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The dialectics of infinitism and coherentism: inferential justification versus holism and coherence

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Abstract

This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification has rather unwelcome consequences—formally resembling the Sorites paradox—as soon as it is iterated and combined with a natural Bayesian perspective on probabilistic inferences. We conclude that strong versions of foundationalism and infinitism should be abandoned. Positively, we provide a rough sketch for a graded formal coherence notion, according to which infinite regresses of epistemic justification will often have more than a minimal degree of coherence.

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Notes

  1. I am very grateful to an anonymous referee for pointing out several weaknesses in an earlier version of this section and the following one; any remaining errors are mine.

  2. Mnemonics: the letter \({\fancyscript{I}}\) abbreviates ‘individual’; \(S\) abbreviates ‘sentence’.

  3. The second half of this requirement is, strictly speaking, redundant—because we have already demanded \(S_1,S_2,\ldots \) to be propositions other than \(S_0\)—and has only been inserted for clarification.

  4. In Peijnenburg’s Peijnenburg (2007) or Peijnenburg and Atkinson’s Peijnenburg and Atkinson (2008) terminology, confirmation is referred to as probabilistic support. Since this is not the standard Bayesian terminology and we use the verb ‘to support’ also in a different formal sense (viz. when referring to the set of probability measures supporting a belief system), we have chosen not to follow Peijnenburg’s example on this minor point.

  5. He was corrected by Reichenbach in a private letter and admitted his error, as explained by Peijnenburg and Atkinson (2008, p. 338).

  6. As a few elementary rearrangements show:

    $$\begin{aligned} P(E|F)>P(E|\complement F)&\Leftrightarrow \frac{P(E\cap F)}{P(F)}>\frac{P(E\setminus F)}{1-P(F)} \\&\Leftrightarrow P(E\cap F)-P(E\cap F)P(F)>P(E\setminus F)P(F)\\&\Leftrightarrow P(E\cap F)>P(E)P(F) \Leftrightarrow P(E|F)>P(E). \end{aligned}$$

  7. On this point, I am indebted to an anonymous referee, who suggested the following example. Suppose there is a 1,000 ticket lottery, \(F\) is the event that ticket #1,000 does not win, and \(E\) is the event that ticket #1 wins. Suppose you learn from a reliable source that \(F\) is true, so you are justified in believing it, and condition (1) in (BPIJ) is met. So is (2): \(P\left( E | F\right) = 1/999 > 1/1\),\(000\). But surely you are not justified in believing \(E\) on the basis of \(F\). In terms of Bayesian confirmation theory, the degree of confirmation for \(E\) offered by \(F\) (according to the relevance measure of confirmation) is minute, viz. just \(1/999 -1/1\),\(000\), which is of order \(10^{-6}\).

  8. A popular version of what is known as the Lockean thesis demands that in order for a proposition \(S_0\) to be considered a full belief of an agent, that agent’s degree of belief in \(S_0\) must exceed a certain threshold. Locke’s Essay contains several passages that suffer such an interpretation (Locke (1979) Book IV, Chapters XIV–XVII).

  9. The choice of such a sequence is possible in light of the consistency theorems for infinite regresses, cf. Sect. 5.

  10. This may be all the more surprising since coherentism was, after all, the position of eminent analytic epistemologists such as Goodman (1951), Hempel (1935a,b), Neurath (1931, 1932), Quine and Ullian (1970), Reichenbach (1938) and Sellars (1963) to name but a few; among influential contemporary epistemologists, coherentism has had adherents such as van Fraassen (1984), and Jeffrey (1992) at the very least shared their opposition to foundationalism.

  11. Reichenbach already proposed a solution to the isolation objection along these lines through the inclusion of “observation sentences” (Reichenbach 1952, p. 159; 1938, p. 83) or “protocol sentences” (Lewis 1952, p. 171.)

  12. Herein, \(\varnothing \) denotes the minimal element of the algebra \({\fancyscript{A}}\) of propositions, viz. the empty set when identifying each proposition in \({\fancyscript{A}}\) with its extension, i.e. the set of worlds in which it holds.

  13. It is interesting in this connection that de Finetti considered probabilistic consistency to be such an important component of a coherence notion that he simply defined coherence as probabilistic consistency (de Finetti 1937, 1970, 1974).

  14. Herein, \(\Omega \) denotes the maximal element of the algebra \({\fancyscript{A}}\) of propositions, viz. the set of all possible worlds when identifying each proposition in \({\fancyscript{A}}\) with its extension (the set of worlds in which it holds).

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Acknowledgments

This work was financially supported by the Alexander von Humboldt Foundation through a Visiting Fellowship of the Munich Center for Mathematical Philosophy at Ludwig Maximilian University of Munich. I am deeply grateful to Professors Hannes Leitgeb and Stephan Hartmann for very helpful discussions, as well as to Professor Jeanne Peijnenburg and an anonymous referee for many insightful comments that helped to improve the paper substantially.

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  1. Faculty of Philosophy, Philosophy of Science and Study of Religion, Munich Center for Mathematical Philosophy, Ludwig Maximilian University of Munich, Geschwister-Scholl-Platz 1, 80539 , Munich, Germany

    Frederik Herzberg

  2. Institute of Mathematical Economics, Bielefeld University, Universitätsstraße 25, 33615 , Bielefeld, Germany

    Frederik Herzberg

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Herzberg, F. The dialectics of infinitism and coherentism: inferential justification versus holism and coherence. Synthese 191, 701–723 (2014). https://doi.org/10.1007/s11229-013-0273-5

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