite regresses of probabilistic support. Peijnenburg and Atkinson (2014) is an exception. There they assume HIP/HIP*.

  11. The assumption that \(\hbox {Pr}(p_{i} {\vert } p_{i+1}) = \alpha \) and \(\hbox {Pr}(p_{i} {\vert } \lnot p_{i+1}) = \beta \) for all i is inessential. A&P show that the target proposition in an infinite regress of probabilistic support can have a high probability even if it is not the case that \(\hbox {Pr}(p_{i} {\vert } p_{i+1}) = \alpha \) and \(\hbox {Pr}(p_{i} {\vert } \lnot p_{i+1}) = \beta \) for all i. See, for example, Atkinson and Peijnenburg (2009), Peijnenburg (2007), and Peijnenburg and Atkinson (2008, 2014).

  12. FJ is similar to some extant construals of foundationalism. See, for example, the construals in Cornman (1977) and Zalabardo (2008).

  13. See Fumerton (2010) for relevant discussion.

  14. Cornman (1977, p. 291) defends a claim to this effect by appeal to the thesis that a proposition is justified for a subject only if it is more reasonable for that subject than is its denial.

  15. See Cornman (1977) and Post (1980) for similar worries with theses similar to IJ1. See Aikin (2011, Chap. 2, Sect. 2.3) for relevant discussion.

  16. IJ1 stands in contrast to:

    Infinitism on Justification 1* (IJ1*)p is justified for S only if p is the target proposition in a regress of probabilistic support RPS such that (a) \(\hbox {Pr}(p) > \mathbf{t}\), (b) RPS has an infinite number of nodes, and (c) none of RPS’s nodes is an ancestor of itself.

    IJ1 gives a putative sufficient condition for justification whereas IJ1* gives a putative necessary condition. The latter, unlike the former, is correct. In fact, it is trivially correct. Any p such that p is justified for S is also such that there is regress of probabilistic support RPS where p is the target proposition, \(\hbox {Pr}(p) > \mathbf{t}\), the number of nodes is infinite, and none of the nodes is an ancestor of itself. See Cling (2004, Sect. 2, p. 103) for a closely related point.

  17. See Roche (2012b) for discussion of a coherentist theory similar in relevant respects to IJ2.

  18. It is important to note that (a) in IJ3 is not redundant. Let \(p_{1}, p_{2}, p_{3},\ldots , p_{n}, \ldots \) be a regress of probabilistic support RPS such that RPS has an infinite number of nodes, none of RPS’s nodes is an ancestor of itself, and the conditional probabilities involved are empirically credible for S. Suppose, consistent with this, that \(\hbox {Pr}(p_{i} {\vert } p_{i+1}) = 2/100\) and \(\hbox {Pr}(p_{i} {\vert } \lnot p_{i+1}) = 1/100\) for all i. Then by (9) it follows that \(\hbox {Pr}(p_{1})\) is roughly equal to 0.010 and thus is less than t. See Herzberg (2014, Sect. 7) for related discussion.

  19. IJ3, understood as IJ3* below, is similar to but importantly different than “(PBPIJ)” in Herzberg (2014, p. 714). IJ3 gives a putative sufficient condition for justification whereas (PBPIJ) gives a putative necessary and sufficient condition for justification.

  20. See also Peijnenburg and Atkinson (2011, p. 124).

  21. Cling (2008, Sect. 3, p. 407, and Sect. 8) and Moser (1989, Chap. 2, Sect. 2.2.2) argue along these lines. See Cling (2004) for related discussion.

  22. There would be a similar point if N2 were broken up into an infinite number of nodes: N2.1: \([\hbox {Cr}(p_{1} {\vert } p_{2}) = 0.99]\), N2.2: [\(\hbox {Cr}(p_{1} {\vert } \lnot p_{2}) = 0.04\)], N2.3: [\(\hbox {Cr}(p_{2} {\vert } p_{3}) = 0.99\)], N2.4: [\(\hbox {Cr}(p_{2} {\vert } \lnot p_{3}) = 0.04],\ldots , \mathrm{N}2.2_{n-1}: [\mathrm{Cr}(p_{n-1} {\vert } p_n) = 0.99], \mathrm{N}2.2_{n-2}: [\mathrm{Cr}(p_{n-1} {\vert } p_{n}) = 0.04],\ldots , \) would need to be modified accordingly. Then the point would be that if FJ* so modified were assumed, if the credences in N5 were not non-inferentially justified for S, and if the case were otherwise the same, then the credences in N2.1, N2.2,...would not be justified for S and so, despite the fact those credences together fully determine \(\hbox {Cr}(p_{1}) = 0.8, \hbox {Cr}(p_{1}) = 0.8\) would not be justified for S.

  23. There is a place in foundationalism for infinite regresses of probabilistic support. The same is true with respect to coherentism and infinitism.

  24. If, instead, \(\hbox {Cr}(p_{1} {\vert } p_{2}) = 0.98, \hbox {Cr}(p_{1} {\vert } \lnot p_{2}) = 0.99, \hbox {Cr}(p_{2} {\vert } p_{3}) = 0.98, \hbox {Cr}(p_{2} {\vert } \lnot p_{3}) = 0.99,\ldots , \hbox {Cr}(p_{n-1} {\vert } p_{n}) = 0.98, \hbox {Cr}(p_{n-1} {\vert } \lnot p_{n}) = 0.99,\ldots \), then \(\hbox {Cr}(p_{1}) \approx 0.980\).

  25. If, instead, \(\hbox {Cr}(p_{1} {\vert } p_{2}) = 0.98, \hbox {Cr}(p_{1} {\vert } \lnot p_{2}) = 0.99, \hbox {Cr}(p_{2} {\vert } p_{3}) = 0.98, \hbox {Cr}(p_{2} {\vert } \lnot p_{3}) = 0.99,\ldots , \hbox {Cr}(p_{99} {\vert } p_{100}) = 0.98, \hbox {Cr}(p_{99} {\vert } \lnot p_{100}) = 0.99\), and \(\hbox {Cr}(p_{100}) = 0.1\), then \(\hbox {Cr}(p_{1}) \approx 0.980\).

  26. See Herzberg (2013), Podlaskowski and Smith (2011, 2014), Smith and Podlaskowski (2013), and Turri (2013) for relevant discussion.

References

  • Aikin, S. (2011). Epistemology and the regress problem. New York: Routledge.

    Google Scholar 

  • Atkinson, D., & Peijnenburg, J. (2006). Probability without certainty: Foundationalism and the Lewis–Reichenbach debate. Studies in History and Philosophy of Science, 37, 442–453.

    Article  Google Scholar 

  • Atkinson, D., & Peijnenburg, J. (2009). Justification by an infinity of conditional probabilities. Notre Dame Journal of Formal Logic, 50, 183–193.

    Article  Google Scholar 

  • Atkinson, D., & Peijnenburg, J. (2010a). Justification by infinite loops. Notre Dame Journal of Formal Logic, 51, 407–416.

    Article  Google Scholar 

  • Atkinson, D., & Peijnenburg, J. (2010b). The solvability of probabilistic regresses. A reply to Frederik Herzberg. Studia Logica, 94, 347–353.

    Article  Google Scholar 

  • Atkinson, D., & Peijnenburg, J. (2012). Fractal patterns in reasoning. Notre Dame Journal of Formal Logic, 53, 15–26.

    Article  Google Scholar 

  • Cling, A. (2004). The trouble with infinitism. Synthese, 138, 101–123.

    Article  Google Scholar 

  • Cling, A. (2008). The epistemic regress problem. Philosophical Studies, 140, 401–421.

    Article  Google Scholar 

  • Cornman, J. (1977). Foundational versus nonfoundational theories of empirical justification. American Philosophical Quarterly, 14, 287–297.

    Google Scholar 

  • Douven, I. (2011). Further results on the intransitivity of evidential support. Review of Symbolic Logic, 4, 487–497.

    Article  Google Scholar 

  • Fumerton, R. (2010). Foundationalist theories of epistemic justification. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (summer ed.). http://plato.stanford.edu/archives/sum2010/entries/justep-foundational/.

  • Gwiazda, J. (2010). Infinitism, completability, and computability: Reply to Peijnenburg. Mind, 119, 1123–1124.

    Article  Google Scholar 

  • Herzberg, F. (2010). The consistency of probabilistic regresses. A reply to Jeanne Peijnenburg and David Atkinson. Studia Logica, 94, 331–345.

    Article  Google Scholar 

  • Herzberg, F. (2013). The consistency of probabilistic regresses: Some implications for epistemological infinitism. Erkenntnis, 78, 371–382.

    Article  Google Scholar 

  • Herzberg, F. (2014). The dialectics of infinitism and coherentism: Inferential justification versus holism and coherence. Synthese, 191, 701–723.

    Article  Google Scholar 

  • Korcz, K. (2015). The epistemic basing relation. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (fall ed.). http://plato.stanford.edu/archives/fall2015/entries/basing-epistemic/.

  • Lewis, C. I. (1952). The given element in empirical knowledge. Philosophical Review, 61, 168–175.

    Article  Google Scholar 

  • Moser, P. (1989). Knowledge and evidence. Cambridge: Cambridge University Press.

    Google Scholar 

  • Peijnenburg, J. (2007). Infinitism regained. Mind, 116, 597–602.

    Article  Google Scholar 

  • Peijnenburg, J. (2010). Ineffectual foundations: Reply to Gwiazda. Mind, 119, 1125–1133.

    Article  Google Scholar 

  • Peijnenburg, J., & Atkinson, D. (2008). Probabilistic justification and the regress problem. Studia Logica, 89, 333–341.

    Article  Google Scholar 

  • Peijnenburg, J., & Atkinson, D. (2011). Grounds and limits: Reichenbach and foundationalist epistemology. Synthese, 181, 113–124.

    Article  Google Scholar 

  • Peijnenburg, J., & Atkinson, D. (2013). The emergence of justification. Philosophical Quarterly, 63, 546–564.

    Article  Google Scholar 

  • Peijnenburg, J., & Atkinson, D. (2014). Can an infinite regress justify everything? In J. Turri & T. Klein (Eds.), Ad infinitum: New essays on epistemological infinitism (pp. 162–178). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  • Podlaskowski, A., & Smith, J. (2011). Infinitism and epistemic normativity. Synthese, 178, 515–527.

    Article  Google Scholar 

  • Podlaskowski, A., & Smith, J. (2014). Probabilistic regresses and the availability problem for infinitism. Metaphilosophy, 45, 211–220.

    Article  Google Scholar 

  • Post, J. (1980). Infinite regresses of justification and of explanation. Philosophical Studies, 38, 31–52.

    Article  Google Scholar 

  • Roche, W. (2012a). Transitivity and intransitivity in evidential support: Some further results. Review of Symbolic Logic, 5, 259–268.

    Article  Google Scholar 

  • Roche, W. (2012b). A reply to Cling’s “The epistemic regress problem”. Philosophical Studies, 159, 263–276.

    Article  Google Scholar 

  • Roche, W. (2015). Evidential support, transitivity, and screening-off. Review of Symbolic Logic, 8, 785–806.

    Article  Google Scholar 

  • Roche, W., & Shogenji, T. (2014). Confirmation, transitivity, and Moore: The screening-off approach. Philosophical Studies, 168, 797–817.

    Article  Google Scholar 

  • Silva, P. (2015). On doxastic justification and properly basing one’s beliefs. Erkenntnis, 80, 945–955.

    Article  Google Scholar 

  • Smith, J., & Podlaskowski, A. (2013). Infinitism and agents like us: Reply to Turri. Logos & Episteme, 4, 125–128.

    Article  Google Scholar 

  • Turri, J. (2009). On the regress argument for infinitism. Synthese, 166, 157–163.

    Article  Google Scholar 

  • Turri, J. (2013). Infinitism, finitude and normativity. Philosophical Studies, 163, 791–795.

    Article  Google Scholar 

  • Zalabardo, J. (2008). Internalist foundationalism and the problem of the epistemic regress. Philosophy and Phenomenological Research, 77, 34–58.

    Article  Google Scholar 

Download references

Acknowledgements

Thanks to David Atkinson, Jeanne Peijnenburg, Adam Podlaskowski, Tomoji Shogenji, Joshua Smith, and two anonymous referees for helpful comments and/or discussion.

Author information

Authors and Affiliations

  1. Department of Philosophy, Texas Christian University, Fort Worth, TX, USA

    William Roche

Authors
  1. William Roche
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William Roche.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roche, W. Foundationalism with infinite regresses of probabilistic support. Synthese 195, 3899–3917 (2018). https://doi.org/10.1007/s11229-016-1289-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-016-1289-4

Keywords

Search

Navigation