Abstract
Epistemic infinitism, advanced in different forms by Peter Klein, Scott Aikin, and David Atkinson and Jeanne Peijnenburg, is the theory that justification of a proposition for a person requires the availability to that person of an infinite, non-repeating chain of propositions, each providing a justifying reason for its successor in the chain. The reductio argument is the argument to the effect that infinitism has the consequence that no one is justified in any proposition, because there will be an infinite chain of reasons supporting any proposition (and similarly, a chain supporting its negation). Four ways of defending infinitism against the reductio argument are considered and found wanting: Peijnenburg and Atkinson’s use of probabilistic chains of reasons; Klein’s concept of emergent justification; Aikin’s insistence that there be non-propositional input in the justification of any proposition; and Klein’s use of the distinction between reasons that are and are not available to a person. I contend that, in the absence of some further defence, the reductio argument makes infinitism untenable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Epistemic infinitism has been elaborated and defended by Peter Klein in an extensive range of papers. See especially Klein (1999, 2007 and 2014a), and Turri and Klein (2014b). Some others of Klein’s works are listed in the references. Other important defenders of infinitism are Scott (Aikin 2005, 2011 and 2014), and Atkinson and Peijnenburg (2017). A recent collection of essays on the topic is Turri and Klein (2014a).
The term “reductio argument” was used as a label for this sort of argument in Klein (1999), and I have followed this usage. Peijnenburg and Atkinson (2014) and Atkinson and Peijnenburg (2017) adopt the same terminology. Turri and Klein (2014b) refer to the type-(b) argument as the “AC/DC argument”, where the letters stand for “affirmation chain” and “denial chain”. Aikin calls the arguments “conceptual arguments from arbitrariness” (Aikin 2005, p. 192 ff). (There are other quite different objections to infinitism that could be framed as reductio arguments, but no confusion with these should arise).
For a discussion of the problems faced by the infinitist in connection specifically with doxastic justification, see Oakley (2017).
For Klein’s account of propositional and doxastic justification, and the point that one may be propositionally justified in a proposition without believing it, see, e.g. Klein (2007), p. 6; Klein (2014a), p. 96 ff; Klein (2014b), p. 111 ff. Klein notes particularly that we are dealing with technical senses of justification in (Klein 2005), p157.
John F Post speaks of logical implications rather than entailments, a difference that should not affect the present argument. He provides a more detailed and elaborated account of this argument, with the inclusion of (both logical and justificational) non-circularity and relevance conditions on the implications, in Section 1 of Post (1980).
In fact, for any proposition, p, there will be not just one Post Chain, but infinitely many. (One only has to think of the fact that any actual proposition could be substituted for qin the schema above, and there is an infinite number of propositions).
This is true only on the assumption that the chains of evidence supporting pand not-pare of equal strength. However we are clearly justified in such an assumption where the two chains consist entirely of deductive links, as in Post Chains. And for any proposition, there will be such deductive chains.
It will of course require reasons of great complexity to justify a claim to the effect that there is not counter-evidence outweighing evidence one has for some proposition. This should not in itself be seen as an objection to infinitism, of course. Our everyday reasoning demands some such reasoning, whenever we seek to have TAE justification in anything—and as remarked, TAE justification is what we are normally concerned to have.
Peijnenburg and Atkinson (2014); Atkinson and Peijnenburg, (2017, especially Ch. 6). In their 2014 article, the authors are more tentative in their defence of infinitism against the reductio argument, writing, for example, that probabilistic chains are “less susceptible to the reductio-like attack” (2014, p. 174) than are entailment chains, (suggesting that there is still some degree of susceptibility for the probabilistic chains). These and other similar qualifications disappear in the 2017 book, though the supporting arguments do not seem much changed.
The authors make much of the point that the probability of a proposition, p, at the head of a sufficiently long probabilistic chain is determined almost entirely by the conditional probabilities between the propositions in the chain, and scarcely at all by the unconditional probability of the first proposition at the base of the chain. In the case of an infinite chain, it is determined entirely by the conditional probabilities.
They see this last point as vital in their rejection of an objection to infinitism that they refer to as the “no starting point objection” (see especially 2017, 6.1 and 6.2). As I am here concerned entirely with their response to the reductio argument, I will not discuss this objection or their reply.
The arguments in the following three paragraphs largely parallel arguments deployed in much more detail by William Roche in Roche (2016)
Something like the same line of thought is put forward by Frederik Herzberg, though Herzberg intends his remarks to apply to both coherentist and infinitist theories. Herzberg (2014), p. 718, Peijnenburg and Atkinson (2014), Atkinson and Peijnenburg (2017), Ch. 4.3 also present their account, discussed above, in terms of “emergence”.
An alternative conception of emergent coherentism might be that the conjunction of the propositions in the coherent set is justified in virtue of the set’s coherence, and individual propositions are justified in virtue of their being conjuncts within a justified conjunction. In that case, there would be just one very large compound foundational proposition. We still end up with a form of foundationalism.
A similar line of thought is found in Berker (2015), who discusses ways in which sensory experiences may “play a supporting role for beliefs” (p. 334), without acting “as a regress stopper” (p. 335). Berker’s concern is more with coherentism, but he notes correctly that the same ideas can be applied to infinitism. However his account, as applied to infinitism, does no better than Aikin’s in connection with the problems for impure infinitism raised below. (These problems, it should be noted, are problems for impure infinitism, and my arguments are not directed against any form of coherentism).
The parallels between the problems facing infinitism and those facing classical coherentism have been noted by many. There are similar parallels in the attempts to meet these problems. Aikin himself draws attention to the similarity between his own requirement, expressed in EI-2, and Bonjour’s ‘Observation Requirement’, found in Bonjour (1985, Ch. 7, sec 1). (Aikin 2011, p. 105).
Aikin, though he recognises the distinction between propositional and doxastic justification in the course of expounding Klein’s views (2011, p. 90), does not make use of the distinction at all when dealing with impure infinitism as an answer to the reductio (2011, Ch. 3.5; 2014). Much of his language in this context suggests that he is thinking primarily in terms of chains of beliefs rather than propositions. For example, he sometimes refers to the non-propositional elements that he claims must enter into justificatory relations as “non-doxastic” rather than “non-propositional” elements (e.g. Aikin 2011, p. 107).
Such picking and choosing seems problematic. The infinitist needs an account of availability that steers a difficult middle course. It must not be so stringent as to have us running out of reasons so that all our chains of reasons are finite. And it (presumably) must not be so relaxed, (as is the account quoted above) that the propositions of Newtonian physics were justified for Aristotle; or indeed, so relaxed that it allows all the propositions in a Post Chain to be available.
References
Aikin, S. (2005). Who is afraid of epistemology’s regress problem? Philosophical Studies, 126, 191–217.
Aikin, S. (2011). Epistemology and the regress problem. New York: Routledge.
Aikin, S. (2014). Knowing better, cognitive command, and epistemic infinitism (pp. 19–36). In Turri and Klein 2014a.
Atkinson, D., & Peijnenburg, J. (2017). Fading foundations: Probability and the regress problem. Springer Open. https://doi.org/10.1007/978-3-319-58295-5.
Audi, R. (1998). Epistemology. New York: Routledge.
Berker, S. (2015). Coherentism via graphs. Philosophical Issues, Normativity, 25, 322–352.
Bonjour, L. (1985). The structure of empirical knowledge. Cambridge, Mass: Harvard University Press.
Herzberg, F. (2014). The dialectics of infinitism and coherentism: Inferential justification versus holism and coherence. Synthese, 191(4), 701–723.
Klein, P. (1999). Human knowledge and the infinite regress of reasons. Philosophical Perspectives, 13, 297–325.
Klein, P. (2005). Infinitism’s take on justification, knowledge, certainty and skepticism. Veritas, 50(4), 153–72.
Klein, P. (2007). Human knowledge and the infinite progress of reasoning. Philosophical Studies, 134(1), 1–17.
Klein, P. (2008). Contemporary responses to Agrippa’s trilemma. In J. Greco (Ed.), The Oxford handbook of skepticism (pp. 484–503). Oxford: OUP.
Klein, P. (2011). Infinitism. In E. Bernecker & D. Pritchard (Eds.), The Routledge companion to epistemology (pp. 245–56). New York: Routledge.
Klein, P. (2014a). No final end in sight. In R. Neta (Ed.), Current controversies in epistemology (pp. 95–115). Hoboken: Taylor and Francis.
Klein, P. (2014b). Reasons, reasoning and knowledge: A proposed rapprochement between infinitism and foundationalism. In Turri and Klein 2014a, pp. 105–126.
Oakley, I. T. (1976). An argument for scepticism concerning justified beliefs. American Philosophical Quarterly, 15(3), 121–8.
Oakley, T. (2017). Infinitism and scepticism. Episteme. https://doi.org/10.1017/epi.2017.31.
Peijnenburg, J., & Atkinson, D. (2014). Can an infinite regress justify anything? In Turri and Klein 2014a.
Pollock, J. (1974). Knowledge and Justification. Princeton: Princeton University Press.
Post, J. (1980). Infinite regresses of justification and of explanation. Philosophical Studies, 38, 12–52.
Roche, W. (2016). Foundationalism with infinite regresses of probabilistic support. Synthese. https://doi.org/10.1007/s11229-016-1289-4.
Turri, J. (2010). On the relationship between propositional and doxastic justification. Philosophy and Phenomenological Research, 80(2), 312–26.
Turri, J., & Klein, P. (Eds.). (2014a). Ad infinitum: New essays on epistemological infinitism. Oxford: OUP.
Turri, J., & Klein. P. (2014b). Introduction (pp 1–18). In Turri and Klein 2014a.
Acknowledgements
I am very grateful for helpful comments on my work on this topic from Frank Jackson, colleagues in the La Trobe University Philosophy Program, and audiences attending presentations on this topic at the University of Melbourne, and at the annual conference of the Australasian Association of Philosophy. I am grateful also for comments from anonymous reviewers that led to improvements in this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Oakley, T. The reductio argument against epistemic infinitism. Synthese 196, 3869–3887 (2019). https://doi.org/10.1007/s11229-017-1629-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-017-1629-z